Case Study Questions

bru19684_fm_i-xvi.indd i 11/28/17 07:28 PM

Real Estate Finance and Investments

Sixteenth Edition

William B. Brueggeman, PhD Corrigan Chair in Real Estate Edwin L. Cox School of Business Southern Methodist University

Jeffrey D. Fisher, PhD Professor Emeritus of Real Estate Kelley School of Business Indiana University President, Homer Hoyt Institute

Final PDF to printer

bru19684_fm_i-xvi.indd ii 11/28/17 07:28 PM

REAL ESTATE FINANCE AND INVESTMENTS, SIXTEENTH EDITION

Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2018 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions © 2016, 2011, 2008, and 2005. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.

Some ancillaries, including electronic and print components, may not be available to customers outside the United States.

This book is printed on acid-free paper.

1 2 3 4 5 6 7 8 9 LWI 21 20 19 18

ISBN 978-1-259-91968-8 MHID 1-259-91968-4

Portfolio Manager: Tim Vertovec Product Developers: Tara Slagle and Jennifer Upton Marketing Manager: Trina Maurer Content Project Managers: Erika Jordan (freelance) Buyer: Sandy Ludovissy Design: Jessica Cuevas Content Licensing Specialists: Deanna Dausener Cover Image: ©Erica Simone Leeds Compositor: SPi Global Typeface: 10/12 STIX MathJax Main–Regular Printer: LSC Communications

All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.

Library of Congress Cataloging-in-Publication Data Names: Brueggeman, William B., author. | Fisher, Jeffrey D., author. Title: Real estate finance and investments / William B. Brueggeman, PhD,    Corrigan Chair in Real Estate, Edwin L. Cox School of Business, Southern    Methodist University, Jeffrey D. Fisher, PhD, Professor Emeritus of Real    Estate, Kelley School of Business, Indiana University, President, Homer Hoyt Institute. Description: Sixteenth Edition. | Dubuque : McGraw-Hill Education, [2018] | Revised edition of the authors’ Real estate finance and investments, [2016] Identifiers: LCCN 2017049308 | ISBN 9781259919688 (alk. paper) Subjects: LCSH: Mortgage loans—United States. | Real property—United States—Finance. Classification: LCC HG2040.5.U5 B78 2018 | DDC 332.7/2—dc23 LC record available at https://lccn.loc.gov/2017049308 2015015605

The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites.

www.mhhe.com

Final PDF to printer

iii

bru19684_fm_i-xvi.indd iii 11/28/17 07:28 PM

Introduction to Real Estate Finance and Investments This book prepares readers to understand the risks and rewards associated with financing and investing both residential and commercial real estate. Concepts and techniques included in the chapters and problem sets are used in many careers related to real estate. These include investing, development financing, appraising, consulting, managing real estate portfolios, leasing, managing property, analyzing site locations, corporate real estate, and managing real estate investment funds. This material is also relevant to individuals who want to better understand real estate when making their own personal investment and financing decisions.

The turmoil in world financial markets during the late 2000s, which was closely tied to events in the real estate market, suggests that investors, lenders, and others who partici- pate in the real estate market need to better understand how to evaluate the risk and return associated with the various ways of investing and lending. This requires an understanding of the legal issues that can impact the rights of lenders and investors, the characteristics of the various vehicles for lending and investing in real estate, the economic benefits of loans and investments, and how local economies may affect the investment performance of properties as well as the goals of lenders and investors.

This book is designed to help both students and other readers understand these many fac- tors so that they can perform the necessary analysis and make informed real estate finance and investment decisions. As the book’s title suggests, we discuss both real estate finance and real estate investments. These topics are interrelated. For example, an investor who purchases a property is making an investment. This investment is typically financed with a mortgage loan. Thus, the investor needs to understand both how to analyze the investment and how to assess the impact that financing the investment will have on its risk and return.

Similarly, the lender, by providing capital for the investor to purchase the property, is also making an investment in the sense that he or she expects to earn a rate of return on funds that have been loaned. Therefore, the lender also needs to understand the risk and return of making that loan. In fact, one of the risks associated with making loans secured by real estate is that, if a borrower defaults, the lender may take ownership of the property. This means that the lender also should evaluate the property using many of the same tech- niques as the investor purchasing the property.

Organization of the Book From the above discussion it should be clear that many factors have an impact on the risk and return associated with property investments and the mortgages used to finance them. This is true whether the investment is in a personal residence or in a large income-producing investment such as an office building.

Part I begins with a discussion of the legal concepts that are important in the study of real estate finance and investments. Although a real estate investor or lender may rely heavily on an attorney in a real estate transaction, it is important to know enough to be able to ask the right questions. We focus only on those legal issues that relate to real estate investment and financing decisions.

Part II begins with a discussion of the time value of money concepts important for ana- lyzing real estate investments and mortgages. These concepts are important because real estate is a long-term investment and is financed with loans that are repaid over time. This leads to a discussion of the primary ways that mortgage loans are structured: fixed rate and adjustable rate mortgage loans.

Preface

Final PDF to printer

iv Preface

bru19684_fm_i-xvi.indd iv 11/28/17 07:28 PM

Part III considers residential housing as an investment and covers mortgage loan underwriting for residential properties. This is relevant for individuals making personal financial decisions, such as whether to own or rent a home, as well as for lenders who are evaluating both the loan and borrower.

Part IV covers many topics related to analyzing income property investments. We pro- vide in-depth examples that include apartments, office buildings, shopping centers, and warehouses. Many concepts also may be extended to other property types. These topics include understanding leases, demonstrating how properties are appraised, how to analyze the potential returns and risks of an investment, and how taxes impact investment returns. We also consider how to evaluate whether a property should be sold or renovated. Finally, we look at how corporations, although not in the real estate business per se, must make real estate decisions as part of their business. This could include whether to own or lease the property that must be used in their operations, as well as other issues.

While the first four parts of this book focus on investing or financing existing prop- erties, Part V discusses how to analyze projects proposed for development. Such develop- ment could include land acquisition and construction of income-producing property of all types to acquisition of land to be subdivided and improved for corporate office parks or for sale to builders of residential communities. This section also includes how projects are financed during the development period. Construction and development financing is very different from the way existing, occupied properties are financed.

Part VI discusses various alternative real estate financing and investment vehicles. We begin with joint ventures and show how different parties with specific areas of exper- tise may join together to make a real estate investment. We use, as an example, someone with technical development expertise who needs equity capital for a project. A joint ven- ture is created with an investor who has capital to invest but doesn’t have the expertise to undertake the development. We then provide a financial analysis for the investment including capital contributions from, and distributions to, partners during property acqui- sition, operation, and its eventual sale. In this section, we also discuss how both residential and commercial mortgage loan pools are created. We then consider how mortgage-backed securities are (1) structured, (2) issued against such pools, and (3) traded in the secondary market for such securities. This also includes a discussion of the risks that these invest- ments pose. Part VI also includes a discussion of real estate investment trusts (REITs). These public companies invest in real estate and allow investors to own a diversified port- folio of real estate by purchasing shares of stock in the company.

Finally, in Part VII, we discuss how to evaluate real estate in a portfolio that also includes other investments such as stocks and bonds. This includes understanding the diversification benefits of including real estate in a portfolio as well as ways to diversify within the real estate portfolio (including international investment). This is followed by a chapter on real estate investment funds that are created for high net worth individuals and institutional investors. We discuss different fund strategies and structures and how to ana- lyze the performance of the funds relative to various industry benchmarks.

Wide Audience

From the above discussion, it is clear that this book covers many topics. Depending on the purpose of a particular course, all or a selection of topics may be covered. If desired, the course also may emphasize either an investor’s or a lender’s perspective. Alternatively, some courses may emphasize various industry segments such as housing and residential real estate, commercial real estate, construction and development, mortgage-backed secu- rities, corporate real estate, or investment funds. In other words, this book is designed to allow flexibility for instructors and students to cover a comprehensive range of topics or to emphasize only those topics that are the focal point of a specific subject. 

Final PDF to printer

Preface v

bru19684_fm_i-xvi.indd v 11/28/17 07:28 PM

Changes to the Sixteenth Edition

In addition to updating material throughout the text, we have added new material in several chapters. We have expanded Chapter 23 which is a chapter that was first introduced in the previous edition and provides extensive coverage of real estate investment funds. These funds now play a major role in the ownership of both residential and commercial real estate. Typically, these funds are created by professional investment managers and private equity firms that offer opportunities to high net worth investors, pension plan sponsors, endowments, and other institutional investors to invest in professionally managed portfo- lios of real estate. We have expanded the discussion of how to evaluate a fund’s perfor- mance compared to a benchmark index.

The discussion of derivatives in Chapter 22 was revised to reflect newer products that have recently been introduced such as the use of Up Shares and Down Shares based on changes in values of properties in the NCREIF Property Index (NPI).

We have added Monte Carlo Simulation to Chapter 13 that covers Risk Analysis. This technique has become increasingly popular as a helpful tool that may be used when analyz- ing investment risk. The Excel workbook that comes with the text includes a spreadsheet that replicates the example used in the chapter.

In the previous edition, we introduced a discounted cash flow program designed to provide students to analyse valuation and investment problems. In this edition, we have extended this feature by allowing students to sign up for a more sophisticated cloud-based, lease by lease, discounted cash flow program that is designed to do more advanced invest- ment analysis and valuation of real estate income property investments.

Excel Spreadsheets and RealNex Software

This book is rigorous yet practical and blends theory with applications to real-world prob- lems. These problems are illustrated and solved by using a blend of financial calculators, Excel spreadsheets, and specialized software designed to analyze real estate income prop- erty. Excel spreadsheets, provided on the book’s website at www.mhhe.com/bf16e, are an aid for students to understand many of the exhibits displayed in chapters throughout the text. By modifying these exhibits, students also may solve many end-of-chapter problems without having to design new spreadsheets.

Students can also register online to get free access to a cloud-based real estate valuation program called RealNex. We chose this program because it is very easy and convenient to use by anyone with an Internet connection (including iPads and other mobile devices). RealNex is used in several chapters to supplement the use of Excel spreadsheets when doing investment analysis and solving valuation problems. Once students (or professors) register, they will also have access to data files that replicate examples in the book. Stu- dents can register at the following website: www.info.realnex.com/edu

Internet Tools and Assets

Making informed real estate investment and financing decisions depends on being able to obtain useful information. Such information may include national and local market trends, interest rates, and properties available for acquisition, financing alternatives, and the opin- ions of experts concerning the outlook for various real estate sectors.

The Internet provides a rich source of information to real estate investors and lenders. Knowing how to find information on the web is an important part of the due diligence that should be done before making any real estate investments. This edition includes a number of Web App boxes that provide exercises that require finding relevant information on the Internet. These Web App boxes provide practical examples of the types of data and other

Final PDF to printer

vi Preface

bru19684_fm_i-xvi.indd vi 11/29/17 02:36 PM

resources that are available on the Internet. The fifteenth edition also contains website ref- erences that students can use to research various real estate topics. In addition to research, these resources provide readers with an opportunity to remain current on many of the top- ics discussed in the book.

The book’s website, located at www.mhhe.com/bf16e, contains additional helpful materials for students such as web links, multiple-choice quizzes, Excel spreadsheets, and appendixes to the text. Using a password-protected instructor log-in, instructors can find a solutions manual, test bank, and PowerPoint presentations.

Supplements

Several ancillary materials are available for instructor use. These include ∙ Solutions Manual—developed by Jeffrey Fisher and William Brueggeman ∙ Test Bank—developed by Scott Ehrhorn, Liberty University ∙ PowerPoint slides—developed by Joshua Kahr, Columbia University

Acknowledgments

We would like to thank several people who contributed to recent editions by either being a reviewer or providing feedback to us in other ways that helped improve the current edition: Edward Baryla East Tennessee State University

Robert Berlinger, Jr. University Institute of Technology

Roy T. Black Georgia State University

Thomas P. Boehm University of Tennessee-Knoxville

Thomas Bothem University of Illinois at Chicago

Wally Boudry University of North Carolina-Chapel Hill

Grace Wong Bucchianeri Wharton School, University of Pennsylvania

Brad Case NAREIT

Ping Cheng Florida Atlantic University

Joe D’Alessandro Real Estate Insights

Ron Donohue Homer Hoyt Institute

John Fay Santa Clara University

Michael Fratantoni Georgetown University

Eric Fruits Portland State University

Deborah W. Gregory University of Arizona

Arie Halachmi Tennessee State University (USA) Sun Yat-Sen University (China)

Barry Hersh NYU-SCPS Real Estate Institute

Samuel Kahn Touro College

Joshua Kahr Columbia University

Youguo Liang Abu Dhabi Investment Authority

W. Keith Munsell Boston University

Michael Schonberger Rutgers University-New Brunswick

Tracey Seslen University of Southern California

Rui Shi L&B Realty Advisors

Carlos Slawson Louisiana State University

Jan Strockis Santa Clara University

Final PDF to printer

Preface vii

bru19684_fm_i-xvi.indd vii 11/28/17 07:28 PM

Several people played an important role in providing comments to help revise the cur- rent edition. Brad Case with the National Association of Real Estate Investment Trusts (NAREIT) and Ron Donohue with the Homer Hoyt Institute helped revise the chapter on real estate investment trusts. Joe D’Alessandro and Rui Shi helped with the revision of the chapter on real estate funds. Rhea Thornton with FNMA provided comments on the chap- ter that discusses underwriting residential loans. Susanne Cannon with Megalytics helped with the insert on Crowd Funding. Jeanne Milazzo helped in the preparation and submis- sion of the manuscript. A special thanks to Tara Slagle, Senior Content Project Manager at MPS North America LLC for working with the authors throughout the production stage to make the revision process as smooth as possible.

Much of the material in the current edition benefited from many people who provided input into previous editions. Youguo Liang at ADIA provided significant input on the structure of joint ventures. Charles Johnson and Aaron Temple helped with web refer- ences. Jacey Leonard helped prepare the Excel templates for the previous edition that were used in this edition. Anand Kumar helped with web references and spreadsheets. Ji’ Reh Kore helped with research on recent trends impacting the real estate finance industry, as well as with the preparation of the Solutions Manual. Diem Chau helped with the Solu- tions Manual and with chapter exhibits. Nathan Hastings helped update the legal chapters and provided input on the ownership structures used for real estate.

We will miss the late Theron Nelson, who contributed to prior editions of the book, including creating the original version of several of the spreadsheet templates. We appreci- ate his contributions to this book and to the real estate profession.

Our thanks to the book team at McGraw-Hill Education for their help in developing the new edition: Chuck Synovec, Michele Janicek, Jennifer Upton, Trina Maurer, Melissa Leick, Tim Vertovec, Natalie King, and Xin Lin.

We also continue to be indebted to people who have contributed as authors to previous editions, especially the late Henry E. Hoagland, who authored the first edition of this book, and the late Leo D. Stone, who participated in several editions. Finally, we thank all of the adopters of previous editions of the book, who, because of their feedback, have made us feel that we have helped them prepare students for a career in real estate.

William B. Brueggeman

Jeffrey D. Fisher

Final PDF to printer

viii

bru19684_fm_i-xvi.indd viii 11/28/17 07:28 PM

Preface iii

PART ONE Overview of Real Estate Finance and Investments 1 Real Estate Investment: Basic Legal

Concepts 1 2 Real Estate Financing: Notes and

Mortgages 16

PART TWO Mortgage Loans 3 Mortgage Loan Foundations: The Time

Value of Money 42 4 Fixed Interest Rate Mortgage Loans 78 5 Adjustable and Floating Rate Mortgage

Loans 122 6 Mortgages: Additional Concepts, Analysis,

and Applications 150

PART THREE Residential Housing 7 Single-Family Housing: Pricing,

Investment, and Tax Considerations 185 8 Underwriting and Financing Residential

Properties 222

PART FOUR Income-Producing Properties 9 Income-Producing Properties: Leases,

Rents, and the Market for Space 254 10 Valuation of Income Properties: Appraisal

and the Market for Capital 297 11 Investment Analysis and Taxation of

Income Properties 348

12 Financial Leverage and Financing Alternatives 398

13 Risk Analysis 433 14 Disposition and Renovation of Income

Properties 467 15 Financing Corporate Real Estate 503

PART FIVE Financing Real Estate Development 16 Financing Project Development 526 17 Financing Land Development

Projects 561

PART SIX Alternative Real Estate Financing and Investment Vehicles 18 Structuring Real Estate Investments:

Organizational Forms and Joint Ventures 590

19 The Secondary Mortgage Market: Pass- Through Securities 629

20 The Secondary Mortgage Market: CMOs and Derivative Securities 657

21 Real Estate Investment Trusts (REITs) 698

PART SEVEN Portfolio Analysis and Real Estate Funds 22 Real Estate Investment Performance and

Portfolio Considerations 732 23 Real Estate Investment Funds: Structure,

Performance, Benchmarking, and Attribution Analysis 761

INDEX 800

Brief Contents

Final PDF to printer

ix

bru19684_fm_i-xvi.indd ix 11/28/17 07:28 PM

Preface iii

PART ONE OVERVIEW OF REAL ESTATE FINANCE AND INVESTMENTS

Chapter 1 Real Estate Investment: Basic Legal Concepts 1 Property Rights and Estates 2

Definition of Estate 4 Two General Classifications of Estates 4 Examples of Freehold Estates 4 Estates Not Yet in Possession (Future Estates) 5 Examples of Leasehold Estates 5

Interests, Encumbrances, and Easements 6 Assurance of Title 7

The Meaning of Title 7 Deeds 9

Methods of Title Assurance 9 Abstract and Opinion Method 11 The Title Insurance Method 11

Recording Acts 12 Limitations on Property Rights 13

Chapter 2 Real Estate Financing: Notes and Mortgages 16 Notes 16 The Mortgage Instrument 18

Definition of a Mortgage 18 Relationship of Note to Mortgage 18 Interests That Can Be Mortgaged 19 Minimum Mortgage Requirements 19 Important Mortgage Covenants 20

Assumption of Mortgage 22 Acquiring Title “Subject to” a Mortgage 23

Property Covered by a Mortgage 23 Junior Mortgages 24 Recording of Mortgages 24

Other Financing Sources 25 Seller Financing 25

Land Contracts 25 Default 26

What Constitutes Default? 26

Alternatives to Foreclosure: Workouts 27 Restructuring the Mortgage Loan 27 Transfer of Mortgage to a New Owner 29 Voluntary Conveyance 29 Friendly Foreclosure 30 Prepackaged Bankruptcy 30 Short Sale 31

Foreclosure 31 Judicial Foreclosure 31 Redemption 32 Sales of Property 32 Effect of Foreclosure on Junior Lienors 35 Deficiency Judgment 35 Taxes in Default 36

Bankruptcy 37 Chapter 7 Liquidation 37 Chapter 11 38 Chapter 13 39

PART TWO MORTGAGE LOANS

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 42 Compound Interest 42 Compound or Future Value 43

Calculating Compound Interest Factors 47 Using Financial Functions: Calculators and Spreadsheets 49 Present Value 52

A Graphic Illustration of Present Value 52 Expanding the Use of Calculators for Finding Present Values 54

Compound or Future Value of an Annuity 56 Use of Compound Interest Factors for Annuities 58

Present Value of an Annuity 60 Use of the Present Value of an Annuity Factors 61

Accumulation of a Future Sum 64 Determining Yields, or Internal Rates of Return, on Investments 65

Investments with Single Receipts 65 Yields on Investment Annuities 68 Equivalent Nominal Annual Rate (ENAR): Extensions 70 Solving for Annual Yields with Partial Periods: An Extension 72

Table of Contents

Final PDF to printer

x Table of Contents

bru19684_fm_i-xvi.indd x 11/28/17 07:28 PM

Chapter 4 Fixed Interest Rate Mortgage Loans 78 Determinants of Mortgage Interest Rates: A Brief Overview 78

The Real Rate of Interest: Underlying Considerations 79 Interest Rates and Inflation Expectations 79 Interest Rates and Risk 80 A Summary of Factors Important in Mortgage Loan Pricing 82

Understanding Fixed Interest Rate Mortgage (FRM) Loan Terms 82 Calculating Payments and Loan Balances—Fixed Interest Rate Loans 84

The Importance of Accrued Interest and Loan Payments 84 Loan Amortization Patterns 84 Fully Amortizing, Constant Payment Mortgage (CPM) Loans 85 Partially Amortizing, Constant Payment Mortgage (CPM) Loans 89 Zero Amortizing, or Interest-Only—Constant Payment Mortgage (CPM) Loans 90 Negative Amortizing, Constant Payment Mortgage (CPM) Loans 91

Summary and Comparisons: Fixed Interest Rate, Constant Payment Mortgage (CPM) Loans with Various Amortization Patterns 92

Determining Loan Balances 94 Finding Loan Balances—Other Amortization Patterns 95 Loan Closing Costs and Effective Borrowing Costs 96 Loan Fees and Early Repayment: Fully Amortizing Loans 99 Charging Fees to Achieve Yield, or When “Pricing” FRMs 103

Financing Loan Fees and Other Closing Costs 104 Other FRM Loan Patterns—Declining Payments and Constant Amortization Rates 104

Amortization Schedules and Callable Loans 105 “Reverse Mortgages” 106

Appendix Inflation, Mortgage Pricing, and Payment Structuring 113

Chapter 5 Adjustable and Floating Rate Mortgage Loans 122 The Price Level Adjusted Mortgage (PLAM) 124

PLAM: Payment Mechanics 124 ARMs and Floating Rate Loans: An Overview 126 Variations: ARM and Floating Rate Loans 129

Risk Premiums, Interest Rate Risk, and Default Risk 133 Expected Yield Relationships and Interest Rate Risk 135 More Complex Features 136 ARM Payment Mechanics 138 Expected Yields on ARMs: A Comparison 143

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 150 Incremental Borrowing Cost 150

Early Repayment 152 Origination Fees 153 Incremental Borrowing Cost versus a Second Mortgage 154 Relationship between the Incremental Cost and the Loan-to-Value Ratio 154 Differences in Maturities 157

Loan Refinancing 158 Early Repayment: Loan Refinancing 159 Effective Cost of Refinancing 161 Borrowing the Refinancing Costs 161 Other Considerations 162

Early Loan Repayment: Lender Inducements 164 Market Value of a Loan 165 Effective Cost of Two or More Loans 166

Second Mortgages and Shorter Maturities 168 Effect of Below-Market Financing on Property Prices 169

Assuming a Lower Loan Balance 172 Cash Equivalency 172 Cash Equivalency: Smaller Loan Balance 173 Cash Equivalency: Concluding Comments 174 Wraparound Loans 174 Buydown Loans 177 Appendix After-Tax Effective Interest Rate 181

PART THREE RESIDENTIAL HOUSING

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 185 Overview 185

House Prices 185 Income and Employment 186 Renting versus Owning 187

Final PDF to printer

Table of Contents xi

bru19684_fm_i-xvi.indd xi 11/28/17 07:28 PM

Analyzing Expected House Prices 193 Economic Base Analysis—Location Quotients 197

Housing Supply: An Overview 198 Submarkets: Neighborhoods/Municipalities 199 Capitalization Effects: Price Premiums 199 Pricing Property in Specific Submarkets/Locations 201

Investing in “Distressed Properties” 209 Financial Framework for Analyzing Distressed Properties 210 Acquisition Phase 210 Holding Period Phase 214 Disposition Phase—Exit Strategies 218

Chapter 8 Underwriting and Financing Residential Properties 222 Underwriting Default Risk 222 Classification of Mortgage Loans 223

Conventional Mortgage Loans 223 Insured Conventional Mortgage Loans 224 FHA-Insured Mortgage Loans 226 VA-Guaranteed Mortgage Loans 226

The Underwriting Process 227 Borrower Income 227 Verification of Borrower Assets 229 Assessment of Credit History 229 Estimated Housing Expense 230 Other Obligations 230 Compensating Factors 230

The Underwriting Process Illustrated 232 Underwriting Standards—Conventional and Insured Conventional Mortgages 233 Underwriting Standards—FHA-Insured Mortgages 234 Underwriting Standards—VA-Guaranteed Mortgages 235 Underwriting and Loan Amounts—A Summary 237

The Closing Process 239 Fees and Expenses 239 Prorations, Escrow Costs, and Payments to Third Parties 240 Statutory Costs 242 Requirements under the Real Estate Settlement and Procedures Act (RESPA) 242

Settlement Costs Illustrated 244 Federal Truth-in-Lending (FTL) Requirements 246 Truth-in-Lending Sample Disclosure 247 Establishing the APR under Federal Truth-in-Lending Requirements 247 ARMs and Truth-in-Lending Disclosure 248

PART FOUR INCOME-PRODUCING PROPERTIES

Chapter 9 Income-Producing Properties: Leases, Rents, and the Market for Space 254 Property Types 254 Supply and Demand Analysis 256

Local Market Studies of Supply and Demand 259 Location and User-Tenants 260

The Business of Real Estate 262 The “Market” for Income-Producing Real Estate 263 Income Potential—Real Estate Assets 264

Vacancy 265 Underwriting Tenants 266

General Contents of Leases 266 Leases and Rental Income 270 Leases and Responsibility for Expenses (Recoveries) 270 Comparing Leases: Effective Rent 273 Other Financial Considerations 275

Developing Statements of Operating Cash Flow 278 Case Example: Office Properties 279

Rent Premiums and Discounts for Office Space 279 Pro Forma Statement of Cash Flow—Office Properties 282

Case Example: Industrial and Warehouse Properties 283

Pro Forma Statement of Cash Flow—Industrial/ Warehouse Properties 284

Case Example: Retail Properties 285 The Retail Leasing Environment 285 CAM Charges—Recoveries 287 Pro Forma Statement of Cash Flow—Retail Properties 288

Case Example: Apartment Properties 290

Chapter 10 Valuation of Income Properties: Appraisal and the Market for Capital 297 Introduction 297 Valuation Fundamentals 297 Appraisal Process and Approaches to Valuation 298 Sales Comparison Approach 299 Income Approach 301

Capitalization Rate 303 Capitalization Rates—A Note of Caution 306 Discounted Cash Flow Techniques 307

Final PDF to printer

xii Table of Contents

bru19684_fm_i-xvi.indd xii 11/28/17 07:28 PM

Land Values: Highest and Best Use Analysis 314 Volatility in Land Prices 315 “Highest and Best Use” Analysis—Vacant Site 315 “Highest and Best Use” Analysis—Improved Property 316

Mortgage-Equity Capitalization 317 Reconciliation: Sales Comparison and Income Capitalization Approaches 319 Exploring the Relationships between Changing Market Conditions, Cap Rates, and Property Values 319 A Closing Note on Cap Rates and Market Conditions 324 A Word of Caution—Simultaneous Effects of Real Market Forces and Interest Rates on Property Values 324 Leases: Valuation of a Leased Fee Estate 324 Cost Approach 325 Valuation Case Study—Oakwood Apartments 329

RealNex Solution 331 Appendix RealNex Inputs and Output for Apartment Analysis 341

Chapter 11 Investment Analysis and Taxation of Income Properties 348 Motivations for Investing 348 Real Estate Market Characteristics and Investment Strategies 349

The Real Estate Cycle 349 Investment Strategies 351

Market Analysis 354 Supply of Space 356 Market Rents 358 Forecasting Supply, Demand, Market Rents, and Occupancy 359

Making Investments: Projecting Cash Flows 361 Office Building Example 361

Base Rent 362 Market Rent 362 Expense Stops 363 Net Operating Income 364 Expected Outlays for Replacements and Capital Improvements 365 Estimated Sale Price 365

Introduction to Investment Analysis 367 Internal Rate of Return (IRR) 367 Present Value 367

Introduction to Debt Financing 368 Measures of Investment Performance Using Ratios 369

Before-Tax Cash Flow from Sale 369 Summary of Investment Analysis Calculations 370

Taxation of Income-Producing Real Estate 371 Taxable Income from Operation of Real Estate 372

Depreciation Allowances 372 Loan Points 374 Tax Liability and After-Tax Cash Flow 374

Taxable Income from Disposal of Depreciable Real Property 374 After-Tax Investment Analysis 375

After-Tax Cash Flow from Operations 375 After-Tax Cash Flow from Sale 377 After-Tax IRR 377 Effective Tax Rate 378

A Note about Passive Losses 378 Special Exceptions to PAL Rules 380

Appendix A Approaches to Metro Area Market Forecasting 384 Appendix B RealNex Office Example 390

Chapter 12 Financial Leverage and Financing Alternatives 398 Introduction to Financial Leverage 398

Conditions for Positive Leverage—Before Tax 399 Conditions for Positive Leverage—After Tax 403

Break-Even Interest Rate 405 Risk and Leverage 407 Underwriting Loans on Income Properties 409

Market Study and Appraisal 409 Borrower Financials 409 The Loan-to-Value Ratio 410 The Debt Coverage Ratio 410

Other Loan Terms and Mortgage Covenants 411 Alternatives to Fixed Rate Loan Structures 413 Participation Loans 414

Lender Motivations 414 Investor Motivations 415 Participation Example 415

Sale-Leaseback of the Land 419 Effective Cost of the Sale-Leaseback 421

Interest-Only Loans 421 Accrual Loans 423

Structuring the Payment for a Target Debt Coverage Ratio 423

Convertible Mortgages 425 Lender’s Yield on Convertible Mortgages 425

Comparison of Financing Alternatives 427 Other Financing Alternatives 429

Final PDF to printer

Table of Contents xiii

bru19684_fm_i-xvi.indd xiii 11/28/17 07:28 PM

Chapter 13 Risk Analysis 433 Introduction 433

Comparing Investment Returns 433 Types of Risk 434 Due Diligence in Real Estate Investment Risk Analysis 436 Sensitivity Analysis 436 Partitioning the IRR 440 Variation in Returns and Risk 441

Retail Case Study—Westgate Shopping Center 445 Westgate Shopping Center Scenario Analysis 448

Lease Rollover Risk 448 Market Leasing Assumptions with Renewal Probabilities 450

Market Rent 450 Months Vacant 450 Leasing Commissions 451 Tenant Improvements 451

Industrial Case Study—Worthington Distribution Center 451 Risk and Leverage 453

Monte Carlo Simulation 456 Example 458 Extensions of Monte Carlo Simulation 459 Participation Example 459

A “Real Options” Approach to Investment Decisions 461 Traditional Approach to Land Valuation 462 Real Option Approach to Land Valuation 462 Real Options Extensions and Strategy 463

Chapter 14 Disposition and Renovation of Income Properties 467 Disposition Decisions 467

A Decision Rule for Property Disposition 468 IRR for Holding versus Sale of the Property 469 Return to a New Investor 472

Marginal Rate of Return 472 Refinancing as an Alternative to Disposition 476

Incremental Cost of Refinancing 476 Leveraged Return from Refinancing and Holding an Additional Five Years 477 Refinancing at a Lower Interest Rate 479

Other Disposition Considerations—Portfolio Balancing 480 Tax-Deferral Strategies upon Disposition 480

Installment Sales 481 Tax-Deferred Exchanges 486

Renovation as an Alternative to Disposition 493 Renovation and Refinancing 496 Rehabilitation Investment Tax Credits 496

Low-Income Housing 498

Chapter 15 Financing Corporate Real Estate 503 Lease-versus-Own Analysis 504

Leasing versus Owning—An Example 504 Cash Flow from Leasing 505 Cash Flow from Owning 505 Cash Flow from Owning versus Leasing 507 Return from Owning versus Leasing 507 Importance of the Residual Value of Real Estate 508 The Investor’s Perspective 510 A Note on Project Financing 511 Factors Affecting Own-versus-Lease Decisions 512

The Role of Real Estate in Corporate Restructuring 518 Sale–Leaseback 518 Refinancing 521 Investing in Real Estate for Diversification 521 Appendix Real Estate Asset Pricing and Capital Budget Analysis: A Synthesis 524

PART FIVE FINANCING REAL ESTATE DEVELOPMENT

Chapter 16 Financing Project Development 526 Introduction 526 Overview: The Planning and Permitting Process 526 The Development of Income-Producing Property 530

Market Risks and Project Feasibility 531 Project Risks 532

Project Development Financing—An Overview 534 Lender Requirements in Financing Project Development 535

Interest Rates and Fees 541 Project Development Illustrated 541

Project Description and Project Costs 541 Market Data and Tenant Mix 546 Pro Forma Construction Costs and Cash Flow Projections 547

Feasibility, Profitability, and Risk—Additional Issues 551 Profitability before and after Taxes 551 Sensitivity Analysis, Risk, and Feasibility Analysis 555

Final PDF to printer

xiv Table of Contents

bru19684_fm_i-xvi.indd xiv 11/28/17 07:28 PM

Chapter 17 Financing Land Development Projects 561 Characterization of the Land Development Business 561 The Land Development Process—An Overview 563

Acquisition of Land—Use of the Option Contract 563 Financing and Development 565

Lender Requirements in Financing Land Development 568

Detailed Cost Breakdowns 570 General Contracts and Subcontracts 570

Residential Land Development Illustrated 571 Market Conditions and Site Plan 572 Estimating Development Cost and Interest Carry 574 Estimating Release Prices per Parcel Sold 582 Loan Request and Repayment Schedule 582

Project Feasibility and Profitability 583 Project IRR and Net Present Value 585 Entrepreneurial Profits 586 Sensitivity Analysis 587

PART SIX ALTERNATIVE REAL ESTATE FINANCING AND INVESTMENT VEHICLES

Chapter 18 Structuring Real Estate Investments: Organizational Forms and Joint Ventures 590 Introduction 590

Sole Proprietorships 590 Partnerships 591 Limited Liability Companies 593 Corporations 594

Joint Ventures 595 Organizational Forms 596 Profit Sharing 596

Initial Capital Contributions 597 Sharing Cash Flow from Operations 597 Sharing of Cash Flow from Sale 598 Summary of Cash Flows Distributed in Each Operating Year 599 Cash Flow from Sale 601 IRR to Each Joint Venture Party 601 Variation on the Preferred IRR—“The Lookback IRR” 602 Syndications 603

Use of the Limited Partnership in Private and Public Syndicates 604 Private Syndication Problem Illustrated 605

Financial Considerations—Partnership Agreement 606 Operating Projections 607 Statement of Before-Tax Cash Flow (BTCF) 608 Calculation of Net Income or Loss 608 Calculation of Capital Gain from Sale 609

Capital Accounts 609 Distribution of Cash from Sale of Asset 610 Calculation of After-Tax Cash Flow and ATIRR on Equity 611

Partnership Allocations and Substantial Economic Effect 613 Capital Accounts and Gain Charge-Backs 614 Use of the Limited Partnership in Private and Public Syndicates 616

Use of Corporate General Partners 617 Private versus Public Syndicates 617 Accredited Investors—Regulation D 618

Regulation of Syndicates 622 Investment Objectives and Policies 623 Promoters’ and Managers’ Compensation 623 Investor Suitability Standards 624

Federal and State Securities Authorities 624

Chapter 19 The Secondary Mortgage Market: Pass-Through Securities 629 Introduction 629 Evolution of the Secondary Mortgage Market 629

Early Buyers of Mortgage Loans 630 The Secondary Market after 1954 630

FNMA’s Changing Role 631 The Government National Mortgage Association 631

Mortgage-Backed Securities and the GNMA Payment Guarantee 632

The Federal Home Loan Mortgage Corporation 633 Operation of the Secondary Mortgage Market 633

Direct Sale Programs 634 The Development of Mortgage-Related Security Pools 634

Mortgage-Backed Bonds 635 Pricing Mortgage-Backed Bonds 636 Subsequent Prices 638

Mortgage Pass-Through Securities 639 Important Characteristics of Mortgage Pools 641 Mortgage Pass-Through Securities: A General Approach to Pricing 644

Final PDF to printer

Table of Contents xv

bru19684_fm_i-xvi.indd xv 11/28/17 07:28 PM

Mortgage Pass-Through Payment Mechanics Illustrated 646 Prepayment Patterns and Security Prices 648 Prepayment Assumptions 649

The Effects of Prepayment Illustrated 651 Security Prices and Expected Yields 652 Market Interest Rates and Price Behavior on Mortgage Pass-Throughs 653 A Note on MBBs and MPTs 654

Chapter 20 The Secondary Mortgage Market: CMOs and Derivative Securities 657 Introduction 657 Mortgage Pay-Through Bonds (MPTBs) 657 Collateralized Mortgage Obligations 658

CMOs Illustrated 659 CMO Mechanics 661 CMOs: Pricing and Expected Maturities 667 CMO Price Behavior and Prepayment Rates 669 CMO Tranche Variations 671 Subprime Mortgage-Backed Securities 672

Derivatives Illustrated 673 Yield Enhancement 676 IO and PO Strips 676 Convexity 679

Residential Mortgage-Related Securities: A Summary 679 Residential Mortgage-Related Securities: Some Closing Observations 681 Commercial Mortgage-Backed Securities (CMBSs) 682

Rating Commercial Mortgage-Backed Securities 685 Collateralized Debt Obligations (CDOs) 687 Mortgage-Related Securities and REMICs 690 REMICs: Other Considerations 691

Appendix Duration—An Additional Consideration in Yield Measurement 695

Chapter 21 Real Estate Investment Trusts (REITs) 698 Introduction 698

Legal Requirements 698 Tax Treatment 702 Violation Penalties and Status Termination 702 Taxable REIT Subsidiaries 702

TYPES of REITs 703 Equity REITs 703

The Investment Appeal of Equity REITs 704 Public Nonlisted REITs 706 Importance of FFO (Funds from Operations) 709 REIT Expansion and Growth 711

Important Issues in Accounting and Financial Disclosure: Equity REITs 715

Tenant Improvements and Free Rents: Effects on FFO 716 Leasing Commissions and Related Costs 716 Use of Straight-Line Rents 717 FFO and Income from Managing Other Properties 717 Types of Mortgage Debt and Other Obligations 718 Existence of Ground Leases 718 Lease Renewal Options and REIT Rent Growth 718 Occupancy Numbers: Leased Space or Occupied Space? 719 Retail REITs and Sales per Square Foot 719 Additional Costs of Being a Public Company 720

The Investment Appeal of Mortgage REITs 720 Financial Analysis of an Equity REIT Illustrated 722

Valuing REITs as Investments 725 Valuation of Midwestern America Property Trust 725

PART SEVEN PORTFOLIO ANALYSIS AND REAL ESTATE FUNDS

Chapter 22 Real Estate Investment Performance and Portfolio Considerations 732 Introduction 732 The Nature of Real Estate Investment Data 732 Sources of Data Used for Real Estate Performance Measurement 733

REIT Data: Security Prices 733 Hybrid and Mortgage REITs 733 NCREIF Property Index: Property Values 734 Data Sources for Other Investments 735

Cumulative Investment Return Patterns 735 Computing Holding Period Returns 736

Comparing Investment Returns 738 Risk, Return, and Performance Measurement 738

Risk-Adjusted Returns: Basic Elements 739 Elements of Portfolio Theory 740

Calculating Portfolio Returns 742 Portfolio Risk 742 Portfolio Weighting: Trading Off Risk and Return 745

Final PDF to printer

xvi Table of Contents

bru19684_fm_i-xvi.indd xvi 11/28/17 07:28 PM

Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification 747

Portfolio Diversification: EREITs and Other Investments 747 Public versus Private Real Estate Investments 749 Real Estate Performance and Inflation 750 Diversification by Property Type and Location 750 Global Diversification 753 Risks of Global Investment 754 Use of Derivatives to Hedge Portfolio Risk 756 Example—Swap Office for Retail 757 Up Shares and Down Shares 757

Chapter 23 Real Estate Investment Funds: Structure, Performance, Benchmarking, and Attribution Analysis 761 Investor Goals and Objectives 763 General Explanation of Possible Provisions in Fund Offerings 763

Reporting Fund Performance 771 Measuring and Reporting Investment Returns 771 Summary of Major Activity during Quarter 772

Calculating Returns 774 Calculating Returns at the Property Level 776 Comparing Returns: Fund Level versus Property Level 777 Returns: Before and After Fees 778 Calculating Historical Returns 778 Time-Weighted Returns 779

Choosing IRR versus TWR for Performance Measurement 782

Target Returns and Benchmarks 783 Investment Multiple 784 Attribution Analysis 785 Attribution Analysis Mathematics 787 Interpreting Sector Allocation 788 Evaluating Risk Differences 790 Jensen’s Alpha 794

INDEXES 800

Final PDF to printer

1

bru19684_ch01_001-015.indd 1 10/31/17 06:22 PM

Chapter 1 Real Estate Investment: Basic Legal Concepts This is not a book about real estate law; however, a considerable amount of legal terminol- ogy is used in the real estate business. It is very important to understand both the physical nature and property rights being acquired when making real estate investments. In this chapter, we survey many important terms pertaining to real estate. Additional legal terms and concepts will appear in later chapters of this book on a “need to know” basis.

Many of the legal terms currently used in the real estate business have evolved from English common law, which serves as the basis for much of the property law currently used in the United States. For example, the term real in real estate comes from the term realty, which has, for centuries, meant land and all things permanently attached (the latter would include immovable things such as buildings and other structures). All other items not con- sidered realty have been designated as personalty, which includes all intangibles and mov- able things (e.g., automobiles, shares of stock, bank accounts, and patents). The term estate has evolved to mean “all that a person owns,” including both realty and personalty. Hence, the portion of a person’s estate that consists of realty has come to be known as real estate. However, in current business practice, although the term “realty” is sometimes used, we generally use the term real estate to mean land and all things permanently attached.

Understanding the distinction between realty and personalty is important because our legal system has evolved in a way that treats the two concepts very differently. For example, long ago in England, disputes over real estate usually involved issues such as rightful own- ership, possession, land boundaries, and so forth. When such disputes were brought before the court, much of the testimony was based on oral agreements, promises, and the like, allegedly made between the opposing parties, and these disputes were difficult to resolve. Decisions that had to be rendered were extremely important (recall that England’s economy was very heavily dependent on agriculture at that time) and affected people’s livelihood. Court decisions may have required one of the parties to vacate the land plus turn over any permanent improvements that had been made (houses, barns, etc.) to other parties. As the number of disputes increased, a pragmatic solution evolved requiring that all transactions involving real estate be evidenced by a written, signed contract in order to be enforceable.1

Parallel developments included (1) a system, whereby land locations and boundaries could be more accurately surveyed and described in contracts and (2) an elaborate system of public record keeping, whereby ownership of all realty within a political jurisdiction

1 This requirement was included as part of the Statute of Frauds and Perjuries, which was passed in England in 1677 with the intent of reducing the number of disputes and questionable transactions brought before the court.

Final PDF to printer

2 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch01_001-015.indd 2 10/31/17 06:22 PM

could be catalogued. Any transactions involving realty could then be added to this record, thereby creating a historical record of all changes in ownership and providing notice of such changes to the general public and especially to any parties contemplating purchas- ing or lending money on real estate. Similar practices continue today in the United States as we require written contracts, requirements, survey methods, and public record systems detailing the ownership of real estate within all counties in every state. We should note that many transactions involving personalty are not subject to the same contractual require- ments as real estate and that oral contracts may be enforceable.

When investing in real estate, in addition to acquiring the physical assets of land and all things permanently attached, investors also acquire certain rights. Examples of these rights include the right to control, occupy, develop, improve, exploit, pledge, lease, exclude, and sell real estate. These have come to be known as property rights. Hence, the terms real property and real property rights have evolved.2 As a practical matter, in business discus- sions, the terms real estate and real property are sometimes used interchangeably. However, as we will see, many of the property rights acquired when investing in real estate are inde- pendent and can be separated. For example, real estate may be leased or pledged to others in exchange for rent or other consideration. This may be done without giving up owner- ship. Indeed, understanding the nature of property rights and how they can be bundled and creatively used to enhance value is one goal of this textbook. The reader should refer to Exhibit 1–1 for an outline of these concepts.

Property Rights and Estates

As pointed out above, the term real estate is used to refer to things that are not movable such as land and improvements permanently attached to the land, and ownership rights associated with the real estate are referred to as real property. Real property has also been contrasted with personal property.3

It is important to distinguish between physical real estate assets and ownership rights in real property because many parties can have different ownership rights in a given parcel of real estate. Our legal system offers ways for the person financing or investing in real estate to be creative and to apportion these various interests among parties.

We generally refer to property rights as the right of a person to the possession, use, enjoyment, and disposal of his or her property. With respect to its application to real estate, interest is a broad legal term used to denote a property right. The holder of an interest in real estate enjoys some right, or degree of control or use, and, in turn, may receive payment for the sale of such an interest. This interest, to the extent that its value can be determined, may also be bought, sold, or used as collateral for a loan.

The value of a particular parcel of real estate can be viewed as the total price individuals are willing to pay for the flow of benefits associated with all of these rights. An individual does not have to be an owner per se to have rights to some of the benefits of real estate. For example, a person who leases land, a lessee, may have the right to possession and 2 For nonrealty, the term personal property has evolved, and personal property rights would include the bundle of rights which are similar to those listed above but pertaining to personalty. 3 We should also point out that there are some items known as fixtures. These are items that were once personal property but have become real property because they have either been attached to the land or building in a somewhat permanent manner or are intended to be used with the land and building on a permanent basis. Examples include built-in dishwashers, furnaces, and garage door openers. There is significant case law on the subject of fixtures. In practice, when properties are bought and sold, a detailed list of all items that could be considered as either personal property or as a fixture will be documented and included as a part of the contract for purchase and sale. This is done to reduce ambiguity as to the property being conveyed from the seller to the buyer.

Final PDF to printer

Chapter 1 Real Estate Investment: Basic Legal Concepts 3

bru19684_ch01_001-015.indd 3 10/31/17 06:22 PM

exclusive use of a property for a period of time. This right of use has value to the lessee, even though the term of the lease is fixed. In exchange for the right to use the property, the lessee is willing to pay a rent for the term of the lease. A holder of a mortgage also has some rights as a nonowner in real estate pledged as security for a loan. These rights vary with state law and the terms of the mortgage, but in general, the lender (or mortgagee) has a right to repossess or bring about the sale of a property if the borrower defaults on the mortgage loan. Although a lender may not possess or use the real estate, the mortgage document provides the lender with evidence of a secured interest. Obviously, this right has value to the lender and reduces the quantity of rights possessed by the owner.

It should be clear that some understanding of the legal characteristics of real estate is essential to analyzing the relative benefits that accrue to the various parties who have some rights in a particular property. In most real estate financing and investment transactions, we generally think in terms of investing, selling, or borrowing based on one owner possessing

(1) (2) (3) (4)

The General Nature of Property

Classification of “Things” Examples

Property Ownership: Evolution of Legal

Requirements/Evidence

Any “thing” tangible or intangible that can be possessed, used, enjoyed, controlled, developed, or conveyed and that has utility or value is considered to be property.

A. Real Property (Realty)

A. Land and all things permanently affixed (buildings, sidewalks, etc.). Immovables. Fixtures.

A. Written contracts, legal descriptions, surveys, deeds, wills, possession. Public notice.

B. Personal Property (Personalty)

B. Intangibles and all movable things (e.g., autos, stocks, patents, furniture).

B. Contracts, oral or written, purchase orders/invoices, and so on.

Property Rights

Rights that can be exercised by the property owner. These include possession, use, enjoyment, control, and the creation of estates in property.

C. Property owner leases the use of realty to tenant, creates a leasehold estate.

C. Written document (lease) describing realty and the terms of possession in exchange for rent.

Interests in Property

Created by owners of real estate who pledge and encumber property in order to achieve an objective without giving up ownership.

D. Property owner pledges real estate as security for a loan.

D. Mortgage liens, easements, and so on.

E. Property owner grants an easement to another party to cross land in order to gain access to another site.

EXHIBIT 1–1 Basic Property Concepts Important in Real Estate Finance and Investment

Final PDF to printer

4 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch01_001-015.indd 4 10/31/17 06:22 PM

all property rights in the real estate. However, as we have discussed, all or a portion of these rights may be restricted or transferred to others. For example, a property owner may lease a property and pledge it as security for a mortgage loan. Remarkably, these parties generally enjoy their respective rights in relative harmony. However, conflicts arise occa- sionally concerning the relative rights and priorities among holders of these interests. The potential for such conflicts may also affect rents that individuals may be willing to pay or the ability to obtain financing from lenders and, ultimately, the value of property.

Definition of Estate The term estate means “all that a person owns.” The term real estate means all realty owned as a part of an individual’s estate. The term estates in real property is used to describe the extent to which rights and interests in real estate are owned. A system of modi- fiers has evolved, based on English property law, that describes the nature or collection of rights and interests being described as a part of a transaction. For example, a fee simple estate represents the most complete form of ownership of real estate, whereas a leasehold estate usually describes rights and interests obtained by tenants when leasing or renting a property. The latter is also a possessory interest and involves the general right to occupy and use the property during the period of possession.

Two General Classifications of Estates

(1) Based on Rights: Estates in Possession versus Estates Not in Possession (Future Possession) Two broad categories of estates can be distinguished on the basis of the nature of rights accompanying the ownership of such estates. An estate in possession (a present estate in land) entitles its owner to immediate enjoyment of the rights to that estate. An estate not in possession (a future estate in land), on the other hand, does not convey the rights of the estate until some time in the future, if at all. An estate not in possession, in other words, represents a future possessory interest in property. Generally, it does not convert to an estate in posses- sion until the occurrence of a particular event. Estates in possession are by far the more com- mon. When most people think of estates, they ordinarily have in mind estates in possession. Obviously, lenders and investors are very interested in the nature of the estate possessed by the owner when considering the purchase or financing of a particular estate in property.

(2) Based on Possession and Use: Freehold versus Leasehold Estates Estates in possession are of two general types: freehold estates and leasehold estates. These types of estates are technically distinguished on the basis of the definiteness or certainty of their duration. A freehold estate lasts for an indefinite period of time; that is, there is no definitely ascertainable date on which the estate ends. A leasehold estate, on the other hand, expires on a definite date. Aside from this technical distinction, a freehold estate connotes ownership of the property by the estate holder, whereas a leasehold estate implies only the right to possess and use the property owned by another for a period of time.

Examples of Freehold Estates It is beyond the scope of this chapter to review all the possible types of freehold estates. We will discuss two of the most common examples, however, to convey the importance of knowing the type of estate that is associated with a particular transaction.

Fee Simple Estate A fee simple estate, also known as a fee simple absolute estate, is the freehold estate that represents the most complete form of ownership of real estate. A holder of a fee simple estate is free to divide up the fee into lesser estates and sell, lease, or borrow against them

Final PDF to printer

Chapter 1 Real Estate Investment: Basic Legal Concepts 5

bru19684_ch01_001-015.indd 5 10/31/17 06:22 PM

as he or she wishes, subject to the laws of the state in which the property is located. Apart from government restrictions, no special conditions, limitations, or restrictions are placed on the right of a holder of a fee simple estate to enjoy the property, lease it to others, sell it, or even give it away. It is this estate in property that investors and lenders encounter in most investment and lending transactions.

Life Estates It is possible to have a freehold estate that has fewer ownership rights than a fee simple estate. One example is a life estate, which is a freehold estate that lasts only as long as the life of the owner of the estate or the life of some other person. Upon the death of that person, the property reverts back to the original grantor (transferor of property), his or her heirs, or any other designated person. Most life estates result from the terms of the convey- ance of the property. For example, a grantor may wish to make a gift of his or her property prior to death, yet wish to retain the use and enjoyment of the property until that time. This can be accomplished by making a conveyance of the property subject to a reserved life estate. A life estate can be leased, mortgaged, or sold. However, parties concerned with this estate should be aware that the estate will end with the death of the holder of the life estate (or that of the person whose life determines the duration of the estate). Because of the uncertainty surrounding the duration of the life estate, its marketability and value as collateral are severely limited.

Estates Not Yet in Possession (Future Estates) The preceding discussion concerned estates in possession, which entitled the owner to immediate enjoyment of the estate. Here, we discuss estates not in possession, or future estates, which do not convey the right to enjoy the property until some time in the future. The two most important types of future estates are the reversion and the remainder.

Reversion A reversion exists when the holder of an estate in land (the grantor) conveys to another per- son (a grantee) a present estate in the property that has fewer ownership rights than the grant- or’s own estate and retains for the grantor or the grantor’s heirs the right to take back, at some time in the future, the full estate that the grantor enjoyed before the conveyance. In this case, the grantor is said to have a reversionary fee interest in the property held by the grantee. A reversionary interest can be sold or mortgaged because it is an actual interest in the property.

Remainder A remainder exists when the grantor of a present estate with fewer ownership rights than the grantor’s own estate conveys to a third person the reversionary interest the grantor or the grantor’s heirs would otherwise have in the property upon termination of the grantee’s estate. A remainder is the future estate for the third person. Like a reversion, a remainder is a mortgageable interest in property.

Examples of Leasehold Estates There are two major types of leasehold estates: estates for years and estates from year to year. There are two other types, but they are not common.4 Leasehold estates are classified on the basis of the manner in which they are created and terminated.

4 Estate at Will: An estate at will is created when a landlord consents to the possession of the property by another person but without any agreement as to the payment of rent or the term of the tenancy. Such estates are of indefinite duration. Estate at Sufferance: An estate at sufferance occurs when the tenant holds possession of the property without consent or knowledge of the landlord after the termination of one of the other three estates.

Final PDF to printer

6 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch01_001-015.indd 6 10/31/17 06:22 PM

Estate for Years: Tenancy for Terms An estate for years is the type of leasehold estate investors and lenders are most likely to encounter. It is created by a lease that specifies an exact duration for the tenancy. The period of tenancy may be less than one year and still be an estate for years as long as the lease agreement specifies the termination date. The lease, as well as all contracts involving transactions in real estate, is usually written. Indeed, a lease is generally required by the statute of frauds to be in writing when it covers a term longer than one year. The rights and duties of the landlord and tenant and other provisions related to the tenancy are normally stated in the lease agreement.

An estate for years can be as long as 99 years (by custom, leases seldom exceed 99 years in duration), giving the lessee the right to use and control the property for that time in exchange for rental payments. To the extent that the specified rental payments fall below the market rental rate of the property during the life of the lease, the lease has value (leasehold value) to the lessee. The value of this interest in the property can be borrowed against or even sold. For example, if the lessee has the right to occupy the prop- erty for $1,000 per year when its fair market value is $2,000 per year, the $1,000 excess represents value to the lessee, which may be borrowed against or sold (assuming no lease covenants prevent it).

While a property is leased, the original fee owner is considered to have a leased fee estate. This means that he or she has given up some property rights to the lessee (the lease- hold estate). The value of the leased fee estate will now depend on the amount of the lease payments expected during the term of the lease plus the value of the property when the lease terminates and the original owner receives the reversionary interest. Hence, a leased fee estate may be used as security for a loan or may be sold.

Estate from Year to Year An estate from year to year (also known as an estate from period to period, or sim- ply as a periodic tenancy) continues for successive periods until either party gives proper notice of its intent to terminate at the end of one or more subsequent periods. A “period” usually corresponds to the rent-paying period. Thus, such a tenancy com- monly runs from month to month, although it can run for any period up to one year. Such estates can be created by explicit agreement between the parties, although a defi- nite termination date is not specified. Since these estates are generally short term (a year or less), the agreement can be, and frequently is, oral. This type of estate can also be created without the express consent of the landlord. A common example is seen when the tenant “holds over” or continues to occupy an estate for years beyond the expiration date, and the landlord accepts payment of rent or gives some other evidence of tacit consent.

If present tenants are to remain in possession after the transfer or sale of property, the grantee should agree to take title subject to existing leases. The agreement should provide for prorating of rents and the transfer of deposits to the grantee. Buyers of property encum- bered by leases should always reserve the right to examine and approve leases to ensure that they are in force, are not in default, and are free from undesirable provisions.

Interests, Encumbrances, and Easements

An interest in real estate can be thought of as a right or claim on real property, its revenues, or production. Interests are created by the owner and conveyed to another party, usually in exchange for other consideration. In real estate, an interest is usually thought to be less important than an estate. For example, an owner of real estate in fee simple may choose

Final PDF to printer

Chapter 1 Real Estate Investment: Basic Legal Concepts 7

bru19684_ch01_001-015.indd 7 10/31/17 06:22 PM

to pledge or encumber his property as a condition for obtaining a loan (mortgage loan). In this case, the lender receives only a secured interest, but not possession, use, and so on, of the property. The nature of the secured interest is usually documented in a mortgage which explains the actions that a lender may take in the event that the loan terms are not met by the property owner. In the interim, the property owner retains possession and use of the property. Another example of the creation of an interest in real property occurs when an owner encumbers a property by granting an easement, or the right to ingress or egress his property, to another party.

An easement is a nonpossessory interest in land. It is the right to use land that is owned or leased by someone else for some special purpose (e.g., as a right of way to and from one’s property). An easement entails only a limited user privilege and not privileges associated with ownership.5 Examples of easements would be the following: property owner A allows property owner B to use a driveway on A’s land to provide owner B with better access to his property. In some retail developments, owners A and B may execute reciprocal easements to allow access across both properties, thereby enhancing customer traffic flow and shopping opportunities.

Assurance of Title

When making real estate investments, buyers of property typically want assurance that they will become the legal owner of the property and that the seller is lawfully possessed and has the right to convey title. Exhibit 1–2 contains a basic flow diagram that should help the reader understand concepts relating to real estate ownership.

When considering the purchase of real estate, buyers must be in a position to assess the quantity and quality of ownership rights that they are acquiring. Title assurance refers to the means by which buyers of real estate “(1) learn in advance whether their sellers have and can convey the quality of title they claim to possess and (2) receive compensation if the title, after transfer, turns out not to be as represented.”6 Lenders are also concerned about title assurance because the quality of title affects the collat- eral value of the property in which they may have a secured interest. Before we exam- ine the mechanisms used for title assurance, we must briefly review the concepts of title and deed.

The Meaning of Title Title is an abstract term frequently used to link an individual or entity who owns property to the property itself. When a person has “title,” he is said to have all of the elements, including the documents, records, and acts, that prove ownership. Title establishes the quantity of rights in real estate being conveyed from seller to buyer. The previous section briefly examined some of the various types of ownership rights and possessory interests that can be involved in a parcel of real estate. We saw, for example, that one person may hold title in fee simple ownership, convey title to a life estate to someone else, and convey the right to reversion upon termination of the life estate to yet another person. Hence, there are many possible combinations of rights and interests.

5 When a property owner provides another with an interest such as an easement, the property owner is said to have encumbered the property. This may be transferred as a part of subsequent sales to successive owners unless it is defeated, or the owner of the interest releases or recognizes the interest to the property owner. 6 Grant S. Nelson and Dale A. Whitman, Real Estate Transfer, Finance and Development, 2nd ed. (St. Paul, MN: West Publishing, 1981), p. 167.

Final PDF to printer

8 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch01_001-015.indd 8 10/31/17 06:22 PM

EXHIBIT 1–2 Flowchart: Ownership of Real Property

Concept Discussion

Ownership When a person or other legal entity has lawful possession of realty and real property rights they are said to have “ownership.”

Proof of ownership Proof is usually accomplished with documents such as deeds, contracts, wills, grants, property records, and/or evidence of continuous possession and use, and so on.

Title When a person or entity has legal evidence, or “proof,” of ownership, they are said to have “title” to a property. This evidence links ownership by a person to a specific property.

Assurance of title When investing in real estate, the investor must be able to evaluate the quality and/or completeness of title that they will receive. This is important in the event that the buyer wants to obtain financing and/or resell the property in the future. As part of the contract negotiations, the seller usually agrees to convey title and to provide a warranty or guarantee.

(a) General warranty deed When the seller conveys a general warranty deed, she warrants (1) that she is in lawful possession of the property and all property rights, (2) that no other individuals or entities have an ownership interest in the property, and (3) that the title is unencumbered or free of imperfections (with any specific exceptions noted: e.g., easements, leases, or liens). In the event that a buyer who relies on the seller’s warranty incurs a loss because of title imperfections, the seller may be liable.

(b) Qualified warranty deeds In cases when the seller is unsure of the quality of title or is unwilling to provide a general warranty deed, the seller may qualify assurance of title by conveying a “special warranty deed,” a “bargain and sale deed,” or a “quit claim deed.”

Evidence as to the nature and quality of title being conveyed

How can the investor in a property be assured that the seller legally possesses the property and that the record of ownership is clear, or that the title is unencumbered?

(a) Attorney’s opinion An attorney reviews public property records and other evidence to ascertain whether or not the “chain of title” is “clear.” When a title is clear, this usually means that all individuals who may have had an ownership interest in the property have conveyed or relinquished such interests in previous conveyances of title. When the possibility exists that other parties may have an ownership or other interest, these may be referred to as title “imperfections or defects.” If an investor wants clear title, action must be taken to “cure” such defects. This is usually done by an attorney who will contact relevant parties in the chain of title and negotiate a release or conveyance of their interest, possibly in exchange for some consideration.

(b) Title insurance More commonly, an insurance policy indemnifying against a loss due to possible title imperfections is purchased (usually by the buyer). This may be done because the seller’s warranty may be effectively limited. This could happen if the seller files for bankruptcy or does not have the financial capacity to reimburse the buyer for losses due to title imperfections. Title insurance also may be used in lieu of an attorney’s opinion because the latter protects the buyer only to the extent that the title search was done negligently by the attorney or her abstractor. Title insurance companies usually conduct a review of the title chain before issuing a title insurance policy.

Final PDF to printer

Chapter 1 Real Estate Investment: Basic Legal Concepts 9

bru19684_ch01_001-015.indd 9 10/31/17 06:22 PM

An abstract of title is a historical summary of the publicly recorded documents that affect a title. The quality of the title conveyed from seller to buyer depends upon the effect these documents have upon the seller’s rightful possession of his or her property.

Essentially, title exists only for freehold estates. A leasehold estate, on the other hand, is typically created by a contract (called a lease) between a person who holds the title (the lessor) and another person (the lessee), whereby possession of the property is granted by the owner to the other person for a period of time. The existence of leases on a property will, however, affect the nature of the rights that can be conveyed to a new buyer because lease terms are binding on the new owner unless waived by the lessee or, in some juris- dictions, unless title is acquired at a foreclosure sale. Because investors and lenders are concerned about the nature and extent of the rights they are acquiring or financing, leases encumbering the property can have a profound impact on a property’s value.

Deeds Usually title is conveyed from one person (the grantor) to another (the grantee) by means of a written instrument called a deed. (We use the term grantor instead of seller because title may also be transferred by the owner [grantor] to an heir [grantee] by means of a will; hence the terms grantor and grantee.) To be a valid conveyance of ownership interests in real property, all deeds must be in writing and meet certain other legal requirements of the state in which the property is located.7

Generally, a purchaser wants the deed to convey a good and marketable title to the prop- erty. A good title is one that is valid in fact; that is, the grantor does lawfully have the title he or she claims to have to the property. However, a good title, because of the lack of suf- ficient documentation or encumbrances on the property, may be unmarketable. A market- able title is one that is not merely valid in fact but is also “free from reasonable doubt,” one that is “reasonably free from litigation,” and “one which readily can be sold or mortgaged to a reasonably prudent purchaser or mortgagee (mortgage lender).”8

Encumbrances on a title, such as easements, leases, and mortgages (secured interests), do not automatically make it unmarketable. A purchaser may be willing to take title to the property subject to encumbrances. But the deed should note all encumbrances on the title so that a potential purchaser can rationally decide whether to purchase the property and to arrive at the appropriate price given any risks, costs, or restrictions posed by the encumbrances.

Methods of Title Assurance

There are three general ways in which a buyer has assurance that a title is good and market- able. First, the seller may provide a warranty as part of the deed. Second, there may be a search of relevant recorded documents to determine whether there is reason to question the quality of the title. This is usually done by an attorney and is accompanied by a legal opin- ion. Third, title insurance may be purchased to cover unexpected problems with the title.

7 A deed is not the only way by which ownership rights in real property are conveyed. Titles are also transferred by wills, court decrees, and grants of land from the government to private persons. In addition, lawful title to property can be acquired by means of adverse possession. It should also be pointed out that although we use the terms buyers and sellers in this book, the more general terms grantor and grantee are frequently used in contracts or other documents in real estate. Grantors include sellers but also include property owners who may be transferring title by gift (not sale), by will, and so on. Grantees include buyers in a transaction but also may include persons who receive title by gift, as an heir in a will, and so on. 8 Black’s Law Dictionary, 7th ed. (St. Paul, MN: West Publishing, 1999).

Final PDF to printer

10 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch01_001-015.indd 10 10/31/17 06:22 PM

General Warranty Deed It is important to understand that any deed, no matter how complete the warranties con- tained therein, can only convey the quality of title that the grantor actually has to the property. This is why most buyers of real estate usually obtain independent assurance of the validity and marketability of the title from a third party. A general warranty deed is the most commonly used deed in real estate transactions and the most desirable type of deed from the buyer’s perspective. It offers the most comprehensive warranties about the quality of the title. Essentially, the grantor warrants that the title he or she conveys to the property is free and clear of all encumbrances other than those specifically listed in the deed. As pointed out above, encumbrances listed in a deed could include easements and leases. Generally, the most significant covenants contained in such a deed are the follow- ing: (1) a covenant that the grantor has good (legally valid) title to the property, (2) a cov- enant that the grantor has the right to convey the property, (3) a covenant to compensate the grantee for loss of property or eviction suffered by the grantee as a result of someone else having a superior claim to the property, and (4) a covenant against encumbrances on the property other than those specifically stated in the deed. In a general warranty deed, these covenants cover all conveyances of the property from the time of the original source of title to the present.

Special Warranty Deed A special warranty deed makes the same warranties as a general warranty deed except that it limits their application to defects and encumbrances that occurred only while the grantor held title to the property. Unlike the warranties in a general warranty deed, those in a special warranty deed do not apply to title problems caused or created by previous owners.

Bargain and Sale Deed A bargain and sale deed conveys property without seller warranties. This is sometimes referred to as an “as is” deed. The buyer of property takes title with no assurances from the seller and must take the initiative to determine whether any imperfections exist and, if desired, how to cure such defects.

Sheriff’s Deed–Trustee’s Deed A sheriff’s deed–trustee’s deed is a type of bargain and sale deed received by a buyer from a foreclosure or other forced sale because the sheriff or trustee is acting in a represen- tative capacity. No warranties are added.

Quitclaim Deed A quitclaim deed offers the grantee the least protection. Such a deed simply conveys to the grantee whatever rights, interests, and title that the grantor may have in the property. No warranties are made about the nature of these rights and interests or of the quality of the grantor’s title to the property. The quitclaim deed simply says that the grantor “quits” whatever “claim” he or she has in the property (which may well be none) in favor of the grantee.9

9 Quitclaim deeds are appropriately and frequently used to clear up technical defects or “clouds” on the title to a property. Where the record indicates a person may have any potential claim to the property, obtaining a quitclaim deed from him will eliminate the risk that such a claim will be made in the future.

Final PDF to printer

Chapter 1 Real Estate Investment: Basic Legal Concepts 11

bru19684_ch01_001-015.indd 11 10/31/17 06:22 PM

Very few buyers of real estate rely solely on the guarantees of title provided in deeds of conveyance by the seller. The two methods that buyers employ most often to obtain assurance of title independently of the guarantees provided by the seller are an attorney’s opinion of title and title insurance.

Abstract and Opinion Method Obtaining a lawyer’s opinion of title used to be the most common method of title assur- ance before the widespread availability of title insurance. Essentially, the abstract and opinion method is a two-step process. First, there is a search of the title record, which involves locating and examining all of the instruments in the public records that have affected the title of the property in question.10 Second, when the title search is completed, a lawyer studies the relevant public records and other facts and proceedings affecting the title for the purpose of arriving at an expert opinion of the character of the title. Based upon this study of the abstract or the record, the lawyer will give his or her judgment whether the title is good and marketable. If the title is found to be “clouded,” the opinion should state what defects or encumbrances were uncovered by an examination of the records, and it should also state what the lawyer thinks can and should be done to “cure” the defects uncovered.

Because a lawyer’s responsibility is limited to what appears in the records, the lawyer can- not be held liable for any defect in the title not disclosed therein. Any liability borne by the lawyer is based upon proof of his or her negligence or lack of professional skill in the exami- nation of the records. Rather than relying on the lawyer’s opinion, the title insurance industry has evolved. Many lenders and investors now prefer title insurance, which reduces this risk.

The Title Insurance Method Title insurance was developed to cure the inadequacies of title validation accomplished through an abstract and legal opinion. Title insurance does all that a carefully drawn abstract and a well-considered opinion by a competent lawyer are expected to do. In addition, it adds the principle of insurance to spread the risk of unseen hazards among many property owners.

Elimination of risk arising from unseen hazards in the public record has caused many investors and lenders to prefer this method of title assurance. In fact, title insurance is required for any mortgage that is traded in the secondary mortgage market. The title insurance pro- cess starts with a careful analysis of the records. The information available to the commercial title insurance company may be even more complete than that found in the public records.

10 Most of the instruments that affect title to real estate are recorded, in accordance with the recording acts of the various states, at what is typically called the county recorder’s office. But some instruments that affect title may be recorded in other places. The nature of these other places where records are filed varies from state to state.

The American Land Title Association (www.alta.org), founded in 1907, is the national trade association for the title insurance industry. ALTA members search, review, and insure land titles to protect home buyers and mortgage lenders who invest in real estate. ALTA is

headquartered in Washington, DC. There is a “Consumer Information” link on this site that includes a discussion of common title problems. Outline the types of problems that can be encountered due to a problem with the title for a property.

Web App

Final PDF to printer

12 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch01_001-015.indd 12 10/31/17 06:22 PM

Skilled technicians at title insurance companies examine all available evidence of the title to determine its character. If their conclusions warrant, the title company will insure the title to a property and assume risks that are not even disclosed in the public records or in its own files. In short, title insurance ensures that the title is good and marketable.

What title insurance is supposed to add to the abstract system and the opinion of skilled lawyers may be summarized as follows: (1) definite contract liability to the premium payer, (2) reserves sufficient to meet insured losses, (3) supervision by an agency of the state in which the title insurance company operates, and (4) protection to the policyholder against financial losses that may show up at any future time because of any kind of title defect, disclosed or hidden. Despite these advantages, the abstract and opinion method may still be used because of its lower cost. In general, one method, but not both, is used when pur- chasing property, to avoid the duplication of effort and cost.

Kinds of Title Insurance Policies There are two kinds of title insurance policies. The owner’s policy insures the interests of a new property owner. The lender’s (or mortgagee) policy insures the interests of the mortgagee. The owner’s policy is payable to the owner (or to the heirs of the owner); the lender’s policy is payable to the mortgagee.

Both policies are paid for with a one-time premium. In many states, premiums are regu- lated by a state insurance commission, as are financial requirements to incorporate and continue to do business. The one-time premium for the owner’s policy insures the owner for the entire period of time that she owns the property. The insurance premium may be paid by either the seller or the buyer, depending on the terms of the purchase contract, which are influenced by local custom and market conditions. It is almost universal practice for the borrower to pay the cost of the mortgagee’s policy which will insure the lender for the term of the loan. In cases where properties are refinanced by the same owner, a title search may be required by a new lender. In these cases it may be possible to obtain a new title insurance policy from the same company at a reduced cost.

Recording Acts

All states have enacted statutes known as recording acts. Although the recording acts are not uniform among the states, these acts in general provide a publicly accessible system for assessing and establishing claims or interests in real estate as against all other parties. These statutes also provide a set of authoritative rules for resolving priority disputes among com- peting claimants to interests in real estate. As part of this system, procedures have been estab- lished for placing documents affecting claims to real estate interests on the public record and for maintaining these records to make information available concerning almost all interests in real estate. Once an instrument creating a claim on an interest in real estate has been duly recorded, the recording is deemed to give constructive notice of this interest “to the world.” Constructive notice means that the recording acts deem a person to have whatever informa- tion is contained in the public records—information that could be obtained by a reasonably diligent investigation of the records whether or not the investigator actually has knowledge of the information recorded. Instruments affecting virtually all interests in real estate, including deeds, mortgages, assignments of mortgages, liens, land contracts, long-term leases, ease- ments, restrictive covenants, and options to buy, are covered by recording acts.

Most recording acts say that in order to establish and preserve a claim to an interest in real estate that will take precedence in law against future claimants, the instrument creating that claim must be recorded in accordance with state law. These acts were designed in part to pro- tect an innocent person who purchased an interest in real estate in good faith unaware that the

Final PDF to printer

Chapter 1 Real Estate Investment: Basic Legal Concepts 13

bru19684_ch01_001-015.indd 13 10/31/17 06:22 PM

interest had already been acquired by another. For example, if A conveyed to B, who did not record the instrument establishing his claim, and later A conveyed the same interest to C, who did record, C’s claim would be superior to B’s if C was unaware of the prior conveyance and paid valuable consideration to A. B’s only claim would be to file a suit against A for fraud.

Mechanics’ Liens One cloud on the title which may not be disclosed by the public records is a mechanics’ lien. In general, mechanics’ liens give unpaid contractors, workers, and material suppliers the right to attach a lien on the real estate to which they added their labor or materials. To obtain the payment owed them, they may foreclose such liens by forcing a judicial sale of the encumbered property. They are then paid from the proceeds of the sale. Use of mechan- ics’ liens exists in every state, although the nature of the statutes varies.

Mechanics’ liens are permitted to be recorded “after the fact.” In other words, state laws generally give contractors, laborers, or suppliers of materials a certain period of time fol- lowing the completion of work or delivery of materials during which to file their lien. When the lien is filed, it “relates back” and takes priority over all liens filed after the time when materials were first delivered or work was first performed on the real estate. As a result, until the end of the time allowed for filing (generally 60 days), a purchaser of an interest in newly constructed or improved real estate cannot be sure that the interest will be unencum- bered or that the interest will have the priority bargained for. As a precaution, lenders and purchasers of such real estate should require the seller to provide an affidavit stating that at closing, all moneys due to contractors and subcontractors have been fully paid. In the event that liens are filed after the closing, a breach of the seller’s covenants in the affidavit can easily be proven, and the seller can be held liable for the discharge of those liens. In prac- tice, owners of properties that are newly constructed or renovated should require contrac- tors, workers, and material suppliers to sign a lien waiver. This is an acknowledgment that they have been compensated and that they agree to waive all lien rights. In many situations, if a lender is advancing funds for such work and material, a signed waiver will be required at each stage of construction before additional funds are released.

Limitations on Property Rights

Government Restrictions Throughout this chapter, we have stressed the importance of property rights in real estate. We should also point out that although our form of government protects the rights of indi- viduals to own real estate and to enjoy real property rights, these rights are not unrestricted. Government restrictions on private property rights do exist. Land use regulations are most prominent at the state and local level. The right to regulate emanates from the “police powers of the state,” which are based on the protection of the health, safety, and general welfare of its citizens (societal considerations). As the population in an area grows, it may apply to the state to become incorporated as a city, township, or municipality. At this point, the state usually delegates some areas of land use regulation. Incorporated areas then may modify and expand land use controls and develop restrictions on land use. These items are usually enumerated in zoning ordinances and building codes. Common restrictions used to implement controls include zoning ordinances, allowable uses, height restrictions, park- ing requirements, and building codes, permits, and inspections. The state usually retains control over water or riparian rights, mineral rights, eminent domain, and the like, while the federal government regulates housing and loan discrimination, interstate land sales and securities, and environmental restrictions (pollution of water and air, and endangered spe- cies, as well as effects of property use and development on wet lands).

Final PDF to printer

14 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch01_001-015.indd 14 10/31/17 06:22 PM

Private Deed Restrictions In some cases, property owners may choose to incorporate certain deed restrictions that limit the use of property by all subsequent owners of that property. Property owners may use such restrictions to achieve personal or business objectives. One example of a personal objective would be to add a deed restriction explicitly prohibiting the sale or consumption of alcoholic beverages on the property forever. In the event that this restriction is violated, the restriction may stipulate that the title will revert to the owner who incorporated the restric- tion, or to his heirs. An example of a business objective that is commonly achieved through deed restrictions may involve subdivision of a large tract of land into smaller individual tracts to be sold to builders and developers. In order to assure the initial buyers of the sub- divided tracts that subsequent buyers will build improvements that conform in quality and use, the owner of the initial larger tract may deed restrict each of the subdivided tracts. Such restrictions may require a minimum and/or maximum building size, minimum quality build- ing materials, landscaping, and the like, thereby providing all owners with some assurance of conformity and general standards in design and building quality. However, resolution of any future violations of deed restrictions may prove to be problematic, particularly after a long period of time. In the first example, the original property owner or all of his heirs would have to bring an action against the current owner to regain title to the property if the deed restriction prohibiting the sale of alcohol were to be violated. In the case of the subdi- vision, usually a property owners association representing owners of the subdivided proper- ties would have to bring legal action against the property owner who is in violation. In this instance, the court may require the owner in violation to cure the problem or pay the owners association for any loss in property value as opposed to forcing the sale of the property.

abstract of title, 9 bargain and sale deed, 10 deed, 9 deed restrictions, 14 easement, 7 estate, 4 estate for years, 6 estate from year to year, 6 fee simple estate, 4 freehold estate, 4 future estates, 5 general warranty deed, 10

leasehold estate, 4 lender’s (or mortgagee)

policy, 12 lessee, 2 lessor, 9 life estate, 5 mechanics’ lien, 13 nonpossessory interest, 7 owner’s policy, 12 ownership rights, 2 personal property, 2 property rights, 2

quitclaim deed, 10 real estate, 2 real property, 2 recording acts, 12 remainder, 5 reversion, 5 secured interest, 3 sheriff’s deed–trustee’s

deed, 10 special warranty deed, 10 title, 7 title assurance, 7

Key Terms

This chapter discussed legal considerations important in creating and defining various rights to real property. This is important in the study of real estate finance since it is these rights that are pur- chased, sold, and mortgaged. Thus, an understanding of the various rights associated with real estate is necessary to properly evaluate a real estate financial decision. Legal considerations affect the risk of receiving the economic benefit associated with one’s property rights. For example, we have discussed the importance of having a marketable title. Any defects in the title may result in a loss of benefits to the owner and jeopardize the collateral value of the real estate for the mortgage lender. To some extent, this risk is controlled and minimized by the use of title assurance methods, including title insurance and the use of general warranty deeds.

Knowing the various ways of partitioning property rights may also result in maximizing the value of a particular property, since it allows parties with different needs (e.g., users, equity investors, and lenders) to have claims on the property rights that best meet those needs. Thus, the total value of all the rights associated with a property could exceed the total value of the property itself if there are no leases or other ways to separate rights.

Conclusion

Final PDF to printer

bru19684_ch01_001-015.indd 15 10/31/17 06:22 PM

Chapter 1 Real Estate Investment: Basic Legal Concepts 15

Useful Web Sites

1. What is the difference between real property and personal property? 2. What is meant by an estate? 3. How can a leased fee estate have a value that could be transferred to another party? 4. What is an abstract of title? 5. Name the three general methods of title assurance and briefly describe each. Which would you

recommend to a friend purchasing a home? Why? 6. Would it be legal for you to give a quitclaim deed for the Statue of Liberty to your friend?

Questions

www.alta.org—The American Land Title Association—Provides information related to title insurance. www.reals.com—This is a real estate directory for such subjects as commercial real estate, international real estate, and professional services. www.findlaw.com—A good source of legal information, including real estate. www.investorwords.com—InvestorWords.com provides all of the necessary keys for decoding what can often seem like an encrypted language, regardless of your investing experience. InvestorWords.com provides definitions for over 6,000 financial terms and includes 20,000 links between related terms. The glossary is completely free to use. It also provides a list of great investing and personal finance Web sites, but most of them assume you already have a certain level of experience, or even a certain vocabulary. www.fiabci.com—This site is a good source for a comparison between legislation, professional standards, taxation, and licensing among different countries. It also gives a comparative snapshot of various requirements for commercial leases in several countries. www.china-window.com/china_market/china_real_estate/index.shtml—This Web site gives information about the real estate market in China. It also gives useful information about the laws and regulations concerning real estate, different Web sites related to real estate in China, and contact information for different government agencies. www.epra.com—This site is hosted by The European Public Real Estate Association (EPRA), which is a not-for-profit body established under Dutch law. This Web site gives quarterly review reports of developments in the European Real Estate Sector. It also provides different research reports published related to real estate.

Final PDF to printer

16

bru19684_ch02_016-041.indd 16 10/31/17 03:15 PM

Chapter 2 Real Estate Financing: Notes and Mortgages Financing can be a very important component of investing in real estate. In general, when investors desire to obtain financing, they usually pledge, or hypothecate, their ownership of real estate as security for loans. In many cases, investors also pledge personal property to obtain loans. What follows is an introduction to notes and mortgages, two legal instru- ments that are used frequently in real estate financing.

Notes

A promissory note is a document that serves as evidence that debt exists between a bor- rower and a lender. It usually contains the terms under which the loan must be repaid and the rights and responsibilities of both parties. Unless stated otherwise, the borrower is personally liable for payment of all amounts due under the terms of the note. (These loans are said to be made “with recourse” to the borrower.) While many loan provisions may be included, notes usually contain at least the following: A. The amount borrowed—generally the face amount of the note, which is usually

advanced in total when the loan agreement is executed. However, in cases involv- ing construction loans, amounts could be advanced as a construction progresses, not to exceed a maximum amount.

B. The rate of interest—a fixed rate of interest or an adjustable rate. If it is the latter, exactly how the rate may be adjusted (changed) will be specified.

C. The dollar amount, due dates, and number of payments to be made by the borrower— (e.g., $500 per month due on the first of each month following the closing date for 300 consecutive months).

D. The maturity date—the time at which time all remaining amounts due under the terms of the loan are to be repaid.

E. Reference to the real estate serving as security for the loan as evidenced by a mort- gage document (to be discussed).

F. Application of payments, which are usually made first to cover any late charges/ fees/penalties, then to interest, and then to principal reduction.

G. Default—borrower’s failure to perform one or more covenants under the terms of the note. Default usually occurs because of nonpayment of amounts due.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 17

bru19684_ch02_016-041.indd 17 10/31/17 03:15 PM

H. Penalties for late payment and forbearance provisions—the latter specify any grace periods during which late payments can be made up (usually with penal- ties) without the lender declaring that the borrower is in default. The lender does not give up the right to declare that the borrower is in default at some future date by allowing a grace, or forbearance, period. Forbearance is used by lenders when they believe that borrowers will make up late payments. They allow time for borrowers to make up such payments when they believe that benefits from this course of action will exceed the time and the expense of declaring the loan in default and embarking on foreclosure proceedings and, perhaps, forcing the sale of the property.

I. Provisions, if any, for unscheduled (early) payments or the full or partial prepay- ment of outstanding balances—when included, this is usually referred to as a “pre- payment privilege.” It allows borrowers to make early payments, or to repay the loan, in part or fully before maturity. If allowable, the note will indicate whether future payments will be reduced or whether the loan maturity date will be short- ened. This provision is a privilege and not a right because the dollar amount and number of payments to be made by the borrower are specified in (C). A prepay- ment provision is generally included in residential mortgage loans. However, when financing income-producing properties, it may be highly restricted and require pay- ment of a fee or penalty.

J. Notification of default and the acceleration clause—requirement that the lender notify the borrower that he or she is in default in the event of past due payments, etc. The lender may then accelerate on the note by demanding that all remaining amounts owed under the loan agreement be paid immediately by the borrower.

K. Nonrecourse clause—a provision in the note, whereby the lender agrees not to, or specifies conditions under which it will not, hold the borrower personally liable in the event of a default. As noted above, when a borrower executes a note, he is per- sonally liable, or the loan is made “with recourse.” This means that if he defaults on the loan, the lender may bring legal action that may result in the sale of the bor- rower’s other assets (stocks, bonds, other real estate) in order to satisfy all amounts past due under the terms of the note. In contrast, the “nonrecourse clause” provides that the lender may only bring an action to force the sale of the property serving as security for the loan. The borrower is released from personal liability. This clause is very important to real estate investors and developers.

L. Loan assumability clause—clause indicating the conditions, if any, under which a borrower will be allowed to substitute another party in his place, who will then assume responsibility for remaining loan payments. This could occur if the bor- rower wishes to sell a property to another while allowing the new buyer to retain favorable financing terms that may have been previously negotiated. Lenders who deny borrowers this right can do so by expressly prohibiting it and/or by includ- ing a “due on sale” clause which requires that all remaining amounts due be paid upon sale of, or transfer of title to, the property. However, if the note provides that a new owner may assume the loan, the lender usually requires that the credit of the new owner be equivalent to that of the previous owner, or be acceptable to the lender. The note will also specify whether or not the original borrower remains personally liable or is released from liability when the loan is assumed by the new borrower.

M. The assignment clause—clause giving the lender the right to sell the note to another party without approval of the borrower.

Final PDF to printer

18 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 18 10/31/17 03:15 PM

N. Future advances—provision under which the borrower may request additional funds up to some maximum amount or maximum percentage of the current prop- erty value under the same terms contained in the original loan agreement. These advances may be subject to an adjustment in the rate of interest.

O. Release of lien by lender—agreement by lender to release or extinguish its lien on the property when the loan is fully repaid.

The Mortgage Instrument

The following is a general discussion of mortgages. Much of this discussion applies to all mortgages. Provisions that are specific to residential and commercial properties and construction loans will be discussed as these topics are introduced. Utilization of mortgage financing has been the most common method of financing the purchase of real estate. This process usually entails the buyer borrowing funds from a lender and then using these and other funds to purchase a property. Funds are usually borrowed with the express intent of using the proceeds to acquire real estate that will serve as a security for a loan. However, loans also may be refinanced from time to time and a new mortgage is made serving as loan security. Real estate is generally regarded by lenders as excellent security for a loan, and lenders acquire a secured interest in the real estate with a mortgage.

Definition of a Mortgage In its most general sense, the mortgage document is created in a transaction, whereby one party pledges real property to another party as security for an obligation owed to that party. A promissory note (discussed previously) is normally executed contemporaneously with the mortgage. This note creates the obligation to repay the loan in accordance with its terms and is secured by the mortgage. The elements essential to the existence of a mort- gage are an obligation to pay or perform and a pledge of property as security for that obli- gation.1 In general, when a loan is made by a seller to a buyer (borrower) to purchase real estate consisting of an existing property and improvement, it is referred to as a purchase- money mortgage (discussed in more detail later in this chapter). This is in contrast to con- struction loans, loans made to refinance existing loans, and so on.

Relationship of Note to Mortgage Normally, the underlying obligation secured by a mortgage is evidenced by a separate promissory note. As pointed out in the discussion of notes, unless the note contains a nonrecourse clause, it provides evidence of the debt and generally makes the borrower (mortgagor) personally liable for the obligation. The mortgage is usually a separate docu- ment that pledges the designated property as security for the debt. Therefore, the lender (mortgagee) has two sources from which amounts borrowed can be repaid: (1) the bor- rower, who is personally liable and (2) the property that serves as security for the note. In case of default, the mortgagee may elect to disregard the mortgage and sue on the note. The judgment awarded the mortgagee as a result of a suit on the note may be attached to other property of the mortgagor which, when sold to satisfy the judgment lien, may enable the mortgagee to recover the amount of the claim more readily than if he or she foreclosed on the mortgage. In practice, the mortgagee will normally elect to sue on the note and

1 The obligation secured by a mortgage need not be monetary. It may be, for example, an agreement to perform some service or to perform some other specified actions. An obligation that is not itself an explicitly monetary one must be reducible to monetary terms. In other words, a dollar value must be placed on it.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 19

bru19684_ch02_016-041.indd 19 10/31/17 03:15 PM

foreclose on the mortgage simultaneously. Mortgages typically include clauses containing important covenants for both the mortgagor and mortgagee. These covenants are prom- ises, duties, and responsibilities of the borrower, in addition to payments required under the terms of the note. These are frequently repeated in the promissory note, or the note may incorporate these covenants by reference to the mortgage.

Interests That Can Be Mortgaged Most people are accustomed to thinking of a mortgage in relation to full, or fee simple, ownership. But any interest in real estate that is subject to sale, grant, or assignment— that is, any interest that can be transferred—can be mortgaged. Thus, such diverse interests as fee simple estates, life estates, estates for years, remainders, reversions, leasehold inter- ests, and options to purchase real estate, among others, are all mortgageable interests as far as legal theory is concerned. Whether, as a matter of sound business judgment, mortgagees would be willing to lend money against some of the lesser interests in land is quite another question.

Minimum Mortgage Requirements A mortgage involves a transfer of an interest in real estate from the property owner to the lender. Accordingly, the statute of frauds requires that it must be in writing. The vast volume of mortgage lending today is institutional lending, and institutional mortgages are standardized, formal documents. There is, however, no specific form required for a valid mortgage. Indeed, although most mortgages are formal documents, a valid mortgage could be handwritten. The requirements of a valid mortgage document are: (1) wording that appropriately expresses the intent of the parties to create a security interest in real property for the benefit of the mortgage and (2) other items required by state law.

In the United States, mortgage law has traditionally been within the jurisdiction of state law; by and large, mortgages continue to be governed primarily by state law. Thus, to be enforceable, a mortgage must meet requirements imposed by the law of the state in which the property offered as security is located.

Whether a printed form of mortgage instrument is used or an attorney draws up a spe- cial form, the following subjects should always be included: 1. Appropriate identification of mortgagor and mortgagee. 2. Proper description of the property serving as security for the loan. 3. Covenants of seisin and warranty.2

2 A covenant is a promise or binding assurance. Seisin is the state of owning the quantum of title being conveyed.

The Equal Credit Opportunity Act (ECOA) and the Fair Housing Act (FHA) protect you against discrimina- tion when you apply for a mortgage to purchase, refi- nance, or make home improvements. Find out what your rights are under these acts. Go to a website like www.findlaw.com and use the search feature on the

site to find information on mortgage discrimination. Alternatively, search for information on “mortgage dis- crimination” using one of the general search engines like www.yahoo.com or www.google.com. Give exam- ples of what would be considered illegal discrimination by mortgage lenders.

Web App

Final PDF to printer

20 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 20 10/31/17 03:15 PM

4. Provision for release of dower rights.3 5. Any other desired covenants and contractual agreements.

All of the terms and contractual agreements included in the note can be included in the mortgage as well by making reference to the note in the mortgage document.

Although the bulk of mortgage law remains within the jurisdiction of state law, a wide range of federal regulations also are operative in the area of mortgage law. Moreover, in recent years the federal government has acted to directly preempt state law in a number of areas (e.g., overturning state usury laws,4 overturning state restrictions on the operation of due-on-sale clauses, and establishing conditions for allowing prepayment of the mortgage debt and for setting prepayment penalties). This has been particularly true in legislation affecting residential mortgages. Commercial property lending and mortgages have gener- ally been exempted from such federal legislation.

In addition, the federal government has exerted a strong but indirect influence on mort- gage transactions by means of its sponsorship of the agencies and quasi-private institutions that support and, for all practical purposes, constitute the secondary market for residential mortgages. The Federal National Mortgage Association (FNMA) and the Federal Home Loan Mortgage Corporation (FHLMC) have adopted joint standardized mortgage forms for the purpose of facilitating secondary-market transactions on a nationwide basis. The joint FNMA-FHLMC uniform mortgage form has been so widely adopted by residential mortgage lenders that it has largely replaced the use of mortgage forms used by individual institutions. One reason for the popularity of this form with residential lenders is that it is readily acceptable by the major secondary market institutions, should the lender desire to sell the mortgage after it has been originated.

Important Mortgage Covenants It is beyond the scope of this chapter to discuss all the clauses and covenants (promises made by the borrower to the lender) that might be found in a mortgage document. We will mention some of the more important covenants, however, so that the reader gains an appre- ciation of the effect these clauses may have on the position of the borrower and lender. Because loans are secured by properties and are made for very long periods of time, lend- ers want assurance that borrowers will keep properties in good repair, pay property taxes and generally preserve the value and marketability of properties serving as security for loans. The reader should keep in mind that lenders always want to protect the value of the property serving as security for loans. These covenants are anticipatory in nature as lenders try to protect their interests over the life of a loan.

Funds for Taxes and Private Mortgage Insurance This clause requires the mortgagor to pay amounts needed to cover property taxes plus mortgage insurance premiums, if required by the lender, in monthly installments in advance of when they are due unless such payments are prohibited by state law. These funds are usually kept in an “escrow account” which is usually managed by the lender who collects monthly payments from the borrower, then makes payments to taxing authorities, insurance companies, and so on when payments come due. The purpose of this clause is to enable the mortgagee to pay these charges out of money provided by the mortgagor when they become due instead of relying on the mortgagor to make timely payments on his own.

3 Dower is the interest in a husband’s real estate transferred by law to the widow after his death. The common law counterpart running in favor of the husband as a widower is called curtesy. Many states now have a statutory allowance from the decedent’s estate in lieu of dower and curtesy. 4 Usury laws prohibit charging unconscionable and exorbitant rates or amounts of interest for the use of money. A usurious loan is one whose interest rate exceeds that permitted by usury laws.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 21

bru19684_ch02_016-041.indd 21 10/31/17 03:15 PM

The mortgagee is thereby better able to protect his or her security interest against liens for taxes, which normally have priority over the first mortgage, and against lapses in insurance coverage. Such funds may be held in an escrow or trust account for the mortgagor.

Charges and Liens This clause requires the mortgagor to pay all taxes, assessments, charges, and claims assessed against the property that have priority over the mortgage and to pay all leasehold payments, if applicable. The reason for this clause is that the mortgagee’s security interest can be wiped out if these claims, or liens, are not paid or discharged, since they generally can attain priority over the interests of the mortgagee. For example, if taxes and assess- ments are not paid, a first mortgage on the property can be wiped out at a sale to satisfy the tax lien, unless the mortgagee is either the successful bidder at the tax sale or pays the tax due to keeping the property from being sold at the tax sale.

Hazard Insurance This clause requires the mortgagor to obtain and maintain insurance against loss or dam- age to the property caused by fire and other hazards, such as windstorms, hail, explosion, and smoke. In effect, this clause acknowledges that the mortgagee as well as the mortgagor has an insurable interest in the mortgaged property. The mortgagee’s insurable interest is the amount of the mortgage debt.

Preservation and Maintenance of the Property This clause obligates the mortgagor to maintain the property in good condition and to not engage in or permit acts of waste.5 This clause recognizes that the mortgagee has a valid interest in preventing the mortgaged property from deteriorating to the extent that the col- lateral value of the property is affected.

Breach of Covenants In the event that the borrower–mortgagor does not comply with loan covenants, he is said to have “breached the covenant or to have broken his promise.” In this event, the lender– mortgagee can declare the loan in default and can foreclose. Even if the borrower is making timely payments of interest and principal, breaching a loan covenant constitutes a default although it may be referred to as a “technical default.”

Transfer of Property or a Beneficial Interest in Borrower This clause, known as the due-on-sale clause, allows the mortgagee to accelerate the debt (i.e., to take action to make the outstanding loan balance plus accrued interest imme- diately due and payable) when the property, or some interest in the property, is transferred without the written consent of the mortgagee. The purpose of the due-on-sale clause is to enable the mortgagee to protect his or her security interest by approving any new owner. The clause may also permit the mortgagee to increase the interest rate on the loan to cur- rent market rates. This, of course, reduces the possibility of the new owner assuming a loan with an attractive interest rate.

Borrower’s Rights to Reinstate This clause deals with the mortgagor’s right to reinstate the original repayment terms in the note after the mortgagee has caused an acceleration of the debt. It gives the mortgagor the right to have foreclosure proceedings discontinued at any time before a judgment is

5 Waste is the abuse or destructive use of property which reduces the value and, therefore, the security for the loan.

Final PDF to printer

22 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 22 10/31/17 03:15 PM

entered enforcing the mortgage (i.e., before a decree for the sale of the property is given) if the mortgagor does the following: 1. Pays to the mortgagee all sums that would then be due had no acceleration occurred. 2. Cures any default of any other covenants or agreements. 3. Pays all expenses incurred by the lender in enforcing its mortgage. 4. Takes such action as the mortgagee may reasonably require to ensure that the mort-

gagee’s rights in the property and the mortgagor’s obligations to pay are unchanged.

Right of Entry: Lender in Possession This clause provides that upon acceleration or abandonment of the property, the mortgagee (or a judicially appointed receiver) may enter the property to protect the security. The lender may collect rents until the mortgage is foreclosed. Rents collected must be applied first to the costs of managing and operating the property, and then to the mortgage debt, real estate taxes, insurances, and other obligations of the mortgagor as specified in the mortgage.

Future Advances While it is expected that a mortgage will always state the total amount of the debt it is expected to secure, this amount may be in the nature of a forecast of the total debt to be incurred in installments. In other words, a mortgage may cover future advances as well as current advances. For example, a mortgage may be so written that it will protect several successive loans under a general line of credit extended by the mortgagee to the mortgagor. In case the total amount cannot be forecasted with accuracy, at least the general nature of the advances or loans must be apparent from the wording of the mortgage.

As an illustration of a mortgage for future advances, sometimes called an open- end mortgage, consider the form of construction loans. Here, the borrower arranges in advance with a mortgagee for a total amount, usually definitely stated in the mortgage, that will be advanced, in stages, under the mortgage to meet the part of the costs of construc- tion as it progresses. As the structure progresses, the mortgagor has the right to call upon the mortgagee for successive advances on the loan. All improvements become security under the terms of the mortgage as they are constructed.

Subordination Clause By means of this clause, a first mortgage holder agrees to make its mortgage junior in priority to the mortgage of another lender. A subordination clause might be used in situ- ations where the seller provides financing by taking back a mortgage from the buyer, and the buyer also intends to obtain a mortgage from a bank or other financial institution, usu- ally to develop or construct an improvement. Financial institutions will generally require that their loans have first mortgage priority. Consequently, the seller must agree to include a subordination clause in the mortgage, whereby the seller agrees to subordinate the pri- ority of the mortgage to the bank loan. This ensures that even if the seller’s mortgage is recorded before the bank loan, it will be subordinate to the bank loan.

Assumption of Mortgage

When the mortgagor transfers his or her rights to another, the question arises, “Does the grantee (buyer) agree to become liable for payment of the mortgage debt and relieve the mortgagor (seller) of his or her personal obligation?” If this is the intention of both parties, the assumption of the mortgage by the grantee may accomplish the purpose. The deed, after specifying the nature of the mortgage which encumbers the property, will contain a

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 23

bru19684_ch02_016-041.indd 23 10/31/17 03:15 PM

clause to the effect that the grantee assumes and agrees to pay the amount of the obliga- tions owed to the mortgagee as part consideration for the conveyance of title. Where an assumption is undertaken by the grantee, it should be couched in language that leaves no doubt about the intent.

An assumption agreement takes the form of a contract of indemnity. It shifts the respon- sibility for the payment of the debt from the grantor to the grantee. Thereafter, the grantor stands in the position of a surety (guarantee) for the payment of the debt. However, such an arrangement binds only the parties to it: the grantor and the grantee. Since the mortgagee is not ordinarily a party to such an agreement, he or she is not bound by it. As a consequence, the mortgagee may still hold the original mortgagor liable. Thus, if a property is sold with a loan assumption and the new owner defaults on the loan, the lender can hold the previous owner liable unless the previous owner was released from the debt.

Release of Grantor from Assumed Debt When a mortgagor owning property grants that property to another and the grantee assumes the grantor’s mortgage, the lender may or may not release the grantor from per- sonal liability for the mortgage debt. The decision of release will depend on the value of the property as security, the grantee’s financial capabilities, and other factors affecting the lender’s attitudes toward the transaction. A mortgagee cannot be expected to release an antecedent mortgagor if the result will be to increase the credit risk unless the mortgagee is compensated in some way (e.g., a higher interest rate).

Acquiring Title “Subject to” a Mortgage

In contrast to the assumption of the personal obligation to pay the debt, grantees may not be willing to accept this responsibility. In this case, they may ask grantors to allow them to take title “subject to” the mortgage. So long as the grantees are financially able and think it will be to their advantage, they will keep up payments on the mortgage and observe its other covenants. Under normal conditions, if they purchased the property at a fair price, it will be to their advantage to avoid default on the mortgage to protect their own equity.

But should the grantees reach the conclusion that there is no longer any advantage to making further payments, or should they become financially unable to do so, they may default on their payments. By so doing, they run the risk of losing whatever equity they have in the property. However, grantees cannot be held personally liable for the amount of the debt that they assumed. Grantors are still personally liable and may be held liable for any deficiency judgment resulting from the foreclosure sale.

It is obviously riskier for grantors to sell property subject to the mortgage. Given a choice, they would generally prefer that responsible grantees assume the mortgage unless they are compensated for the additional risk they undertake as a surety (e.g., by receiving a higher price for the property).

Property Covered by a Mortgage The property that is covered by the mortgage as security for the loan includes not only the land and any existing buildings on the land but also easements and fixtures. In addition, the mortgage agreement may provide that property covered by the mortgage also includes rights to natural resources (e.g., mineral, timber, oil and gas, and water or riparian rights) and even rights to rents and profits from the real estate. An easement that runs with the property is generally regarded by the law as being covered by the mortgage, regardless of whether the easement is created before or after the mortgage is executed. Such an ease- ment, if in existence at the time the property is mortgaged, is covered by the mortgage even

Final PDF to printer

24 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 24 10/31/17 03:15 PM

if it is not mentioned in the mortgage. Foreclosure of the mortgage will not extinguish this easement. An easement created subsequent to the recording of a mortgage, however, will be extinguished by the foreclosure.

Issues involving fixtures have generated a considerable amount of legal controversy. In general, a fixture is an item of tangible personal property (also referred to as chattel) that has become affixed to or is intended to be used with the real estate, so as to be considered part of the property. The law is in general agreement that fixtures are covered by the mort- gage, with the exception of “trade fixtures”6 installed by a tenant.

A mortgage also will usually contain what is called an after-acquired property clause as part of its description of the type of property to be covered by the mortgage. This provi- sion states in effect that property acquired subsequent to the execution of the mortgage that becomes part of the real estate is included in the security covered by the mortgage. After- acquired property includes additional improvements erected on the property or fixtures that become part of the property at any time in the future for as long as the debt remains outstanding. The courts have generally affirmed the validity of after-acquired property clauses, and the Uniform Land Transactions Act (ULTA) expressly accepts their validity.7

Junior Mortgages In simple real estate financing transactions, such as those involving single residences, the character of the mortgage structure is easily defined. The senior or prior mortgage is usu- ally called a first mortgage. All others are given the class name of junior mortgages In any particular situation, there may be one or more junior mortgages or none at all. One junior lien, usually called a second mortgage, is sometimes used to bridge the gap between the price of the property and the sum of the first mortgage and the amount of money available to the purchaser to use as a down payment. Traditionally, second mort- gages are short term and carry a higher rate of interest than first mortgages because of the additional risk associated with their junior status.

Recording of Mortgages Unless the statutes of the state require it, recording is not essential to the validity of a mortgage because it is an agreement between the mortgagor and the mortgagee. The act of recording creates no rights that did not exist before, but it does give others notice of the existence and effect of the mortgage. A recorded mortgage protects its holder by giving him or her priority over the subsequent acts of the mortgagor. For example, if a mortgagee failed to record the mortgage, the mortgagor could mortgage the property to a second lender. If this second lender had no notice of the prior unrecorded mortgage, the second lender would have a lien prior to that of the original mortgagee. In general, the priority of successive liens is determined by the time they are accepted for record.

As we have discussed, the recording acts provide opportunities for the protection of holders of interests in property, but at the same time they place responsibilities upon them to make use of these opportunities. Failure to inspect the records for prior liens or to record the mortgage may result in loss to the mortgagee. In most states, junior lienors of record without notice of the existence of a senior mortgage will have priority over an unrecorded senior mortgage. Even subsequent recording of a senior mortgage lien will generally not elevate it to a higher priority.

6 Trade fixtures are personal property used by tenants in businesses. Such fixtures retain the character of personal property (e.g., shelves used to display merchandise). 7 For a discussion and case law materials related to after-acquired property clauses, see Grant S. Nelson and Dale A. Whitman, Real Estate Transfer, Finance, and Development, 2nd ed. (St. Paul, MN: West Publishing, 1981), pp. 633–39; see also Robert Kratovil and Raymond J. Werner, Modern Mortgage Law and Practice, 2nd ed. (Englewood Cliffs, NJ: Prentice Hall), pp. 114–17.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 25

bru19684_ch02_016-041.indd 25 10/31/17 03:15 PM

Other Financing Sources

Seller Financing A source of credit for a real property buyer is often the seller. If the seller is willing to take back a mortgage as part or full payment of the purchase price, it is referred to as seller financing. This type of financing is used when 1. Third-party mortgage financing is too expensive or unavailable. 2. The buyer does not qualify for long-term mortgage credit because of a low down pay-

ment or difficulty meeting monthly payments. 3. The seller desires to take advantage of the installment method of reporting the gain

from the sale. 4. The seller desires to artificially raise the price of the property by offering a lower-than-

market interest rate on the mortgage, thereby creating more capital gains and less inter- est or ordinary income.8

Any mortgage given by a buyer to the seller to secure payment of all or part of the purchase price of a property is usually called a purchase-money mortgage. It can be a first mortgage, which might be the case if the seller is providing all of the financing neces- sary to consummate the transaction. It also could take the form of a second mortgage that is provided by the seller and is used to bridge the gap between an available first mortgage and the buyer’s down payment. As such, it must be differentiated from mortgages given to secure a loan from a third party for the purchase of the property. The third-party lender (e.g., a financial institution) will normally want its mortgage to be a first mortgage. Thus, the purchase-money mortgage must either be recorded after the third-party loan or contain a subordination clause, as defined earlier.

Land Contracts

One form of financing real estate that has been widely used over the years is commonly referred to as a land contract. The term land contract has a variety of aliases, including real estate contract, installment sales contract, agreement to convey, and contract for deed. As the last term implies, the land contract seller promises to convey title at such time as the purchaser completes the performance of the obligation called for in the contract. Such performance usually means payment of the purchase price in stipulated installments, much the same way as under a note and mortgage.

It should be emphasized that a land contract is not a mortgage. Under the land contract, the sellers retain the title in their name. The deed record shows that the sellers are still the owners of the property, but the land contract is supposed to tie their hands to make sure that the sellers or their assigns ultimately transfer title to the vendees or their heirs or assigns.

The land contract may be used as a substitute for a purchase-money mortgage and would normally not be preferred if the latter were available. However, in cases where there is no down payment or a small down payment, and a very long period of time dur- ing which a buyer must make periodic payments to the seller, sellers of land may refuse to give a deed and take back a mortgage until a very substantial part of the purchase price has been paid.

8 The use of this technique has been limited by the “unstated interest rule.”

Final PDF to printer

26 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 26 10/31/17 03:15 PM

Several points of comparison exist between purchase-money mortgages and land con- tracts. A land contract buyer does not have title to the property and therefore cannot control whether the property will be mortgaged subsequent to the execution of the land contract or be made subject to covenants, easements, or mechanics’ liens in the future by the contract seller. Most land contracts contain a clause allowing the seller to mortgage property up to an amount equal to the buyer’s indebtedness to the seller. The buyer would have this protection if mortgage financing were used because limits would be made explicit and the buyer would have title. Furthermore, the possibility of forfeiture of the land contract inter- est may exist without any of the procedural protections afforded mortgages. It is suggested that all such points of comparison should be considered in making the decision whether to buy or sell on land contract or to obtain mortgage financing. In general, land contracts are used in many of the same situations as purchase-money mortgages (e.g., where the buyer has difficulty obtaining third-party financing).

Recording of Land Contracts State laws provide for the recording of conveyances of land and instruments affecting title. Land contracts generally are considered instruments affecting title and are consequently admissible to record. Recording land contracts is not essential to their validity; it merely gives notice of their existence to third parties.

Default

We have discussed the various property rights associated with real estate. Next, consider some of the problems that result when one of the parties does not fulfill a contractual obligation associated with its property right. The legal ramifications of these problems affect the financial security of other parties’ rights and are thus an important aspect of real estate finance.

One of the most important risks in making a mortgage loan is that the borrower will default on the note in some way, so that the lender may not receive the expected mortgage payments. The risk associated with mortgage loans depends in part on the rights of the lender if and when such default occurs. Thus, it is important to understand the legal rami- fications of mortgage default.

What Constitutes Default? Default is a failure to fulfill a contract, agreement, or duty, especially a financial obligation such as a note. It follows that a mortgage default can also result from any breach of the mortgage contract. The most common default is the failure to meet an installment pay- ment of the interest and principal on the note. However, failure to pay taxes or insurance premiums when due may also result in a default, which may precipitate an acceleration of the debt and a foreclosure action. Indeed, some mortgages have clauses that make specific stipulations to this effect. Even a failure to keep the security in repair may constitute what is commonly referred to as a technical default. However, because a breach of contract resulting in a technical default can usually be cured by a borrower, it seldom results in an actual foreclosure sale. Furthermore, it may be difficult for the mortgagee to prove that the repair clause in the mortgage has been broken unless the property shows definite evidence of the effects of waste. This means that even though there is a breach of contract, the mort- gagee may postpone doing something about it. However, in the case of technical default accompanied by abandonment, the probabilities are that the mortgagee will act quickly to protect his or her interests against vandalism, neglect, and waste. This may occur even though the borrower may be current on the loan payments.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 27

bru19684_ch02_016-041.indd 27 10/31/17 03:15 PM

Alternatives to Foreclosure: Workouts

Foreclosure involves the sale of property by the courts to satisfy the unpaid debt. The details of this process are discussed later. Because of the time involved and the various costs associated with foreclosure (and possibly repair of any damage to the property), lend- ers often prefer to seek an alternative to actual foreclosure.

Although mortgage contracts normally indicate definite penalties to follow any breach therein, experience has shown that in spite of provisions for prompt action in case of a default in mortgage payments, many commitments are not met in strict accordance with the letter of the contract. Instead, whenever mortgagors get into financial trouble and are unable to meet their obligations, adjustments of the payments or other terms are likely to follow if both the borrower and lender believe that the conditions are temporary and will be remedied.

The term workout is often used to describe the various activities undertaken to deal with a mortgagor who is in financial trouble. Many times the parties make a workout agreement that sets forth the rules by which, during a specified period of time, they will conduct themselves and their discussions. The lender agrees to refrain from exercising legal remedies. In exchange the borrower acknowledges his or her financial difficulty and agrees to certain conditions such as supplying current detailed financial and other infor- mation to the lender and establishing a cash account in which any rental receipts from the property are deposited and any withdrawls are subject to lender approval.

Six alternatives can be considered in a workout: 1. Restructuring of the mortgage loan. 2. Transfer of the mortgage to a new owner. 3. Voluntary conveyancy of the title to the mortgagee (lender). 4. A “friendly foreclosure.” 5. A prepackaged bankruptcy. 6. A “short sale” with the lender agreeing to a sale price less than the loan balance.

Restructuring the Mortgage Loan Loans can be restructured in many ways. Such restructuring could involve lower interest rates, accruals of interest, or extended maturity dates. If the original loan is nonrecourse to the borrower, the lender may want to obtain personal recourse against the borrower as part of the loan restructuring agreement. This makes the borrower subject to significantly more downside risk if the restructuring fails. The lender also may want a participation in the performance of the property to enhance the lender’s upside potential as compensation for being willing to restructure the loan. For example, the lender could ask for a percentage of any increase in the income of the property over its current level.

Recasting of Mortgages Once a mortgage is executed and placed on record, its form may change substantially before it is redeemed. It may be recast for any one of several reasons. A mortgage can be renegotiated at any time, but most frequently it is recast by changing the terms of the mort- gage (either temporarily or permanently) to avoid or cure a default.

Where mortgage terms such as the interest rate, amortization period, or payment amounts are changed, mortgagees must exercise care to avoid losing their priority over intervening lienors. The mere extension of time of payment will not generally impair the priority of the extended mortgage. Courts, however, are watchful to protect intervening lienors against prejudice, and mortgages may lose priority to the extent that changes in the

Final PDF to printer

28 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 28 10/31/17 03:15 PM

interest rate, payment amounts, or the amount of indebtedness place additional burdens on the mortgagor.9

Extension Agreements Occasionally, a mortgagor in financial difficulty may seek per- mission from the mortgagee to extend the mortgage terms for a period of time. This is known as a mortgage extension agreement. A mortgagor may request a longer amor- tization period for the remaining principal balance or a temporary grace period for the payment of principal or interest payments or both. In responding to such a request, the mortgagee needs to consider the following issues: 1. What is the condition of the security? Has it been reasonably well maintained or does it

show the effects of waste and neglect? 2. Have there been any intervening liens? These are liens recorded or attached after the

recordation of the mortgage but before any modifications to it. If so, what is their effect upon an extension agreement? If such liens exist, it is possible that the extension of an existing mortgage may amount to a cancellation of the mortgage and the making of a new one. If so, this could advance the priority of intervening liens.

3. What is the surety status of any grantees who have assumed the mortgage? Will an extension of time for the payment of the debt secured by the mortgage terminate the liability of such sureties? The best way for mortgagees to protect themselves against the possibilities implied in these questions is to secure the consent of the extension agree- ment from all sureties to the extension. As parties to it, they can have no grounds for opposing it. But if they are not made parties to the extension—particularly if changes in the terms of the mortgage through the extension agreement tend to increase the obli- gations for which the sureties are liable—then care should be exercised to ensure that those sureties who refuse to sign the agreement are not released by the extension agree- ment. The possibility of foreclosure and a deficiency judgment against them may be a sufficient inducement to obtain their agreement to be parties to the extension. The exact nature of an extension agreement depends upon the bargaining position of

mortgagor and mortgagee. If mortgagors can refinance the loan on more favorable terms, they will probably not apply for an extension agreement. Alternatively, they may have to make changes that favor the mortgagee, such as an increase in the interest rate. Alternative to Extension Agreements An alternative to an extension agreement has the mortgagee agree informally to a temporary extension without making any changes in the formal recorded agreement between the parties. If the mortgagor is unable to meet all monthly mortgage payments, these too may be waived temporarily or forgiven in whole or in part. For example, simply raising the question of such an agreement suggests that the mortgagor cannot pay the matured principal of the loan. Therefore, some informal arrange- ment may be made to permit the mortgagor to retain possession of the property in return for meeting monthly payments, which may or may not include principal installments. The use of this kind of informal agreement can be troublesome, but, in general, if it is reached, the amounts demanded will be adjusted to the present payment capacities of the borrower. Should the borrower’s financial condition improve, the lender may again insist that the originally scheduled payments resume.

9 Recasting of mortgages to admit interests not present at the time the mortgages were executed is sometimes necessary. For example, the mortgage may make no provision for an easement of a public utility company that requires access to the rear of the site covered by the mortgage. Since the installation of the services of the utility will normally add to rather than subtract from the value of the security, the mortgagee will usually be glad to approve the change. Nevertheless, it will require a recasting of the mortgage to the extent indicated.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 29

bru19684_ch02_016-041.indd 29 10/31/17 03:15 PM

The use of such an alternative to a definite extension agreement may serve the tempo- rary needs of both mortgagors and mortgagees. If the latter feel that the security amply protects their lien, the mortgagees can afford to be lenient in helping mortgagors adjust their financial arrangements during a difficult period. If the mortgagors also feel that any real equity exists in the property, they will wish to protect it if at all possible.

Transfer of Mortgage to a New Owner Mortgagors who are unable or unwilling to meet their mortgage obligations may be able to find someone who is willing to purchase the property and either assume the mortgage liability or take the property subject to the existing mortgage. The new purchaser may be willing to accept the transfer of mortgage if he or she thinks the value of the property exceeds the balance due on the mortgage. In either case, the seller retains personal liabil- ity for the debt. However, if the seller is about to default and expects to lose the property anyway, he or she may be willing to take a chance on a new purchaser fulfilling the mort- gage obligation. The risk is that the new buyer will default, and the seller will again have responsibility for the debt and get the property back.

Recall that if purchasers acquire the property subject to the existing debt, they do not acquire any personal liability for the debt. Thus, they can only lose any equity personally invested to acquire the property. This equity investment may be quite small where the sellers are financially distressed and face foreclosure. Thus, the buyers may have little to lose by taking a chance on acquiring the property subject to the mortgage. If it turns out to be a good investment, they will continue to make payments on the debt, but if they find that the value of the property is unlikely to exceed the mortgage debt within a reasonable time frame, they can simply stop making payments and let the sellers reacquire the property. Thus, we see that in this situation buyers of the property subject to a mortgage have in effect purchased an option. The equity that buyers invest is the payment for this option, which allows them to take a chance on the property value increasing after it is acquired. We can therefore see why purchasers might even give the sellers money to acquire a property subject to a mortgage even if the current value of the property is less than the mortgage balance.

For example, suppose that a property has a mortgage balance of $100,000. Property values in the area are currently depressed, and the owner believes that only $99,000 could be obtained on an outright sale. However, a buyer is willing to acquire the property at a price of $101,000 subject to the existing mortgage. Thus, $2,000 is paid for the option of tying up the property in hopes that property values rise above their current level.10 If the property does not rise in value to more than $100,000 (less any additional principal pay- ments that have been made), the purchaser could simply walk away, and the original owner again becomes responsible for the mortgage. If the property rises in value to more than $101,000, the purchaser stands to make a profit and would continue to make payments on the mortgage.

It should be clear that knowledge of various legal alternatives (e.g., being able to pur- chase a property “subject to” vs assuming a mortgage) can allow a buyer and seller to arrive at an agreement that best meets their financial objectives. Thus, legal alternatives can often be evaluated in a financial context.

Voluntary Conveyance Borrowers (mortgagors) who can no longer meet the mortgage obligation may attempt to “sell” their equity to the mortgagees. For example, suppose that the mortgagors are unable to meet their obligations and face foreclosure of their equity. To save the time, trouble, and 10 The seller would receive $1,000 in cash, but since the seller had –$1,000 in equity, he or she receives the economic benefit of $2,000, which is also the difference between the price paid and the market value of the property.

Final PDF to printer

30 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 30 10/31/17 03:15 PM

expense associated with foreclosure, the mortgagees may make or accept a proposal to take title from the mortgagors. If they both agree that the property value exceeds the mortgage balance, a sum may be paid to the mortgagors for their equity. If the value is less than the mortgage balance, the lenders may still be willing to accept title and release the mortgag- ors from the mortgage debt. This voluntary conveyance might be done because the cost of foreclosure exceeds the expected benefit of pursuing that course of action.

When voluntary conveyances are used, title is usually transferred with a warranty or quitclaim deed from mortgagors to mortgagees. The mortgagors should insist upon a release to make sure that they are no longer bound under their note and mortgage, espe- cially in situations where the mortgage balance is near or in excess of the property value. Otherwise, the mortgagors may find that they still have a personal obligation to pay the mortgage note. The conveyance to the mortgagees in exchange for a release from the mort- gage debt is frequently referred to as giving deed in lieu of foreclosure of the mortgage. A deed in lieu of foreclosure has the advantage of speed and minimizes the expense of transferring the property and the uncertainty of litigation. It also avoids the negative pub- licity of foreclosure or bankruptcy. A deed in lieu of foreclosure does not cut off subordi- nate interests in the property. The lender must make arrangements with all other creditors. There are also potential bankruptcy problems. The transfer may be voidable as a prefer- ential transfer. In addition to the legal questions involved in voluntary conveyances, the mortgagee frequently faces very practical financial issues as well. If there are junior liens outstanding, they are not eliminated by a voluntary conveyance. Indeed, their holders may be in a better position than before if the title to the property passes to a more financially sound owner. Unless in some manner these junior liens are released from the property in question—possibly by agreement with their holders to transfer them to other property owned by the mortgagor or even on occasion to cancel them—the mortgagee may find it necessary to foreclose instead of taking a voluntary conveyance because the title conveyed is subject to junior liens. Foreclosure provides the mortgagee with a lawful method of becoming free from the liens of the junior claimants.

Friendly Foreclosure Foreclosure can be time consuming and expensive, and there can be damage to the prop- erty during this time period. A friendly foreclosure is a foreclosure action in which the borrower submits to the jurisdiction of the court, waives any right to assert defenses and claims and to appeal or collaterally attack any judgment, and otherwise agrees to cooperate with the lender in the litigation. This can shorten the time required to effect a foreclosure. This also cuts off subordinate liens and provides better protection in case of the borrower’s subsequent bankruptcy. A friendly foreclosure normally takes more time than a voluntary conveyance but is less time consuming than an unfriendly foreclosure. This is discussed in more detail in the next section.

Prepackaged Bankruptcy The mortgagee must consider the risk that the mortgagor will use the threat of filing for bankruptcy as a way of reducing some of his or her obligation under the original mort- gage agreement. Bankruptcy can have significant consequences for secured lenders. To the extent that the collateral securing the debt is worth less than the principal amount of the debt, the deficiency will be treated as an unsecured debt. In a prepackaged bankruptcy, before filing the bankruptcy petition, borrowers agree with all their creditors to the terms on which they will turn their assets over to their creditors in exchange for a discharge of liabilities. This can save a considerable amount of time and expense compared with the case where the terms are not agreed upon in advance. The consequences of bankruptcy are discussed further in the last section of this chapter.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 31

bru19684_ch02_016-041.indd 31 10/31/17 03:15 PM

Short Sale A short sale is a sale of real estate in which the proceeds from the sale fall short of the balance owed on a loan secured by the property sold. In a short sale, the mortgage lender agrees to discount the mortgage loan balance because of an economic or financial hardship on the part of the mortgagor. This is often done during periods when home prices have declined significantly and the financial hardship is more a result of market conditions than actions of the borrower.

In a short sale, the home owner/borrower sells the mortgaged property for less than the outstanding balance of the loan and then turns over the proceeds of the sale to the lender, usually in full satisfaction of the loan. In some cases, the lender may still pursue a deficiency judgment. The lender has the right to approve or disapprove a proposed sale. Typically a short sale is executed to prevent a home foreclosure, because the lender believes that it will result in a smaller financial loss than foreclosing. The decision to proceed with a short sale represents the most economical way for the lender to recover the amount owed on the property. In contrast to a foreclosure, if the borrower has been making payments up until the time the short sale is approved, the short sale may not adversely affect the bor- rower’s credit report, because the lender has agreed to discount the loan. In the event that the property is sold for less than its outstanding low balance and the lender does not pursue a deficiency judgment, this may result in a forgiveness of debt by the lender and could be a taxable event for the owner/borowee.

Foreclosure

In practice, most mortgagees are not anxious to take property from mortgagors, particu- larly where the mortgagors have candidly communicated with the mortgagees concerning the default and have made realistic proposals to cure the default over a reasonable period of time. Because the management and disposal of property requires skills that are usually outside of the range of expertise of most lenders and therefore costly to acquire, mortgag- ees prefer to collect the amounts owed them and are likely to be lenient and patient when circumstances warrant it. Seldom do mortgagees insist upon the exact letter of their con- tract. Nor do they rush into court to insist upon foreclosure at the first evidence of default, but after patience and leniency have been extended to delinquent mortgagors, eventually a settlement becomes necessary and foreclosure proceedings are started.

Judicial Foreclosure In general, the mortgagee possesses two types of remedies to protect his or her interests in case of default by the mortgagor. First, the lender may obtain judicial foreclosure: that is, to sue on the debt, obtain judgment, and execute the judgment against property of the mortgagor. In a judicial foreclosure, property subject to attachment and execution11 is not limited to the mortgaged property. This judgment may be levied against any of the mort- gagor’s property not otherwise legally exempt12 from execution. 11 Attachment is the act or process of seizing property of a debtor by court order in order to secure the debt of a creditor in the event judgment is rendered. Execution is the process of authorizing the sheriff or other competent officer to seize and sell property of the debtor in satisfaction of a judgment previously rendered in favor of a creditor. 12 Most states provide by statute that a certain amount of a borrower’s property shall be free from all liability from levy and sale as a result of the enforcement (execution) of a money judgment. These statutes typically provide that some amount of personal property and equity in a borrower’s home not secured by a purchase-money lien shall be set off and free from seizure and sale in order to provide the borrower with a minimum amount of property to maintain his or her family on their road to financial recovery.

Final PDF to printer

32 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 32 10/31/17 03:15 PM

Second, the lender may bring a foreclosure suit and obtain a decree of foreclosure and sale. If the sale of the mortgaged property realizes a price high enough to meet the expenses of the sale and the claims of the mortgagee and still leave a balance, this balance goes to the mortgagor. While foreclosure and sale of the property may be undertaken in two separate actions, they are usually pursued simultaneously in practice.

Redemption Redemption is the process of canceling or annulling a title conveyed by a foreclosure sale by paying the debt or fulfilling the other conditions in the mortgage. It can be accom- plished by paying the full amount of the debt, interest, and costs due to the mortgagee. The equity of redemption13 must be asserted prior to foreclosure. Once the foreclosure sale has been confirmed, the mortgagor can no longer redeem the property, except in states that provide for a statutory period for redemption after foreclosure. The right to redeem after foreclosure is called the right of statutory redemption, which exists in about half of the states. Generally, the period for statutory redemption runs about six months to one year after the foreclosure sale. In a number of states, instead of granting the mortgagor a right to redeem after the foreclosure sale, state laws postpone the sale to provide a longer period of time to pay a debt that is in default.

Sales of Property The advertising of the sale, the place where it takes place, and the method of sale are gov- erned by state law. While details differ, the results are approximately the same in all states.

Fixing a Price A mortgage foreclosure sale emanates from the assumption that a public auction is a sat- isfactory way to realize the best possible price in selling property. Hence, in some juris- dictions the highest bidder gets the property irrespective of its cost, the amount of liens against it, or any other consideration. Despite this requirement of a public sale, in most cases only the mortgagee or the mortgagee and a small number of bidders appear at the foreclosure sale and, as a result, the mortgagee is usually the successful bidder. The mort- gagee can use his or her claims as a medium of exchange in the purchase, except for costs, which must be paid in cash. Others must pay cash for their purchases (which may be in the form of a loan obtained from another lender with an agreement granting to it the new mort- gage), unless the successful bidder can arrange with the mortgagee to keep his or her lien alive by renegotiating or assuming the existing indebtedness. As a consequence, frequently only the mortgagee makes any serious bid for the property. Because lenders generally pre- fer to avoid owning and liquidating foreclosed properties, they will normally bid the full amount of their claim only where it is less than or equal to the market value of the security less foreclosure, resale, and holding costs. Rarely will lenders bid in excess of their claim in an attempt to outbid other buyers at the sale.

In a few states, an “upset” price is fixed in advance of the sale. This means that an appraisal by agents of the court fixes a minimum value for the property that must be reached in the bidding or the court will refuse to confirm the sale. This is not a common practice because it is quite difficult for the court to fix the price that the property must bring at the foreclosure sale. On the one hand, the court is interested in doing justice to the mortgagor. Since a deficiency judgment may be decreed in case the mortgagee is not completely satisfied from the proceeds of the sale, the lower the price, the larger the defi- ciency judgment. On the other hand, the mortgagee’s rights also must be protected. If the

13 The equity of redemption is the right of a mortgagor to redeem his or her property from default, the period from the time of default until foreclosure proceedings are begun.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 33

bru19684_ch02_016-041.indd 33 10/31/17 03:15 PM

court insists on too high a price, no sale would be effected, and hence the mortgagee would receive no satisfaction of his or her claims.

Deed of Trust The historical development of the law has commonly led, in some jurisdictions, to the finance of real estate by a deed of trust instead of a regular mortgage. There are three par- ties to a loan secured by a deed of trust. The borrower (creator of the trust) conveys the title to the property to be used as security to a trustee, who holds it as security for the benefit of the holder of the note executed by the borrower when the loan was made. The conveyance to the trustee is by deed, but the transfer is accompanied by a trust agreement, either as a part of the deed or in addition to it, setting forth the terms of the security arrangement and giving the trustee the power of sale in event of default.

The deed of trust is commonly used in Alabama, Arkansas, California, Colorado, the District of Columbia, Delaware, Illinois, Mississippi, Missouri, Nevada, New Mexico, Tennessee, Texas, Utah, Virginia, and West Virginia. Deeds of trust are not used exten- sively in other states because courts there have held that any conveyance of real estate given to secure a debt is a mortgage, irrespective of the form of the instrument used. This interpretation greatly restricts the trustee’s power of sale, often requiring the expense and delay of a court process up to and including foreclosure. States imposing this restriction have sought to ensure that a reasonable sale price and all other appropriate benefits are obtained for both borrower and noteholder before the property is sold.

Where the deed of trust is used according to its terms, the trustee is authorized in case of default to foreclose the borrower’s equity by a sale of the property at public auction. After a proper time period for advertisement, the trustee must account to both parties for the proceeds of the sale. The parties are entitled to their share as their interest may appear, after expenses of the sale, including compensation to the trustee, have been met. The deed of trust has the advantage of normally being more expeditious than a mortgage foreclosure.

Deed of Trust and Mortgage Compared The deed of trust is such a mixture of trust and mortgage law that anyone using it should act under the counsel of a local real estate lawyer. In general, however, the legal rules surrounding the creation and evidence of the debt in the form of a note, rights of the bor- rower left in possession, legal description of the property, creation of a valid lien on after- acquired property, and recording are the same for mortgages and deeds of trust. Similarly, a property subject to a deed of trust may be sold subject to the deed of trust either with or without an assumption of the debt by the purchaser. Borrowers may sell their interest or borrow money using the interest as security. Technically, borrowers have a reversionary interest in the property, and title to the property reverts to them upon payment of the debt. In the event of failure or refusal of a trustee to execute a reconveyance when the borrowers repay their debt, the trustee may be forced to act by legal process, whereby the borrowers would obtain a court order forcing the trustee to act.

In California, where deeds of trust and mortgages are used side by side, several distinc- tions are made between the two instruments. While a mortgage may be discharged by a simple acknowledgment of satisfaction on the record, a reconveyance of title is considered necessary to extinguish a deed of trust.14 Recording requirements for mortgages and deeds of trust also differ. Under the recording laws of most states, mortgage assignments may be,

14 Some states do not require reconveyance to extinguish a deed of trust. Instead, the secured beneficiary of the trust (noteholder) signs a request for release of the deed of trust, which is presented by the borrower to the trustee together with the canceled note and the deed of trust. The trustee issues a release of trust, which is then recorded at the appropriate office of public records for the county.

Final PDF to printer

34 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 34 10/31/17 03:15 PM

and in some states must be, recorded. Assignments of a deed of trust, however, need not be recorded, and in some states are not eligible for recordation. The recording of the original deed of trust gives notice of the lien against the property, and only the trustee has the power to clear the record through a reconveyance of the property.

Nature of Title at Foreclosure Sale The purchaser of property at a foreclosure sale is, in effect, the purchaser of the rights of the mortgagor whose interests are cut off by the sale. Even though the sale is conducted under court supervision, the court makes no representation concerning the nature of the title that a buyer will receive. Any title defects that existed prior to the foreclosure sale will continue with the title as it passes to the purchaser. If a junior lienor has been omitted in the suit for foreclosure, his or her claims will not be cut off by such suit. As long as lienor claims are not cut off, the purchaser acquires the property subject to those liens instead of a fee simple unencumbered.

Parties to Foreclosure Suit When the holders of a senior mortgage bring suit to foreclose their mortgage, they must join in the suit all who share the mortgagor’s interest. These include not only junior mortgage holders but judgment creditors, purchasers at an execution sale, and trustees in bankruptcy, if any. Failure to include all of these might improve their position with the foreclosure of the senior lien. For example, should the senior mortgagee become the successful bidder at the foreclosure sale, and should a junior lienor of record not be joined in the suit, it is possible that when the senior mortgagee takes title to the land, the junior mortgagee may acquire the position of a senior lienor. To avoid this possibility, every foreclosure action should be preceded by a careful search of the record to discover all junior lien claimants who should be joined in the foreclosure suit.

Should any junior lienors think that they have an equity to protect, they have the right to purchase the property at a foreclosure sale, paying off or otherwise providing for the interests of the claimants whose liens are superior to theirs. It might be, for example, that a senior mortgagee has a $50,000 lien on a property that a junior mortgagee with a $10,000 lien considers to be worth more than $50,000. If the junior lienor does not bid for the prop- erty, the senior mortgagee may bid it in for $50,000 (in the absence of other bidders) and cut off the junior lienor’s equity, causing a loss to the junior lienor. By taking over respon- sibility for the senior mortgage, the junior lienor could bid up to $60,000 for the property without providing additional funds. In this event, it is not uncommon for a senior claimant to agree in advance upon the method of settlement of his or her claims. This may include an agreement to renew the senior mortgagee’s claim, either with or without a reduction in the amount.

The purchaser at the foreclosure sale takes over the property free of the lien of the mort- gage being foreclosed, but also free of all holders of junior liens who have been joined in the foreclosure action. If the senior mortgage holder or a third party purchases the property at a foreclosure sale, all such junior liens are of no further force or effect.

If junior lienholders bring suit for foreclosure, they should not join the senior lienhold- ers in the suit. Instead, they should sue subject to the senior lien, but this means they are not obligated to pay off the senior lienholders. Junior lienholders may prefer to keep the senior mortgage alive. Holders of the senior lien may join the action voluntarily and some- times do so to make sure that their interests are fully protected. They may wish to have the court determine the amount to be assumed by the purchaser which is due them. Or should there be any questions about the order of priority of this lien, senior lienholders may join the foreclosure action to have this question answered. Again, they may have a side agree- ment with the junior lienors to continue their mortgage unchanged in amount. In case the

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 35

bru19684_ch02_016-041.indd 35 10/31/17 03:15 PM

junior mortgage holders plan to buy the property at the foreclosure sale, they may prefer to pay off the senior lien as well. This must be done with the consent of the lienholders if they are not a party to the suit. This practice represents a redemption of the senior mortgage and follows the English maxim of “redeem up, but foreclose down.” This concept is fairly obvious. It simply means that junior mortgagees must honor the prior position of senior mortgagees, but junior mortgagees may wipe out liens junior to theirs. For example, say a property now worth $100,000 is encumbered as follows:

In a foreclosure action, mortgagee B has a buying power of $110,000 without raising additional funds if he is able to keep the first mortgage undisturbed, or if he refinances it. If he buys the property at the foreclosure sale for no more than $110,000, the third mortgage lien will be completely cut off by foreclosure.

Holders of junior liens destroyed in a foreclosure action are entitled to have the surplus of sale price over senior mortgage claims applied to their claims. If there is no surplus, they are entitled to a judgment for the full amount of their claims. From that time on, they are merely general, unsecured creditors of the mortgagor, unless the latter should own other real estate to which such judgments would attach.

Effect of Foreclosure on Junior Lienors If a senior mortgage holder brings foreclosure suit and joins junior claimants in the suit, the question arises, “What happens to the claims of those cut off by the foreclosure sale?” Any surplus remaining after satisfying the costs of foreclosure and the claims of the senior lienor is distributed according to the priority rights of junior claims. Sometimes the distri- bution of this surplus is not as simple as it sounds. Frequent disputes concerning the order of priority require action by the court to establish the order of settlement.

Where a senior mortgage is properly foreclosed, it extinguishes the lien of the junior mortgage, but the debt secured by the mortgage is unaffected. Where there is no surplus from the foreclosure sale or where it is insufficient to meet all claims, the holders of such claims still maintain their rights to pursue the mortgagors on whatever personal obligation they have incurred by obtaining the mortgage. This legal right may or may not result in satisfaction of the claims of lienholders. Such obligations are not extinguished and may be enforced at some future time, should the mortgagors ever recover their economic status sufficiently to make pursuit of claims against them worthwhile.

Deficiency Judgment While a sale of the mortgaged property may result in a surplus to which the mortgagor is entitled, it may on the contrary be sold at a price that fails to satisfy the claims of the mortgagee. Any deficit is a continuing claim by the mortgagee against the mortgagor. The mortgagor is personally obligated to pay the debt evidenced by the promissory note. Since mortgages may involve one or more specific properties, the mortgagee will normally look to such property to provide primary security for his or her claim, but any deficiency remains the obligation of the mortgagor. Any deficit remaining after a foreclosure and sale of the property is known as a deficiency judgment.

Deficiency judgments are unsecured claims—unless the mortgagor owns other real estate—and take their place alongside other debts of the mortgagor. Unlike the mortgage from which such judgment springs, the latter gives the holder no right of preference against

First mortgage, A $ 90,000 Second mortgage, B 20,000 Third mortgage, C 10,000 Total mortgage liens $120,000

Final PDF to printer

36 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 36 10/31/17 03:15 PM

any of the non–real estate assets of the debtor.15 Hence, the value of deficiency judgments is always open to serious question. This is true in part because of the ways by which they can be avoided or defeated.

Debtors seeking to avoid the deficiency judgment may plan accordingly. Since such judgments attach only to real estate or other property that the debtors hold or may acquire in the future, the debtors may see that they do not acquire any future property interests or, if they do, they will be careful to have titles recorded in names other than their own.

Considerable sentiment exists in some quarters in favor of legislation to abolish defi- ciency judgments altogether, leaving mortgagees with only the property to protect their claims. Several states strictly limit the applicability of deficiency judgments. Of course, this increases the possibility that a borrower will walk away from a property if its market value falls below the loan balance.

Taxes in Default Payment of property taxes is an obligation of the mortgagor. As such, taxes constitute a prior lien against the security. Transfers of title always take into account accrued but unpaid taxes. Mortgages commonly contain tax clauses giving the mortgagee the right to pay taxes not paid regularly by the mortgagor. The amounts so paid are then added to the claims of the mortgagee. While the lien of taxes gives tax-collecting authorities the right to foreclose in case of default, this right is seldom exercised on first or even second default. Instead, the taxing authority from time to time may pursue an alternative policy of selling tax liens with deeds to follow. Since tax liens constitute superior liens prior to the claims of mortgagees if the taxing authorities have observed statutory procedure, and since they customarily carry high effective rates of interest, mortgagees may prefer to maintain the priority claim of tax liens by paying delinquent taxes and adding them to their claims.

If foreclosure becomes necessary, mortgagees include all taxes they have paid. At the time of a foreclosure sale, the purchaser usually is expected to pay all delinquent taxes, thus making the tax status of the property current.

Tax Sales Where mortgagees do not act to protect their interests against tax liens, sooner or later tax- ing authorities will bring pressure to collect delinquent taxes. In effect, if not in form, the tax sale procedure is intended to parallel that followed in the foreclosure of mortgages. At the time of the tax sale, the purchaser receives a tax certificate, which is then subject to redemption in nearly all states. The period of redemption is usually two or three years. If the property is not redeemed by the delinquent taxpayer within this period, the purchaser at the tax sale is then entitled to receive a deed to the property.

Tax titles are usually looked upon as weak evidence of ownership. The interest of the tax collector is to find someone willing and able to pay taxes for someone else in return for a claim against the property. The collector is not greatly concerned about passing good title. There is no suggestion of warranty. In addition to any defects in title regardless of delinquent taxes, the unconcern of the tax collector may in turn result in added clouds on the title. Among the latter, the following may occur: 1. Because of inaccurate description of the property or incorrect records of ownership, the

notice of sale may be defective. 2. The property owner may have been denied due process or his or her day in court.

15 Deficiency judgments become a lien on all real estate owned by the judgment debtor in the county or counties where the judgment is entered. To the extent that there is equity in the real estate that is not exempt from execution, the judgment can be considered secured, and the creditor can enforce his lien through foreclosure and sale of the property to which the lien attaches.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 37

bru19684_ch02_016-041.indd 37 10/31/17 03:15 PM

3. The line of authority for the sale may not be clear. 4. Irregularities and carelessness, even in minor procedural matters, may cause the tax sale

to be invalidated. All of these depend in part upon the recuperative powers of the delinquent taxpayers. If

they have lost interest in the property or lack the financial resources to protect their inter- ests, delinquent taxpayers may interpose no objections to the plans of the purchaser at the tax sale. Nevertheless, the risk is great enough to suggest caution and due attention even to minor details before purchasing tax liens.

In the absence of bidders at a tax sale—which might occur in periods of depression or in the sale of inexpensive vacant land—the property usually reverts to the state, the county, or some other local governmental unit. State and local units can be careless and neglect to take steps to realize a fair price when they dispose of property so acquired. A sale by the governmental unit, given full compliance with statutory requirements, normally offers a very short period of redemption after which the mortgagor and the mortgagee lose to the purchaser all rights to the property. Mortgagees should diligently monitor tax sale notices to ensure that their lien rights on property sold at tax sales are not affected.

Bankruptcy

Bankruptcy may be defined as a proceeding in which the court takes over the property of a debtor to satisfy the claims of creditors. The goal is to relieve the debtor of all liabili- ties, so that he or she may become financially solvent. The potential for bankruptcy under Chapters 7, 11, and 13 of the Bankruptcy Code affects the value of real estate as collateral. Lenders must be aware of the possibility that a borrower may file bankruptcy and must know how such a filing will change their positions. Both real estate investors and lenders must have a basic understanding of their rights in a bankruptcy proceeding to effectively negotiate with one another and resolve their differences short of a bankruptcy proceeding. It should also be stressed that in many states homestead laws protect certain residential and other property and may exclude such property from consideration in bankruptcy proceed- ings. Although a comprehensive examination of the Bankruptcy Code is beyond the scope of this text, several areas of bankruptcy law of particular importance to real estate investors and lenders are discussed below.

Chapter 7 Liquidation The purpose of Chapter 7, or “straight bankruptcy,” is to give debtors a fresh start by dis- charging all of their debts and liquidating their nonexempt assets. Chapter 7 is available to any person regardless of the extent of his or her assets or liabilities. A Chapter 7 petition can be filed voluntarily by a debtor or involuntarily by petitioning creditors, except that a farmer may not be forced into an involuntary proceeding.

Upon the filing of a Chapter 7 petition, the court appoints an interim trustee who is charged with evaluating the financial condition of the debtor and reporting at the first meeting of creditors whether there will be assets available for liquidation and distribution to unsecured creditors. The trustee’s job is to oversee the liquidation of nonexempt assets and to evaluate claims filed by creditors. The ultimate objective of a Chapter 7 bankruptcy is the orderly liquidation of the debtor’s assets and the distribution of the proceeds accord- ing to the legal rights and priorities of the various creditor claimants.

A lender whose loan to the debtor is secured by a mortgage on real estate will normally be paid in full if the value of the security exceeds the balance due under the mortgage. To foreclose on the mortgage and sell the debtor’s property, the lender must first petition

Final PDF to printer

38 Part 1 Overview of Real Estate Finance and Investments

bru19684_ch02_016-041.indd 38 10/31/17 03:15 PM

the bankruptcy court. If the debtor is not behind in the mortgage payments and desires to retain the property, he or she may do so by reaffirming the mortgage debt. This means that although the debtor’s obligation to repay the debt has been discharged in bankruptcy, the debtor makes a new agreement after the discharge to repay the debt.

Chapter 11 An alternative to Chapter 7 is a Chapter 11 bankruptcy, which is available to owners of a business. While a Chapter 7 bankruptcy normally results in the liquidation of the debtor’s assets, a Chapter 11 proceeding looks to the preservation of the debtor’s assets while a plan of reorganization to rehabilitate the debtor is formulated. Within 120 days after filing a Chapter 11 bankruptcy petition, this plan of reorganization must be filed by the debtor with the court. The plan must classify the various claims against the debtor’s assets and specify the treatment of the debts of each class. In a typical reorganization plan, the rights and duties of the parties are redefined in one of two ways. The plan may restructure the debt to provide for reduced payments over an extended period, or the plan may scale down the debt, reducing the debtor’s obligation to an amount less than the full claim.

Once a plan is filed, the proponent of the plan, usually the debtor, must solicit creditor acceptance. Once holders of two-thirds of the total amount of the claims and a majority of the total number of claim holders assent to the plan, the court will analyze the plan and determine whether it meets the technical prerequisites for judicial confirmation. Even if one or more creditor classes dissent, the court can still confirm the plan if it meets certain statutory requirements. When the court decides that the bankruptcy plan is satisfactory in spite of the objections of creditors, the confirmation of the plan is known as cramdown.16

The cramdown provisions under Chapter 11 provide borrowers with the ability to restructure their secured (e.g., mortgage) and unsecured indebtedness by executing a plan of reorganization that outlines the mechanics for getting borrowers back on their feet and states how different classes of claims and interests will be treated. The cramdown pro- visions are essential to keeping the borrowers whole during a reorganization. Without a cramdown provision, secured lenders could continue to block the proposed reorganization by refusing to approve the plan and foreclose on the major assets of the borrower.

Under the Bankruptcy Code, a plan of reorganization may seriously impact secured lenders by impairing their claim. Despite this impairment, the plan may be confirmed by the court over the objections of the secured lenders. The law, however, makes some provi- sion for secured lenders who do not approve the plan. One provision allows the borrower to keep the secured property but requires that the lender must receive present or deferred payments having a present value equal to the value of the collateral. A second provision calls for a sale of the collateral with the lender’s lien attaching to the proceeds of the sale. A final catch-all provision requires the secured lender’s realization of the “indubitable equivalent” of his or her claims.

Chapter 11 bankruptcy proceedings are of great concern to lenders who may find that their security is tied up for years during the reorganization of the debtor’s financial affairs. Even lenders holding mortgages on a Chapter 11 debtor’s personal residence may find that they are unable to foreclose on their liens where such a foreclosure would interfere with the debtor’s plan of reorganization. In sum, the basic object of a Chapter 11 bankruptcy is to provide for a court-supervised reorganization, instead of a liquidation, of a financially troubled business.

16 During 2009, legislation was introduced in Congress that would allow federal judges to modify mortgages for property owners who have filed for bankruptcy and who are seeking to avoid foreclosure. This legislated form of cramdown could allow judges to reduce the mortgage balance or interest rate or change the loan maturity to avoid foreclosure.

Final PDF to printer

Chapter 2 Real Estate Financing: Notes and Mortgages 39

bru19684_ch02_016-041.indd 39 10/31/17 03:15 PM

Chapter 13 A Chapter 13 petition in bankruptcy, also known as a wage earner proceeding, represents an attractive alternative to the liquidation applied in Chapter 7. Like Chapter 11, a Chapter 13 proceeding envisions the formulation of a plan designed for the rehabilitation of the debtor. Such plans provide that funding of the plan will come from future wages and earnings of the debtor. Any debtor with regular income who has unsecured debts of less than $100,000 and secured debts of less than $350,000 qualifies for Chapter 13 relief. Thus, a Chapter 13 bankruptcy is the one most likely to be used by an individual.

The heart of Chapter 13 is the repayment plan, which is proposed by the debtor and, assuming it meets certain tests and conditions, is subject to confirmation by the court over objections of creditors. In a Chapter 13 plan, debtors propose to pay off their obligations and reorganize their affairs. The plan may call for payments over a three- to five-year period. Unlike a Chapter 7 or Chapter 11 bankruptcy that can be filed by debtors only every six years, a Chapter 13 plan can be filed immediately after completion of a prior bankruptcy liquidation or payment plan as long as it is filed in good faith.

During the period covered by the plan, creditors must accept payment as provided in the plan and may not otherwise seek to collect their debts. Assuming successful comple- tion of the plan, debtors receive a discharge of all debts provided for in the plan other than long-term obligations for payments that continue beyond the period of the plan’s duration. However, the plan may not modify the rights of mortgagees whose liens are secured only by property used by the debtors as their personal residence. This “preferred treatment” for such mortgagees under Chapter 13 is justified because the success of a reorganization plan could be jeopardized if foreclosure of this mortgage disrupts the affairs of the debt- ors by forcing them to seek other shelter. Although the plan may not “modify” the rights of secured lenders, lenders desiring to accelerate the balance of any indebtedness upon default to raise the interest rate should be aware of the borrower’s right to cure a default in bankruptcy (by making arrangements to pay amounts currently in default over the period of the plan) and reinstate the mortgage. Thus, although a plan may not “modify” the rights of lenders whose debt is secured by liens on the debtor’s personal residence, the filing of a Chapter 13 will likely prevent an imminent foreclosure and allow for repayment of arrearages existing on the date of the filing to be carried over a reasonable period of time. Where the plan calls for curing the arrearages and no modification of the schedule of cur- rent payments, courts will normally approve the plan because it does not materially affect the rights of such lenders.

This chapter has discussed the legal instruments and ramifications associated with financing real estate, such as default, foreclosure, and bankruptcy. The probability of one or more of these events occurring and the rights of the parties if it occurs ultimately affects the value of the various prop- erty rights. These legal considerations should be kept in mind as we discuss the risks associated with mortgage lending in later chapters. Clearly, the legal rights of borrowers and lenders affect the degree of risk assumed by each party and, thus, the value of entering into various transactions.

The availability of various legal alternatives can be viewed as a way of controlling and shifting risk between the various parties to a transaction. The probability of default or bankruptcy by a bor- rower and the legal alternatives available to each party affect the expected return to the lender from the loan. In later chapters we will discuss how the amount of the loan relative to the value of the property is used by the lender to control risk. The reader should keep in mind the fact that loan cov- enants as discussed in this chapter also control the risk.

Conclusion

Final PDF to printer

bru19684_ch02_016-041.indd 40 10/31/17 03:15 PM

40 Part 1 Overview of Real Estate Finance and Investments

1. Distinguish between a mortgage and a note. 2. What does default mean? Does it occur only when borrowers fail to make scheduled loan

payments? 3. What is meant by mortgage foreclosure, and what alternatives are there to such action? 4. What does it mean when a lender accelerates on a note? What is meant by forbearance? 5. Can borrowers pay off part, or all, of loans any time that they desire? 6. What does “nonrecourse” financing mean? 7. What does “assignment” mean and why would a lender want to assign a mortgage loan? 8. What is meant by a “purchase-money” mortgage loan? When could a loan not be a purchase-

money mortgage loan? 9. When might a borrower want to have another party assume his liability under a mortgage loan? 10. What does a deficiency judgment mean? 11. What is a land contract? 12. How can mechanics’ liens achieve priority over first mortgages that were recorded prior to the

mechanics’ lien? 13. Name possible mortgageable interests in real estate and comment on their risk as collateral to

lenders. 14. Explain the difference between a buyer assuming the mortgage and a buyer taking title subject

to the mortgage. 15. What dangers are encountered by mortgagees and unreleased mortgagors when property is sold

subject to a mortgage? 16. What is the difference between equity of redemption and statutory redemption? 17. What special advantages does a mortgagee have in bidding at the foreclosure sale where the

mortgagee is the foreclosing party? How much will the mortgagee normally bid at the sale? 18. Is a foreclosure sale sometimes desirable or even necessary when the mortgagor is willing to

give a voluntary deed?

Questions

after-acquired property clause, 24

assumption of the mortgage, 22 bankruptcy, 37 covenants, 19 cramdown, 38 deed of trust, 33 deed in lieu of foreclosure, 30 deficiency judgment, 35 due-on-sale clause, 21 extension agreement, 28 first mortgage, 24 fixture, 24

foreclosure, 31 friendly foreclosure, 30 future advances, 22 judicial foreclosure, 31 junior mortgages, 24 land contract, 25 mortgage document, 18 mortgage default, 26 mortgage for future

advances, 22 open-end mortgage, 22 prepackaged bankruptcy, 30 promissory note, 16

purchase-money mortgage, 25

redemption, 32 second mortgage, 24 seller financing, 25 short sale, 31 “subject to” the mortgage, 23 subordination clause, 22 tax sale, 36 transfer of mortgage, 29 voluntary conveyance, 30 with recourse, 16 workout, 27

Key Terms

Useful Web Sites

www.alta.org—American Land Title Association—provides industry and government news, as well as an explanation of consumer interests in land titles. www.mortgagemag.com—Includes real estate-related articles and links to sites covering mortgage banking, legal services, and technology. http://dictionary.law.com—Legal dictionary. http://real-estate-law.freeadvice.com—Many good FAQs about real estate law. Legal advice written by lawyers for nonlawyers.

Final PDF to printer

bru19684_ch02_016-041.indd 41 10/31/17 03:15 PM

Chapter 2 Real Estate Financing: Notes and Mortgages 41

19. What are the risks to the lender if a borrower declares bankruptcy? 20. What is a deficiency judgment and how is its value to a lender affected by the Bankruptcy

Code?

Problems 1. Last year Jones obtained a mortgage loan for $100,000. He just inherited a large sum of money and is contemplating prepaying the entire loan balance to save interest. What are his rights to prepay the loan?

2. Mr. Smith acquired a property consisting of one acre of land and a two-story building five years ago for $100,000. He also obtained an $80,000 mortgage loan from ACE Bank to provide financing to complete the purchase. This year, Mr. Smith constructed another building on the property with his own funds at a cost of $20,000. Mr. Smith has decided after completing the building to approach Duce Bank to borrow and mortgage the new building with a $16,000 loan. Is Duce Bank likely to provide the $16,000 in financing? What other options may Mr. Smith have to consider?

3. Ms. Brown purchased a property consisting of one acre of land and a building for $100,000 five years ago. She obtained an $80,000 mortgage loan from ABC Bank at that time. The building was very old and Ms. Brown has just had it torn down. She now wants to build a new building. Ms. Brown hopes to finance construction with ABC Bank and will call them soon to discuss financing the new project. How will ABC Bank evaluate the possibility of making another loan to Ms. Brown?

Final PDF to printer

42

bru19684_ch03_042-077.indd 42 10/31/17 06:57 PM

Chapter 3 Mortgage Loan Foundations: The Time Value of Money Financing the purchase of real estate usually involves borrowing on a long- or short-term basis. Because large amounts are usually borrowed in relation to the prices paid for real estate, financing costs are usually significant in amount and weigh heavily in the deci- sion to buy property. Individuals involved in real estate finance must understand how these costs are computed and how various provisions in loan agreements affect financing costs and mortgage payments. Familiarity with the mathematics of compound interest is essential in understanding mortgage payment calculations, how loan provisions affect financing costs, and how borrowing decisions affect investment returns. It is also impor- tant for investment analysis calculations that we examine later in this text. This chap- ter provides an introduction to the mathematics of finance, sometimes referred to as the “time value of money,” or TVM. It forms a basis for concepts discussed in financing single- family properties and income-producing properties, and in funding construction and development projects.

Compound Interest

Understanding the process of compounding in finance requires the knowledge of only a few basic formulas. At the root of these formulas is the most elementary relationship, compound interest. For example, if an individual makes a bank deposit of $10,000 that is compounded at an annual interest rate of 6 percent, what will be the value of the deposit at the end of one year? In examining this problem, one should be aware that any com- pounding problem has four basic components: 1. An initial deposit, or present value of an investment of money. 2. An interest rate. 3. Time. 4. Value at some specified future period.

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 43

bru19684_ch03_042-077.indd 43 10/31/17 06:57 PM

In our problem, the deposit is $10,000, interest is to be earned at an annual rate of 6 percent, time is one year, and value at the end of the year is what we would like to know. We have four components, three of which are known and one that is unknown.

Compound or Future Value

In the preceding problem, we would like to determine what value will exist at the end of one year if a single deposit or payment of $10,000 is made at the beginning of the year and the deposit balance earns a 6 percent rate of interest annually. To find the solution, we must introduce some terminology:

PV

=

present value, or principal at the beginning of the year

i

=

the interest rate

I = dollar amount of interest earned during the year FV

=

principal at the end of n years, or future value

n

=

number of years

In this problem, then, PV = $10,000, i = 6 percent, n = one year, and FV, or the value after one year, is what we would like to know.

The value after one year can be determined by examining the following relationship: FV = PV +  I 1

or the future value, FV, at the end of one year equals the deposit made at the beginning of the year, PV, plus the dollar amount of interest, I1, earned in the first period. Because PV = $10,000, we can find FV by determining I1. Since we are compounding annually, FV is easily determined to be $10,600, which is shown in Exhibit 3–1.

Multiple Periods To find the value at the end of two years, we continue the compounding process by tak- ing the value at the end of one year, $10,600, making it the deposit at the beginning of the second year, and compounding again. This is shown in Exhibit 3–2.

I 1

=

PV × i

= $10,000 (.06)

=

$600

Future value at the end of one year (n = 1 year) is determined as

FV

=

PV +  I 1

= $10,000 + $600

= $10,600

or

FV

=

PV (1 + i)

= $10,000 (1 + .06)

= $10,600

EXHIBIT 3–1 Compound Interest Calculation for One Year

Final PDF to printer

44 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 44 10/31/17 06:57 PM

Exhibit 3–2 shows that a total future value of $11,236 has been accumulated at the end of the second year. Note that in the second year, interest is earned not only on the original deposit of $10,000, but also on the interest ($600) that was earned during the first year. The concept of earning interest on interest is an essential idea that must be understood in the compounding process and is the cornerstone of all financial tables and concepts in the mathematics of finance.

From the computation in Exhibit 3–2, it should be pointed out that the value at the end of year 2 could have been determined directly from PV as follows:

FV

=

PV (1 + i) (1 + i)

=

PV (1 + i) 2

In our problem, then, when n = 2 years

FV

=

PV (1 + i) 2

= $10,000 (1 + .06) 2

= $10,000 (1.123600)

=

$11,236

From this computation, the $11,236 value at the end of two years is identical to the result that we obtained in Exhibit 3–2. Being able to compute FV directly from PV is a very important relationship because it means that the future value, or value of any deposit or payment left to compound for any number of periods, can be determined from PV by sim- ple multiplication. Therefore, if we want to determine the future value of a deposit made today that is left to compound for any number of years, we can find the solution with the general formula for compound interest, which is

FV = PV (1 + i) n By substituting the appropriate values for PV, i, and n, we can determine FV for any desired number of years.1

Other Compounding Intervals In the preceding section, the discussion of compounding applies to cases where funds were compounded only once per year. Many savings accounts, bonds, mortgages, and other investments provide for monthly, quarterly, or semiannual compounding. Because we will be covering mortgage loans extensively in a later chapter, which involve monthly compounding almost exclusively, it is very important that we consider the other compounding intervals.

1 At this point, the reader may realize that these problems can be solved with a financial calculator or computer software. We will provide illustrations using notation and keystroke sequences that are consistent with the use of a financial calculator to solve many of the problems in this and other chapters in this book. The reader may choose to change this approach by using computer software in lieu of a financial calculator.

$10,600 (.06)

=

I 2

$636 =

I 2

and value at the end of two years, or n = 2 years , is now

$10,600 +  I 2 = FV

$10,600 + $636 =

$11,236

EXHIBIT 3–2 Compound Interest Calculation for Two Years

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 45

bru19684_ch03_042-077.indd 45 10/31/17 06:57 PM

When compounding periods other than annual are considered, a simple modification can be made to the general formula for compound interest. To change the general formula

FV = PV (1 + i) n where

n

=

years

i = annual interest rate PV

=

deposit

for any compounding period, we divide the annual interest rate (i) by the desired number of compounding intervals within one year. We then increase the number of time periods (n) by multiplying by the desired number of compounding intervals within one year. For example, let m be the number of intervals within one year in which compounding is to occur, and let n be the number of years in the general formula. Then, we have

FV = PV [ 1 +  i __ m ] n⋅m

Therefore, if interest is to be earned on the $10,000 deposit at an annual rate of 6 percent, compounded monthly, to determine the future value at the end of one year, where m = 12, we have

FV

=

$10,000 [ 1 +  .06 ___ 12 ]

1⋅12

=

$10,000 (1.061678)

=

$10,616.78

If we compare the results of monthly compounding with those from compounding annu- ally, we can immediately see the benefits of monthly compounding. If our initial deposit is compounded monthly, we would have $10,616.78 at the end of the year, compared with $10,600.00 when annual compounding is used.

Another way of looking at this result is to compute an effective annual yield (EAY ) on both investments. This is done by assuming that $10,000 is deposited at the beginning of the year and that all proceeds are withdrawn at the end of the year. For the deposit that is compounded monthly, we obtain

EAY

=

FV − PV _______ PV

= $10,616.78 − $10,000.00 _____________________

$10,000

=

6.1678%

The result can be compared with the effective annual yield obtained when annual com- pounding is used, or

EAY

=

$10,600 − $10,000 ________________

$10,000

= 6%

From this comparison, we can conclude that given the same nominal annual rate of inter- est, or 6 percent, the effective annual yield is higher when monthly compounding is used.

Final PDF to printer

46 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 46 10/31/17 06:57 PM

This comparison should immediately illustrate the difference between computing interest at a nominal annual rate of interest and computing interest at the same nominal annual rate of interest, compounded monthly. Both deposits are compounded at the same nomi- nal annual rate of interest (6%); however, one is compounded 12 times at a monthly rate of (.06 / 12) , or .005, on the ending monthly balance, while the other is compounded only once, at the end of the year at the rate of .06. It is customary in the United States to use a nominal rate of interest in contracts, savings accounts, mortgage notes, and other transac- tions. How payments will be made or interest accumulated (i.e., annually, monthly, daily) is then specified in the agreement. It is up to the parties involved in the transaction to ascertain the effective annual yield.

From the above analysis, one result should be very clear. Whenever the nominal annual interest rates offered on two investments are equal, the investment with the more frequent compounding interval within the year will always result in a higher effective annual yield. In our example, we could say that a 6 percent annual rate of interest compounded monthly provides an effective annual yield of 6.168 percent.

Other investments offer semiannual, quarterly, and daily compounding. In these cases, the basic formula for compound interest is modified as follows:

Nominal Annual Rate (%)

Compounding Interval  

Modified Formula

Effective Annual Yield* (%)

6 Annually m = 1 FV = PV (1 + i) n⋅1 6.00

6 Semiannually m = 2 FV = PV [ 1 +  i __ 2 ] n⋅2

6.09

6 Quarterly m = 4 FV = PV [ 1 +  i __ 4 ] n⋅4

6.14

6 Monthly m = 12 FV = PV [ 1 +  i ___ 12 ] n⋅12

6.17

6 Daily m = 365 FV = PV [ 1 +  i ____ 365 ] n⋅365

6.18

*Also known as annual percentage yield (APY).

For example, if a deposit of $10,000 is made and an annual rate of 6 percent compounded daily is to be earned, we have:

FV

=

$10,000 [ 1 +  .06 ____ 365 ]

1.365

= $10,000 (1.061831)

=

$10,618.31

and the effective annual yield would be  $10,618.31 − $10,000  ___________________ $10,000

 = 6.1831 percent. If the money was left on deposit for two years, the exponent would change to 2 × 365, and FV at the end of two years would be $11,274.86.

Many banks and savings institutions disclose what is referred to as the APY (annual percentage yield) on CDs, checking accounts, and so on. Conceptually, the effective annual yield shown here and the APY are generally the same. However, federal regulations

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 47

bru19684_ch03_042-077.indd 47 10/31/17 06:57 PM

require banks to include certain fees and penalties when applicable. Such fees could make the APY differ from the effective annual yield in our examples.

Throughout this book, we will follow the convention of using nominal rates of interest in all problems, examples, and exhibits. Hence, the term interest rate means a nominal, annual rate of interest. This means that when comparing two alternatives with different compounding intervals, the nominal interest rate should not be used as the basis for com- parisons. In these cases, the concept of effective annual yield should be used when devel- oping solutions.

Calculating Compound Interest Factors Finding a solution to a compounding problem involving many periods is very awkward because of the amount of multiplication required. Calculators that are programmed with compound interest functions eliminate much of the detail of financial calculations. Another approach for finding solutions to compound interest problems can be used by calculat- ing interest factors that can be used to solve many problems. We will illustrate how these factors are calculated so the reader will understand the link between the mathematics of finance and calculators that have been programmed to provide solutions more efficiently. We also do this so that in the event that problems with many parts and multiple inputs must be solved, the reader may break the problem down and solve it in steps by using the neces- sary factors.

To become familiar with the factors for various interest rates, recall that, in the prob- lem discussed earlier, we wanted to determine the future value of a $10,000 deposit com- pounded at an annual rate of 6 percent after one year. Looking at the 6 percent column in Exhibit 3–3 corresponding to the row for one year, we find the interest factor 1.060000. When multiplied by $10,000, this interest factor gives us the solution to our problem.

FV

=

$10,000 (1.060000)

= $10,600

The interest factor for the future value of $1, at 6 percent for one year, is 1.060000—the same result had we computed (1 + .06) 1 , or 1.06 from the general formula for compound interest. In other words,

(1 + .06) 1  = 1.06 Calculators can be used to determine interest factors in Exhibit 3–3 for many combina- tions of interest rates and time periods. These factors allow us to find a solution to any compounding problem as long as we know the deposit (PV), the interest rate (i), and the number of periods (n) over which annual compounding is to occur. For example, by using keystrokes on a calculator, we can calculate the factor for 6 percent interest and one year as follows:

  Rate

Year 6% 10% 15% 20%

  1   1.060000 1.100000 1.150000 1.200000

  2   1.123600 1.210000 1.322500 1.440000   3   1.191016 1.331000 1.520875 1.728000   4   1.262477 1.464100 1.749006 2.073600   5  1.338226 1.610510  2.011357 2.488320

EXHIBIT 3–3 Interest Factors for an Amount of $1 at Compound Interest for Various Interest Rates and Compounding Periods

Final PDF to printer

48 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 48 10/31/17 06:57 PM

PV

=

$1

i =

6%

n = 1 PMT

=

0

Solve for FV

=

1.06

Similarly, if we wanted the factor for 10 percent interest and four years, we would solve for FV as follows:

PV

=

$1

i =

10%

n = 4 PMT

=

0

Solve for FV

=

1.464100

Question: What is the future value of $5,000 deposited for four years compounded at an annual rate of 10 percent?

Solution: FV

=

$5,000 (1.464100)

= $7,320.50

As was the case with the interest factors for annual compounding, interest factors for monthly compounding for selected interest rates and years have been computed from the modified formula PV (1 + i / 12) n⋅12 and are compiled in Exhibit 3–4. To familiarize the stu- dent with these interest factors, in Exhibit 3–4 selected interest rates and periods have been chosen and factors have been calculated.

  Rate

Month 6% 8%   1 1.005000 1.006670   2 1.010025 1.013378   3 1.015075 1.020134   4 1.020151 1.026935   5 1.025251 1.033781   6 1.030378 1.040673   7 1.035529 1.047610   8 1.040707 1.054595   9 1.045911 1.061625  

10 1.051140 1.068703   11 1.056396 1.075827   12 1.061678 1.083000  

Year Month 1 1.061678 1.083000 12 2 1.127160 1.172888 24 3 1.196681 1.270237 36 4 1.270489 1.375666 48

EXHIBIT 3–4 Interest Factors for an Amount of $1 at Compound Interest for Various Interest Rates and Compounding Periods

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 49

bru19684_ch03_042-077.indd 49 10/31/17 06:57 PM

In our earlier problem, we wanted to determine the future value of a $10,000 deposit that earned interest at an annual rate of 6 percent, compounded monthly. This can be easily determined by choosing the factor for 6 percent and 12 months, or one year, in Exhibit 3–4. That factor is 1.061678. Hence, to determine the value of the deposit at the end of 12 months, or one year, we have

FV

=

$10,000 (1.061678)

= $10,616.78

In other words, the interest factor for a 6 percent rate of interest compounded monthly for one year is 1.061678, which is the same result that we would obtain if we expanded (1 + .06 / 12) 1⋅12 by multiplying, or

[ 1 +  .06 ___ 12 ] 1.12

 = 1.061678

Question: What is the future value of a single $5,000 deposit earning 8 percent interest, compounded monthly, at the end of two years?

Solution:

FV

=

$5,000 [ 1 +  .08 ___ 12 ] 2⋅12

= $5,000 (1.172888)

=

$5,864.44

Using Financial Functions: Calculators and Spreadsheets

Finding a solution to a compounding problem involving many periods may be greatly sim- plified with the use of a calculator. Calculators programmed with compound interest func- tions eliminate the need for financial tables for many problem situations. Spreadsheets such as Excel are programmed with functions that allow users to input financial variables and solve. We will present alternative solutions to most of the time value of money prob- lems in the remainder of this text using a general function that corresponds to the format of a financial calculator. Refer to your specific calculator manual to confirm whether all operations are similar. Unless specified otherwise, the solutions assume that payments are made at the end of each period, and that money spent is (−) and money received is (+) . When solving problems, we will use the following format:

n

=

number of years, unless stated otherwise

i

=

interest rate per year, unless stated otherwise

PV = present value PMT

=

payments

FV

=

future value

Solutions will follow the format above, with the unknown variable being solved listed last. Most calculations are carried out to at least six decimal places, then final monetary amounts are rounded back to two decimal places.

For example, in the problem discussed earlier, we wanted to determine the future value of a $10,000 deposit compounded at an annual rate of 6 percent after one year.

Final PDF to printer

50

bru19684_ch03_042-077.indd 50 10/31/17 06:57 PM

With the advent of technology, calculations involving the TVM and related concepts in mortgage lending, valuation, and investments have been greatly simplified. Many TVM and related concepts involve equations with exponents, which can make derivations and solving for solutions cumbersome. Professionals in the field of finance have come to use either, or both, financial calculators and computer software (Excel) that are programmed and allow computations to be made much quicker and more efficiently.

What follows is a glossary of functions that are used frequently in the chapters that follow. The reader should become familiar with these functions and the notation.

PMT (n, i, PV, FV)—Function to calculate level payments (annuity) that occur over a speci- fied time period that have a specified present value and may include a final payment in the future.

PV (n, i, PMT, FV)—Function to calculate the present value of level payments (annuity) and/or an amount to be received at a single point in time in the future.

FV (n, i, PV, PMT)—Function to calculate the future value of an annuity and/or level pay- ments (annuity) that occur over a specified time period.

i (n, PV, PMT, FV)—Function to calculate the interest rate (also an IRR) that would be achieved on an investment made in the present that will have level payments over time and/or a future value at the end of the specified investment period (n).

n (i, PV, PMT, FV)—Function to calculate the number of periods (n) required to repay a loan (PV) at a specified rate of interest (i) for various future values (zero, non zero).

Notes:

1. Values for variables in these functions must be adjusted for frequency of receipts and disbursements as well as compounding and discounting intervals within a year.

2. In the most basic applications, these variables are assumed to be constant with respect to time. In those problems requiring that some variables (e.g., PMT) be allowed to vary from period to period, we will provide the proper approach to modify functions and solve for solutions as needed.

3. It will become apparent to the reader after solving TVM and related problems that a recur- ring pattern occurs. This pattern usually involves one equation containing five variables: i, n, PV, FV, and PMT. Most problems provide values (inputs) for four of these variables, leaving one unknown for which a solution is being sought. (See glossary of functions above where the variable listed to the left of the parenthesis is the unknown.) This nota- tion should enable the reader to identify the unknown variable more readily.

Financial Functions Concept Box 3.1

Solution: Function:

n

=

1 year

i

=

6%

PMT = 0 PV

=

− $10,000

Solve for FV

=

$10,600

FV (n, i, PV, PMT)

(Note that this solution is the same as what would have been obtained had we calculated the factor 1.060000 shown in Exhibit 3–3. However, when a calculator is used, the intermediate step in which interest factors are calculated is eliminated.)

The same problem compounded monthly would follow the format listed below. Note: Several calculators include a function for a number of periods. In such cases, the number

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 51

bru19684_ch03_042-077.indd 51 10/31/17 06:57 PM

Solution: Function:

n

=

24  (2 years × 12 periods)

i =

.666% (8% / 12 periods)

PMT = 0 PV

=

− $5,000

Solve for FV

=

$5,864.44

FV (PV, i, n, PMT)

Solution: Function:

n

=

12  (1 year  × 12 periods per year)

i =

.5%  (6%/ 12 periods per year)

PMT = 0 PV

=

− $10,000

Solve for FV

=

$10,616.78

FV (i, n, PV, PMT)

What rate can you earn on your savings today? Go to a website like www.bankrate.com that has interest rates on certificates of deposit (CDs) and see what the current

rate is for a five-year CD. Assuming you have $10,000 today, how much will that accumulate to after five years at the rate you found on the website?

Web App

Solution: Function:

n

=

365  (1 year × 365 periods per year)

i =

.0164 (6% / 365 periods per year)

PMT = 0 PV

=

− $10,000

Solve for FV

=

$10,618.31

FV (i, n, PV, PMT)

Solution: Function:

n

=

4 years

i =

10%

PMT = 0 PV

=

− $5,000

Solve for FV

=

$7,320.50

FV (PV, i, n, PMT)

of periods and interest are typically stated on an annual basis, and the number of periods is entered separately.

(Note that this solution is the same as what would have been obtained had we calculated the factor 1.061678 shown in Exhibit 3–4.)

The same problem compounded daily would look like this.

Question: What is the future value of $5,000 deposited for four years compounded annually at a rate of 10 percent?

Question: What is the future value of a single $5,000 deposit earning 8 percent interest, compounded monthly, at the end of two years?

Final PDF to printer

52 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 52 10/31/17 06:57 PM

Present Value

In the preceding section, we were concerned with determining value at some time in the future; that is, we considered the case where a deposit had been made and compounded into the future to yield some unknown future value.

In this section, we are interested in the problem of knowing the future cash receipts for an investment and of determining how much should be paid for the investment at present. The concept of present value is based on the idea that money has time value. Time value simply means that if an investor is offered the choice between receiving $1 today or receiv- ing $1 in the future, the proper choice will always be to receive the $1 today because this $1 can be invested in some opportunity that will earn interest, which is always preferable to receiving only $1 in the future. In this sense, money is said to have time value.

When determining how much should be paid today for an investment that is expected to produce income in the future, we must apply an adjustment called discounting to income received in the future to reflect the time value of money. The concept of present value lays the cornerstone for calculating mortgage payments, determining the true cost of mortgage loans, and finding the value of an income property, all of which are very important con- cepts in real estate finance.

A Graphic Illustration of Present Value An example of how discounting becomes an important concept in financing can be seen from the following problem. Suppose an individual is considering an investment that prom- ises a cash return of $10,600 at the end of one year. The investor believes this investment should yield an annual rate of 6 percent. The question is how much should the investor pay today if $10,600 is to be received at the end of the year and the investor requires a 6 percent return compounded annually on the amount invested?

The problem can be seen more clearly by comparing it with the problem of finding the compound value of $1 discussed in the first part of this chapter. In that discussion, we were concerned with finding the future value of a $10,000 deposit compounded monthly at 6 percent for one year. This comparison is depicted in Exhibit 3–5.

In Exhibit 3–5 note that with compounding, we are concerned with determining the future value of an investment. With discounting, we are concerned with just the opposite concept; that is, what present value or price should be paid today for a particular invest- ment, assuming a desired rate of interest is to be earned?

Because we know from the preceding section that $10,000 compounded annually at a rate of 6 percent results in a future value of $10,600 at the end of one year, $10,000 is the present value of this investment. However, had we not done the compounding problem in the preceding section, how would we know that $10,000 equals the present value of the investment? Let us again examine the compounding problem considered in the previous section. To determine future value, recall the general equation for compound interest:

FV = PV (1 + i) n

Month

2 4 6 8 10 12

Compounding at 6% $10,000

Future value(?)

Discounting at 6%

Present value(?) $10,600

EXHIBIT 3–5 Comparison of Future Value and Present Value

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 53

bru19684_ch03_042-077.indd 53 10/31/17 06:57 PM

In our present value problem, PV becomes the unknown because FV, or the future value to be received at the end of one year, n = 1 year, is known to be $10,600. Because the interest rate (i) is also known to be 6 percent, PV is the only value that is not known. PV, the pres- ent value or amount we should pay for the investment today, can be easily determined by rearranging terms in the above compounding formula as follows:

FV

=

PV (1 + i) n

PV

= FV 1 ______ (1 + i) n

In our problem, then, we can determine PV directly by substituting the known values into the above expression as follows:

PV

=

FV 1 ______ (1 + i) n

=

$10,600 1 _______

(1 + .06) 1

=

$10,600 1 ____

1.06

=

$10,600 ×  (.943396)

=

$10,000

Note that the procedure used in solving for the present value is simply to multiply the future value, FV,by 1 divided by (1 + i) n . We know from the section on compounding that in our problem (1 + i) n is (1 + .06) 1 , which equals 1.06. Dividing 1 by 1.06 yields .943396. This result is important in present value analysis because it shows the relationship between future value and present value.

Because we see from Exhibit 3–5 that the discounting process is the opposite of compounding, to find the present value of any investment is simply to compound in a “reverse sense.” This is done in our problem by taking the reciprocal of the interest factor for the compound value of $1 at 6 percent, 1 ÷ 1.06 , or .943396, and multiplying it by the future value of the investment to find its present value. We can now say that $10,600 received at the end of one year, when discounted by 6 percent, has a present value of $10,000. Alternatively, if we are offered an investment that promises to yield $10,600 after one year and we want to earn a 6 percent annual return, we should not pay more than $10,000 for the investment (it is on the $10,000 present value that we earn the 6 percent interest).

Calculating Present Value Interest Factors Because the discounting process is the reverse of compounding, and the interest factor for discounting 1 ÷  (1 + i) n is simply the reciprocal of the interest factor for compounding, a series of present value interest factors have been developed. Exhibit 3–6 contains a sample of factors to be used when discounting.

In our problem, we want to know how much should be paid for an investment with a future value of $10,600 to be received at the end of one year if the investor demands an annual return of 6 percent. The solution can be found by calculating or selecting .943396 from the 6 percent column in Exhibit 3–6. The $10,600 future value can now be multiplied by .943396, resulting in a present value (PV) of $10,000. To help the reader understand

Final PDF to printer

54 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 54 10/31/17 06:57 PM

these concepts, this present value factor also may be determined using a financial calculator as follows:

  Rate

Year 6% 10% 15%

  1 .943396 .909091 .869565   2 .889996 .826446 .756144   3 .839619 .751315 .657516   4 .792094 .683013 .571753   5 .747258 .620921 .497177   6 .704961 .564474 .432328   7 .665057 .513158 .375937

EXHIBIT 3–6 Interest Factors for the Present Value Reversion of $1 for Various Interest Rates and Time Periods

Solution:

PV

=

$20,000 ×  1 _______ (1 + .15) 3

= $20,000 (.657516)

=

$13,150.32

Solution: Function:

n

=

1 year

i

= 6%

PMT = $0 FV

=

$1

Solve for PV

=

.943396

PV (n, i, PMT, FV)

Question: How much should an investor pay today for a real estate investment that will return $20,000 at the end of three years, assuming the investor desires an annual return of 15 percent interest on the amount invested?

The investor should pay no more than $13,150.32 today for the investment promising a return of $20,000 after three years if a 15 percent return on investment is desired.2

Expanding the Use of Calculators for Finding Present Values As was the case with compounding, financial calculators allow us to calculate present value solutions directly, as they have been programmed to calculate factors internally and then complete the required operations to present a final answer. Our problem can be solved with a calculator as follows:

2 An accepted convention in finance is that when one refers to a percentage return on investment, a nominal annual interest rate is assumed. If solutions are computed based on different compounding intervals within a year, such as monthly, the solution should be designated as an annual rate of interest compounded monthly. The latter solution may then be converted, if desired, to an effective annual yield, as shown previously.

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 55

bru19684_ch03_042-077.indd 55 10/31/17 06:57 PM

Solution: Function:

FV

=

$1

PMT

=

0

n = 12 months i

=

6% ÷ 12

Solve for PV

=

.941905

PV (FV, PMT, n, i )

Solution: Function:

n

=

1 year × 12 periods = 12

i

=

6% ÷ 12 periods = .5% PMT = 0

FV

=

10,616.80

Solve for PV

=

− $10,000

PV (n, i, PMT, FV )

Solution: Function:

n

=

3 years

i

=

15%

PMT = 0 FV

=

$20,000

Solve for PV

=

− $13,150.32

PV (FV, PMT, n, i )

Because we can use the discounting process to find the present value of a future value when annual compounding is assumed, we can also apply the same methodology assum- ing monthly discounting. For example, in our illustration involving monthly compounding, the future value of $10,000 at an annual rate of interest of 6 percent compounded monthly was $10,616.80. An important question an investor should consider is how much should be paid today for the future value of $10,616.80 received at the end of one year, assuming that a 6 percent return compounded monthly is required?

We could answer this question by finding the reciprocal of the formula used to com- pound monthly, 1 ÷  (1 + i / 12) 1⋅12 , and multiply that result by the future value of $10,616.80 to find the present value (PV). We may calculate this factor with a calculator as

Many factors have been calculated and included in the table shown in Exhibit 3–7. In our problem, we want to determine the present value of $10,616.80 received at the end

of one year, assuming a desired rate of return of 6 percent, compounded monthly. By going to the 6 percent column and the row corresponding to one year (12 months) and selecting the interest factor .941905, we can now multiply $10,616.80 ×  (.941905)  = $10,000 and see that $10,000 is the maximum amount one should pay today for the investment.

Alternatively, if the reader is comfortable with the derivation of these interest factors and the discounting process, a solution may be found more directly with a calculator as follows:

Final PDF to printer

56 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 56 10/31/17 06:57 PM

  Rate  

Month 6% 8% 9%  

1 .995025 .993377 .992556   2 .990075 .986799 .985167   3 .985149 .980264 .977833   4 .980248 .973772 .970554   5 .975371 .967323 .963329   6 .970518 .960917 .956158   7 .965690 .954553 .949040   8 .960885 .948232 .941975   9 .956105 .941952 .934963  

10 .951348 .935714 .928003   11 .946615 .929517 .921095   12 .941905 .923361 .914238  

Year Month

1 .941905 .923361 .914238 12 2 .887186 .852596 .835831 24 3 .835645 .787255 .764149 36 4 .787098 .726921 .698614 48

EXHIBIT 3–7 Interest Factors for the Present Value Reversion of $1 for Various Interest Rates and Time Periods

Question: How much should an investor pay to receive $12,000 three years (36 months) from now, assuming that the investor desires an annual return of 9 percent compounded monthly?

Solution: PV

=

$12,000 (.764149)

= $9,169.79

Solution: Function:

n

=

3 × 12 = 36

i

=

9% ÷ 12 = .75% PMT = 0

FV =

12,000

Solve for PV

=

− $9,169.79

PV (n, i, PMT, FV)

The investor should pay no more than $9,169.79 for the investment, or the present value (PV) of the investment is $9,169.79.

Compound or Future Value of an Annuity

The first section of this chapter dealt with finding the compound or future value of a single deposit or payment made only once, at the beginning of a period. An equally relevant consideration involves a series of equal deposits or payments made at equal intervals. For example, assume deposits of $1,000 are made at the end of each year for a period of five years and interest is compounded at an annual rate of 5 percent. What is the future value

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 57

bru19684_ch03_042-077.indd 57 10/31/17 06:57 PM

at the end of the period for a series of deposits plus all compound interest? In this case, the problem involves equal payments (P) or deposits made at equal time intervals. This series of deposits or payments is defined as an annuity. Because we know how to find the answer to a problem where only one deposit is made, it is logical and correct to assume that the same basic compounding process applies when dealing with annuities. However, that process is only a partial solution to the problem because we are dealing with a series of deposits that occur annually.

To compute the sum of all deposits made in each succeeding year and include com- pound interest on deposits only when it is earned, the general formula for compounded interest must be expanded as follows:

FV = P (1 + i) n−1  + P (1 + i) n−2  + ⋯ +P This may also be written as

FV = P ⋅  ∑ t=1

n−1

(1 + i) t  + P

which simply means that we may take the constant payment or annuity P and multiply it by the “sum of” the series 1 + i expanded from time t = 1 to the period n − 1, plus P.3 Hence, the symbol Σ represents the “sum of” that series and is simply a shortcut notation to be used in place of writing 1 + i repetitively.

In this expression, FV is now future value of an annuity, or the sum of all deposits, P, compounded at an annual rate, i, for n years. The important thing to note in the expression, however, is that each deposit is assumed to be at the end of each year and is compounded through year n. The final deposit does not earn interest because it occurs at the end of the final year. Since we are dealing in our example with a series of $l,000 deposits made over a five-year period, the first $1,000 deposit is compounded for four periods (n − 1) , the $1,000 deposit made at the beginning of the second year is compounded for three periods (n − 2) , and so on, until the last deposit, P, is reached. The last deposit is not compounded because it is deposited at the end of the fifth year.4

To compute the value of these deposits, we could construct a solution like that shown in Exhibit 3–8. Note that each $1,000 deposit is compounded from the end of the year in which the deposit was made to the end of the next year. In other words, as shown in our expanded formula above, the deposit at the end of year l is compounded for four years, the deposit made at the beginning of the second year is compounded for three years, and so on. By carrying this process out one year at a time, we determined the solution, or $5,525.63, when the compounded amounts in the extreme right-hand column are added.

Although the future value of $1,000 per period can be determined in the manner shown in Exhibit 3–8, careful examination of the compounding process reveals another, easier way to find the solution. Note that the $1,000 deposit occurs annually and never changes; it is constant. When the deposits are constant, it is possible to sum all of the individual interest factors (IFs) as 5.525631. By multiplying $1,000 by 5.525631, a solution of $5,525.63 is obtained, as shown at the bottom of the right-hand column in Exhibit 3–8.

3 The formula shown here is the formula for an ordinary annuity, which assumes that all deposits are made at the end of each year. The final P in the expression means that the last payment is not compounded. 4 The reader should be aware that this formulation is used for ordinary annuities or when payments or receipts occur at the end of a period. This is different from the formula for an annuity due, which assumes that deposits are made at the beginning of a period.

Final PDF to printer

58 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 58 10/31/17 06:57 PM

Use of Compound Interest Factors for Annuities Because the IFs in Exhibit 3–8 can be added when annuities are being considered, a series of new interest factors have been calculated for various interest rates. A sample of these factors has been compiled in Exhibit 3–9.

In the problem at hand, to determine the future value of $1,000 deposited annually at 5 percent for five years, note that if we go to the 5 percent column in Exhibit 3–9 and obtain the IF that corresponds to five years, we can find the solution to our problem as follows:

FV

=

$1,000 (5.525631)

= $5,525.63

This amount corresponds to the solution obtained from the long series of multiplications carried out in Exhibit 3–8.

As we have explained, for those readers who understand the compounding process and the equations discussed in the sections above, financial calculators programmed to per- form and store the necessary steps for compounding annuities may be used to obtain an answer more directly as follows:

  Rate

Year 5% 6% 10%

  1 1.000000 1.000000 1.000000   2 2.050000 2.060000 2.100000   3 3.152500 3.183600 3.310000   4 4.310125 4.374616 4.641000   5 5.525631 5.637093 6.105100

  6 6.801913 6.975319 7.715610   7 8.142008 8.393838 9.487171   8 9.549109 9.897468 11.435888  

EXHIBIT 3–9 Interest Factors for the Accumulation of $1 per Period for Various Interest Rates and Time Periods

Year Deposit Interest Factor Future Value

1 $1,000   × 1.215506 = $1,215.51* 2 1,000 × 1.157625 =   1,157.63* 3 1,000 × 1.102500 =   1,102.50  4 1,000 × 1.050000 =   1,050.00  5 1,000 × 1.000000 =   1,000.00

Also 1,000         × 5.525631 = $5,525.63*

*Rounded.

EXHIBIT 3–8 Interest Factors for the Future Value of an Annuity of $1,000 per Year Compounded at 5 Percent Annually

Solution: Function:

n

=

5

i

=

5%

PV = 0 PMT

=

− $1,000

Solve for FV

=

$5,525.63

FV (n, i, PV, PMT)

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 59

bru19684_ch03_042-077.indd 59 11/28/17 02:40 PM

Solution: FV

=

$800 (7.715610)

= $6,172.49

Solution: !V

=

$200 (73.476856)

= $14,695.37

Question: What is the future value of $800 deposited each year for six years, com- pounded annually at 10 percent interest after six years?

Solution: Function:

n

=

6

i

=

10%

PV = 0 PMT

=

− $800

Solve for FV

=

$6,172.49

FV (n, i, PV, PMT)

The same procedure used for compounding annuities for amounts deposited or paid annually can also be applied to monthly annuities. A very simple modification can be made to the formulation used for annual annuities by substituting i/12 in place of i and adding the number of compounding periods per year (m) in the annual formulation, as follows:

FV = P [ 1 +  i ___ 12 ] n⋅m−1

 + P [ 1 +  i ___ 12 ] n⋅m−2

 + ⋯ + P

or

FV = P ⋅  ∑ t=1

n⋅m−1

[ 1 +  i ___ 12 ] t

 + P

However, in this formulation, n⋅m represents months. Deposits or payments, P, are made monthly and are constant in amount. Hence, the interest factors used to compound each monthly deposit may be added (as they were for annual deposits in Exhibit 3–8), and a new series for compounding monthly annuities can be computed. This has been done for selected interest rates and years.5

Question: An investor pays $200 per month into a real estate investment that prom- ises to pay an annual rate of interest of 8 percent compounded monthly. If the investor makes consecutive monthly payments for five years, what is the future value at the end of five years?

5 Like annual compounding, this formulation assumes that deposits are made at the end of each month, or that an ordinary annuity is being compounded.

Final PDF to printer

60 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 60 10/31/17 06:57 PM

In this case, the value of payments earning interest at an annual rate of 8 percent com- pounded monthly = $14,695.37.

Present Value of an Annuity

In the preceding section, our primary concern was to determine the future value of an annuity, or constant payments received at equal time intervals. In this section, we consider the present value of an annuity, or the series of annual income receipts the investment produces over time. Because an investor may have to consider a series of income payments when deciding whether to invest, this is an important problem. Recall that when dealing with the present value of a single receipt, or ending value, PV, we took the basic formula for compounding interest and rearranged it to determine the present value of an investment as follows:

FV = PV (1 + i) n

PV = FV ÷  (1 + i) n

PV = FV ·  1 ______

(1 + i) n

To consider the present value of an annuity, we need only consider the sum of individual present value for all payments/receipts. This can be done by modifying the basic present value formula as follows:

PV = PMT 1 ______ (1 + i) 1

 + PMT 1 ______ (1 + i) 2

 + PMT 1 ______ (1 + i) 3

 + ⋯ +PMT 1 ______ (1 + i) n

or this can be written as

PV = PMT ⋅  ∑ t=1

n

1 _____ (1 + i) t

Note in this expression that each payment (PMT) is discounted for the number of years corresponding to the time when the funds were actually received. In other words, the first payment would occur at the end of the first period and would be discounted only one period, or PMT ⋅  [ 1 ÷  (1 + i) 1 ] . The second receipt would be discounted for two periods, or PMT ⋅  [ 1 ÷  (1 + i) 2 ] , and so on.

Assuming an individual is considering an investment that will provide a series of annual cash receipts of $500 for a period of six years, and the investor desires a 6 percent return, how much should the investor pay for the investment today? We can begin by consider- ing the present value of the $500 receipt in year 1, as shown in Exhibit 3–10. Note that the present value of the $500 receipt is discounted for one year at 6 percent. This is done

Solution: Function:

n

=

5 × 12 = 60 months

i

=

8% / 12 = .666% PV = 0

PMT =

− $200

Solve for FV

=

$14,695.37

FV (n, i, PV, PMT)

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 61

bru19684_ch03_042-077.indd 61 10/31/17 06:57 PM

because the income of $500 for the first year is not received until the end of the first period, and our investor only wants to pay an amount today (present value) that will assure a 6 per- cent return on the amount paid today. Therefore, by discounting this $500 payment by the interest factor for 6 percent, or .943396, the present value is $471.70. Note that the second $500 income payment is received at the end of the second year. Therefore, it should be discounted for two years at 6 percent. Its present value is found by multiplying $500 by the interest factor for 6 percent for two years, or .889996, giving a present value of $445. This process can be continued for each receipt for the remaining three years (see Exhibit 3–10). The present value of the entire series of $500 income payments can be found by adding the series of receipts discounted each month in the far right-hand column, which totals $2,458.66.

However, because the $500 series of payments is constant, we may simply sum all inter- est factors to obtain one interest factor that can be multiplied by $500 to obtain the same present value (see Exhibit 3–10). The sum of all interest factors for 6 percent is 4.917324. When 4.917324 is multiplied by $500, the present value, $2,458.66, found in the lengthy series of multiplications carried out in Exhibit 3–10, is again determined.

Now that the reader has been introduced to the equations and interest factors that result from these equations, a solution can be found directly using a financial calculator as follows:

Year PMT IF Present Value

1 $500 ×   .943396 = $  471.70 2 500 ×   .889996 =      445.00 3 500 ×   .839619 =      419.81 4 500 ×   .792094 =      396.05 5 500 ×   .747258 =      373.63 6 500 ×   .704961 =      352.48

Also $500 × 4.917324 = $2,458.66†

†Rounded.

EXHIBIT 3–10 Present Value of $500 per Year (discounted at 6 percent annually)

Solution: Function:

n

=

6

i

=

6%

PMT = − $500 FV

=

0

Solve for PV

=

$2,458.66

PV (n, i, FV, PMT)

Use of the Present Value of an Annuity Factors As we have illustrated, the interest factors in Exhibit 3–10 may be summed, as long as the income payments are equal in amount and received at equal intervals. The sums of IFs for various interest rates have been compiled in table form and are listed in Exhibit 3–11. In our problem, we want to determine the present value of $500 received annually for six years, assuming a desired annual rate of return of 6 percent. How much should an investor pay for this total investment today and be assured of earning the desired return? We can solve this problem by computing the solution with a calculator or by looking at Exhibit 3–11, finding the 6 percent column, and looking down the column until we locate the IF in the row corresponding to six years, which is 4.917324. Thus,

Final PDF to printer

62 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 62 11/28/17 02:41 PM

Rate

Year 5% 6% 10% 15%

  1   .952381   .943396   .909091   .869565   2 1.859410 1.833393 1.735537 1.625709   3 2.723248 2.673012 2.486852 2.283225   4 3.545951 3.465106 3.169865 2.854978   5 4.329477 4.212364 3.790787 3.352155   6 5.075692 4.917324 4.355261 3.784483   7 5.786373 5.582381 4.868419 4.160420   8 6.463213 6.209794 5.334926 4.487322

EXHIBIT 3–11 Interest Factors for the Present Value of an Ordinary Annuity of $1 per Period for Various Interest Rates and Time Periods

PV

=

$500 (4.917324)

= $2,458.66

This solution corresponds to that obtained in Exhibit 3–10.

Question: An investor has an opportunity to invest in a rental property that will provide net cash returns of $400 per year for three years. The investor believes that an annual return of 10 percent should be earned on this investment. How much should the inves- tor pay for the rental property?

Solution: PV

=

$400 (2.486852)

= $994.74

The investor should pay no more than $994.74 for the investment property. With that amount, a 10 percent return will be earned.

A more direct solution to this problem can be found by using a financial calculator as follows:

Solution: Function:

n

=

3

i

=

10%

PMT = − $400 FV

=

0

Solve for PV

=

$994.74

PV (n, i, PMT, FV)

Based on the logic used in discounting annuities paid or received annually, the same procedure can be applied to cash receipts paid or received monthly. In this case, the for- mula used to discount annual annuities is simply modified to reflect monthly receipts or payments, and the discounting interval is changed to reflect monthly compounding:

PV = P ⎡ ⎢ ⎣ 1 ______ 1 +  i ___

12 ⎤ ⎥ ⎦ 1

 + P ⎡ ⎢ ⎣ 1 ______ 1 +  i ___

12 ⎤ ⎥ ⎦ 2

 + ⋯ + P ⎡ ⎢ ⎣ 1 ______ 1 +  i ___

12 ⎤ ⎥ ⎦ 12⋅n

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 63

bru19684_ch03_042-077.indd 63 10/31/17 06:57 PM

where payments (P) occur monthly, the exponents represent months running from l through n·m, and PV now represents the present value of an annuity received over n·m months.

Like annual discounting, computation of the present value of an annuity can be very cumbersome if one has to expand the above formula for each problem, particularly if the problem involves cash receipts or payments over many months. Hence, a series of inter- est factors have been computed by expanding the above formula for each monthly inter- val and adding the resulting interest factors (this was performed with discounting annual annuities in Exhibit 3–10). Like the annual tables, the factors in Exhibit 3–12 are labeled Present Value of an Ordinary Annuity of $1 per Period because the period in this case is one month. Hence, if an investor wants to know how much he or she should pay today for an investment that would pay $500 at the end of each month for the next 12 months and earn an annual rate of return of 6 percent compounded monthly on the investment, the investor can easily compute the solution with a calculator or determine it by consulting Exhibit 3–12. Looking to the 6 percent column and dropping down to the row correspond- ing to 12 months, you find the factor 11.618932. Multiplying $500 by 11.618932 results in $5,809.47, or the amount that the investor should pay today if a 6 percent rate of return compounded monthly is desired.

The calculator solution would be

Solution: Function:

n

=

12 months

i

=

6% ÷ 12 = .005 PMT = $500

FV

=

0

Solve for PV

=

$5,809.47

PV (n, i, PMT, FV)

Rate

Month 6% 8%

  1   .995025   .993377   2 1.985099 1.980176   3 2.970248 2.960440   4 3.950496 3.934212   5 4.925866 4.901535   6 5.896384 5.862452   7 6.862074 6.817005   8 7.882959 7.765237   9 8.779064 8.707189 10 9.730412 9.642903 11 10.677027   10.572420   12 11.618932   11.495782  

Year Month

  1 11.618932   11.495782   12

  2 22.562866   22.110544   24   3 32.871016   31.911806   36   4 42.580318   40.961913   48

EXHIBIT 3–12 Interest Factors for the Present Value of an Ordinary Annuity of $1 per Period for Various Interest Rates and Time Periods

Final PDF to printer

64 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 64 10/31/17 06:57 PM

Question: A real estate partnership predicts that it will pay $300 at the end of each month to its partners over the next six months. Assuming the partners desire an 8 per- cent return compounded monthly on their investment, how much should they pay?

Solution: PV

=

$300 (5.862452)

= $1,758.74

Solution: Function:

n

=

6 months

i

= 8% ÷ 12 = .6666%

PMT = − $300 FV

=

0

Solve for PV

=

$1,758.74

PV (n, i, PMT, FV)

Accumulation of a Future Sum

The previous two sections have dealt with compounding and discounting single payments on annuities. In some instances, however, it is necessary to determine a series of payments necessary to accumulate a future sum, taking into account the fact that such payments will be accumulating interest as they are deposited. For example, assume we have a debt of $20,000 that must be repaid in one lump sum at the end of five years. We would like to make a series of equal annual payments (an annuity) at the end of each of the five years, so that we will have $20,000 at the end of the fifth year from the accumulated deposits plus interest. Assuming that we can earn 10 percent interest per year on those deposits, how much should each annual payment be?

In this case, we are dealing with accumulating a future sum. Recall from Exhibit 3–5 that this means we will be compounding a series of payments, or an annuity, to achieve that future value. Hence, we can work with the procedure for determining future values by compounding as follows:

FV

=

$20,000

PMT (6.105100)

=

$20,000

PMT

=

$20,000  ÷  6.105100

=

$3,275.95

Solution: Function:

n

=

5

i

=

10%

PV = 0 FV

=

$20,000

Solve for PMT 

=

− $3,275.95

PMT (n, i, PV, FV)

This computation merely indicates that when compounded at an annual interest rate of 10 percent, the unknown series of equal payments (PMT) will result in the accumulation of $20,000 at the end of five years. Given the interest factor for compounding an annual annu- ity at 10 percent from Exhibit 3–9, 6.105100, we know that the unknown payment (PMT),

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 65

bru19684_ch03_042-077.indd 65 10/31/17 06:57 PM

Solution: Function:

n

=

5 × 12 = 60

i

=

10% ÷ 12  = .008333 PV = 0

FV =

$20,000

Solve for PMT

=

− $258.27

PMT (n, i, PV, FV)

when multiplied by that factor, will result in $20,000. Hence, by dividing $20,000 by the interest factor for compounding an annual annuity, we can obtain the necessary annual payment of $3,275.95. The result tells us that if we make payments of $3,275.95 at the end of each year for five years, and each of those payments earns interest at an annual rate of 10 percent, a total of $20,000 will be accumulated at the end of five years.

We can see from the above computation that dividing $20,000 by 6.105100 is equiva- lent to multiplying $20,000 by (1 ÷ 6.105100) , or .163797, and the same $3,275.95 solu- tion results. The factor .163797 is referred to in real estate finance as a sinking-fund factor (SFF), which is also used in other applications in real estate. In the case of monthly payments, if we want to know what monthly payments would be necessary to pay off the $20,000 debt at the end of five years, taking into account that each payment will earn an annual rate of 10 percent compounded monthly, we can obtain a calculator solution as follows:

Required monthly payments would be $258.27.

Determining Yields, or Internal Rates of Return, on Investments

Up to now, this chapter has demonstrated how to determine future values in the case of compounding and present values in the case of discounting. Each topic is important in its own right, but each has also provided tools for determining an equally important compo- nent used extensively in real estate financing, that is, calculating rates of return, or invest- ment yields. In other words, the concepts illustrated in the compounding and discounting processes can also be used to determine rates of return, or yields, on investments, mortgage loans, and so on. These concepts must be mastered because procedures used here will form the basis for much of what follows in succeeding chapters.

We have concentrated previously on determining the future value of an investment made today when compounded at some given rate of interest, or the present investment value of a stream of cash returns received in the future when discounted at a given rate of interest. In this section, we are concerned with problems where we know what an investment will cost today and what the future stream of cash returns will be, but we do not know what yield, or rate of return (compounded), will be earned if the investment is made.

Investments with Single Receipts In many cases, investors and lenders are concerned with the problem of what rate of com- pound interest, or investment yield, will be earned if an investment is undertaken. To illustrate the investment yield concept, assume an investor has an opportunity today to buy an unimproved one-acre lot for $5,639. The lot is expected to appreciate in value and

Final PDF to printer

66 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 66 10/31/17 06:57 PM

to be worth $15,000 after seven years. What rate of interest (or investment yield) would be earned on the $5,639 investment in the property if it were made today, held for seven years, and sold for $15,000? Note from our previous discussion of compounding that the $15,000 also represents the receipt of a future cash flow or future value (FV).

To solve for the unknown rate, we can formulate the problem as follows:

PV

=

FV ⋅  1 ______

(1 + i) n

$5,639 =

$15,000 ⋅  1 ______

(1 + i) 7

We want to know the annual rate of compound interest, i, that, when substituted into the above equation, will make the $15,000 future receipt, or future value, equal to the $5,639 investment outlay, or present value, today.

One approach is to rearrange the above equation as follows:

1 ______ (1 + i) 7

=

5,639 ______ 15,000

(1 + i) 7 = 15,000 / 5,639 1 + i

=

1.15

i

=

.15 or 15%

Another approach is to use trial-and-error to solve for i. A value for i is estimated; then the equation is solved to ascertain whether the future value, or $15,000, when discounted to present value, PV, will equal $5,639. When the correct value for i is found, the solution for present value should yield $5,639.

How do we begin the search for i? One way is to simply guess a solution. Let us try 10 percent. Mathematically we ask, if

PV = $15,000 1 _______ (1 + .10) 7

is PV = $5,639 ? Solving for PV, we have

PV

=

($15,000) (.513158)

= $7,697

We note that $7,697 or PV is much greater than the desired PV, or $5,639. This means that the yield, or rate of compound interest earned on the investment, is greater than 10  percent. Hence, we must continue the discounting process by increasing i.

Our next “trial” will be 15 percent. Substituting, we have

PV

=

$15,000 1 _______

(1 + .15) 7

= $15,000 (.375937)

=

$5,639.06

This time PV equals $5,639. This “guess” was correct. From this result, we have determined that the yield or internal rate of return, i, earned on the investment is equal to 15 percent.

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 67

bru19684_ch03_042-077.indd 67 10/31/17 06:57 PM

Solution: Function:

n

=

7

PV

=

− $5,639 PMT = 0

FV

=

$15,000

Solve for i

=

15%

i (n, PV, PMT, FV)

We have, in essence, “removed” interest compounded at the rate of 15 percent for seven years from the $15,000 receipt of cash (the future value), leaving the initial deposit, or present value, of $5,639.

When trying to find the yield in which only one future value is involved, we can use an approach where the interest factor in the financial tables is first determined as follows:

$5,639

=

$15,000 1 ______

(1 + i) 7

$5,639.06 ÷ $15,000  =

.375937

=

The above calculations show that the interest factor is .375937, but we still do not know the interest rate. However, we do know that the time period over which the investment is to appreciate in value is seven years. Because our solution is .375937 and the term of invest- ment is seven years, the interest tables in Exhibit 3–6 allow us to easily find the correct interest rate. Since the FV or cash return of $15,000 is a single receipt, we need only locate a factor for the present value reversion of $1 equal to .375937 in the row corresponding to seven years for some interest rate. We begin the search for the interest rate by choosing an arbitrary interest rate, say 6 percent. The 6 percent column in Exhibit 3–6 shows the factor in this column for seven years is .665057, which is larger than .375937. Moving to the 10 percent column, the factor for seven years is .513158, which is lower than the factor at 5 percent but comes closer to the solution that we are looking for. If we continue this trial-and-error process, the 15 percent column indicates that the factor for seven years is .375937; therefore, the interest rate we desire is 15 percent. We know this is the correct answer because $15,000  (.375937)  = $5,639.06.

A more efficient approach to finding the yield or internal rate of return is to use a finan- cial calculator. For calculators that have the capability to solve for yields such as required by the problem at hand, we have

What does this interest rate, or yield, mean? It means that the $5,639 investment made today, held for seven years, and sold for $15,000, is equivalent to investing $5,639 today and letting it compound annually at an interest rate of 15 percent (note the correspondence between the terms interest rate and yield).6 This fact can be determined with the following computation:

FV

=

$5,639 (2.660020)

= $15,000

6 We are now using the terms yield and internal rate of return for i, instead of the interest rate. It is generally accepted practice to use the terms yield or internal rate of return when evaluating investments. The term interest rate is generally used when loan terms are being quoted by lenders. The two concepts are very similar, but the reader should become accustomed to these differences in usage.

Final PDF to printer

68 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 68 10/31/17 06:57 PM

This calculation simply shows that $5,639 compounded annually at an interest rate of 15 percent for seven years is $15,000. Hence, making this investment is equivalent to earn- ing a rate of return of 15 percent. This rate of return is usually referred to as the investment yield or the internal rate of return.

Solution: Function:

n

=

7

i 

=

15%

PV = − $5,639 PMT

=

0

Solve for FV

=

$15,000

FV (n, i, PV, PMT)

The internal rate of return integrates the concepts of compounding and present value. It represents a way of measuring a return on investment, expressed as a compound rate of interest, over the entire investment period. For example, if an investor is faced with making an investment in an income-producing venture, regardless of how the cash returns are pat- terned, the internal rate of return provides a guide or comparison for the investor. It tells the investor what the equivalent compound interest rate will be on the investment being considered. In the example of the unimproved one-acre lot, the 15 percent yield or internal rate of return is equivalent to making a deposit of $5,639 and allowing it to compound annually at an interest rate of 15 percent for seven years. After seven years, the investor would receive $15,000, which includes the original investment of $5,639 plus all com- pound interest. With the internal rate of return known, the investor can make an easier judgment about what investment to make. If the 15 percent return is adequate, it will be made; if not, the investor should reject it.7

The concepts of the internal rate of return or yield, present value, and compounding are indispensable tools that are continually used in real estate finance and investment. The reader should not venture beyond this section without a firm grasp of the concepts that have been explained. These concepts form the basis for the remainder of this chapter and the chapters that follow.

Yields on Investment Annuities The concepts illustrated for a single receipt of cash (when the unimproved lot was sold) also apply to situations where a series of cash receipts is involved. Consequently, a yield or internal rate of return also can be computed on these types of investments.

Suppose an investor has the opportunity to make an investment in real estate cost- ing $3,170 that would provide him with cash income of $1,000 at the end of each year for four years. What investment yield, or internal rate of return, would the investor earn on the $3,170? In this case, we have a series of receipts that we wish to discount by an unknown rate to make the present value of the $1,000 annuity equal the original invest- ment of $3,170. We need to find a solution for i in this problem, or the rate of interest that will make the present value of the $1,000 four-year annuity equal to $3,170. Recalling the notation for the present value of an annuity, we have

PV = PMT ⋅  ∑ t=1

n

1 _____ (1 + i) t

7 When comparing different investments, the investor must also consider any differences in risk. This topic is discussed in later chapters.

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 69

bru19684_ch03_042-077.indd 69 10/31/17 06:57 PM

Substituting gives

$3,170 = $1,000  ∑ t=1

n

1 _____ (1 + i) t

Using our shorthand notation, we can express our problem as follows:

$3,170 ÷ $1,000

=

∑ t=1

n

1 _____ (1 + i) t t

3.170000 =

∑ t=1

n

1 _____ (1 + i) t t

Solution: Function:

n

=

4

PV

=

− $3,170 PMT = $1,000

FV

=

0

Solve for i

=

10%

i (n, PV, PMT, FV)

This procedure is similar to solving for the yield, or internal rate of return, on single receipts discussed in the preceding section, except that we are now dealing with an annuity. Using the same procedure as before, we solve for the interest factor for a four-year period that will correspond to some interest rate. To determine what the interest rate is, search the factors in Exhibit 3–11 (p. 62) in the four-year row until you find a column containing a factor very close to 3.1700. A careful search reveals that the factor will be found in the 10 percent column (the reader should verify this). Hence, based on this procedure, we have determined that the investment yield or internal rate of return (IRR) on the $3,170 invested is 10 percent. A more in-depth analysis of what the internal rate of return means is pre- sented in Exhibit 3–13.

An important component of this analysis is to first determine if the investment outlay of $3,170 will be recovered from total cash inflows. In Exhibit 3–13 we can see that cash inflows (cash received in years 1–4) total $4,000. Therefore, in addition to recovering the investment of $3,170, $830 in additional cash flow will be received and we can say that the investment will be profitable, or that the investment yield (IRR) must be positive.

When the internal rate of return is computed, two additional characteristics are pres- ent (see Exhibit 3–13). One is the recovery of capital in each period, and the other is interest earned in each period. In other words, when the IRR is computed based on the $3,170 investment and the $1,000 received each year, implicit in the cash flows recov- ered each year during the four-year period is the full recovery of the $3,170 investment plus interest. Note also that the total interest/profit that will be received equals $830 or ($4,000 − $3,170) . Our goal is to simplify this investment result by finding a rate of com- pound interest for this investment. This result can be compared with compound rates of interest in other investments that may have different investment and cash flow patterns. Comparing interest rates (IRRs) on various investments is easier than comparing cash flows. We also benefit because the time value of money (TVM) is taken into account. Hence, the 10 percent investment yield is really a rate of compound interest earned on an outstanding investment balance, after each capital recovery is taken into account, from year to year. Of the total $4,000 received during the four-year period, total interest earned

Final PDF to printer

70 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 70 10/31/17 06:57 PM

is $830 and capital recovery is $3,170. This is also equivalent to earning a 10 percent annual rate of compound interest on our investment.

Monthly Annuities: Investment Yields A similar application for investment yields can be made in cases where monthly cash annuities will be received as a return on investment. For example, assume that an investor makes an investment of $51,593 and will receive $400 at the end of each month for the next 20 years (240 months). What annual rate of return, compounded monthly, would be earned on the $51,593?

Year

1 2 3 4

Investment (balance) $3,170 $2,487   $1,736   $   910   IRR at 10% 317 249* 174* 91* Cash received $1,000 $1,000  $1,000  $1,000  Less: Cash yield at 10%      317      249       174          90*

Recovery of investment $   683 $   751  $   826  $   910  Investment (beginning of year) $3,170 $2,487 $1,736 $   910  Less: Recovery of investment      683      751      826      910 

Investment (end of year) $2,487 $1,736 $   910 $        0 

*Rounded.

EXHIBIT 3–13 Illustration of the Internal Rate of Return (IRR) and Components of Cash Receipts

Solution: Function:

n

=

20 × 12 = 240

PV

=

− $51,593

PMT

=

$400

FV

=

0

Solve for i

i  (monthly)

=

0.5833%

i  (annualized)

=

.005833  × 12, or 7%

i (n, PV, PMT, FV)

As was the case with finding the IRR for investments with annual receipts, we find that the IRR is 7 percent compounded monthly on the $51,593 investment. Both the recovery of $51,593 and the $44,407 in interest were embedded in the stream of $400 monthly cash receipts ($96,000 in total receipts) over the 20-year period.

Equivalent Nominal Annual Rate (ENAR): Extensions Earlier in this chapter, we dealt with the problem of determining equivalent annual yields in cases where more than one compounding interval exists within a year. In our example, we showed the effective annual yield for a $10,000 investment compounded annually, monthly, and daily to be 6, 6.17, and 6.18 percent, respectively. In many situations, we may already know the effective annual yield (EAY) and would like to know the nominal annual rate of interest compounded monthly (or for any period less  than one year). For example, we considered a problem in which compounding occurred monthly based on a nominal annual rate of interest of 6 percent. Because compounding occurred in monthly intervals, the effective annual interest rate (6.17%) was larger than the nominal rate (6%).

Final PDF to printer

bru19684_ch03_042-077.indd 71 10/31/17 06:57 PM

In Exhibit 3–13, we introduced the IRR concept in the context of an investment with cash inflows of $1,000 per year, or a level annuity. In many situations investors must evaluate investments with cash inflows that vary from period to period. Investors in these situations also must know the IRR. However, when cash inflows vary, solving for the IRR is slightly more complicated. To illustrate, assume that we have an investment with these characteristics:

PV __________ Investment __________

$8,182

Cash Flows  ("#) _________________________________

Yr.1 _______ $1,000

Yr.2 _______ $2,000

Yr.3 _______ $3,000

Yr.4 _______ $4,000

To solve for the IRR (i), we have

PV =  " # 1 ______ (1 + i) 1

 +  " # 2 ______ (1 + i) 2

 +  " # 3 ______ (1 + i) 3

 +  " # 4 ______ (1 + i) 4

Substituting

$8,182 =  $1,000 ______ (1 + i) 1

 +  $2,000 ______ (1 + i) 2

 +  $3,000 ______ (1 + i) 3

 +  $4,000 ______ (1 + i) 4

Summing the cash inflows shows that a total of $10,000 will be received over four years; therefore, we know that because this total exceeds the PV of $8,182, the investment will be profitable and (i) will also be positive. (At this point, the reader should verify that the current value for (i) needed to make the right side of the equation equal to the PV of $8,182 is 7 percent.) However, as the reader may realize, solving for (i) is very cumbersome.

Introduction of the CFj Function. Many financial calculators and software programs have been designed to more efficiently solve for IRRs when cash flows vary from period to period. These programs use a “trial and error” or “iterative” approach to solve for (i). This approach begins by first choosing a very large value for (i), substituting it in the above expression, and then solving for PV. The difference between the value calculated for PV and $8,182 is deter- mined to ascertain how close this difference is to zero. The process continues by selecting values for (i) and recalculating PV. By using successively higher, then lower values for (i), PVs are calculated until an (i) is found such that the difference between the calculated PV and $8,182 is equal to zero.

With advances in electronic technology, these many calculations can be carried out very quickly by using the CFj and nj functions. This involves entering cash flows (CFj) per period (nj), then solving for (i). In our example, we would have

Solution:

Additional Financial Functions Concept Box 3.2

Enter CF Enter nj

C F j

=

− $8,182

C F j

=

   $1,000

C F j

=    $2,000

C F j

=

   $3,000

C F j

=

   $4,000

Solve for  (i )

=

   7%

n $

=

1

n $

=

1

n $ = 1 n $

=

1

n $

=

1

When each cash flow is for a single period, we will use the following notation for the IRR function:

IRR  ( CF 1 ,  CF 2 ,… , C F n )

For the above example, we would have IRR (− 8182, 1000, 2000, 3000, 4000)  = 7%.

71

Final PDF to printer

72 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 72 10/31/17 06:57 PM

Assuming that we wanted to know what the nominal annual rate of interest, compounded monthly,  would have to be to provide a desired EAY of 6 percent, we can employ the following formula, where ENAR is the equivalent nominal annual rate, compounded monthly:

ENAR =  [ (1 + EAY) 1/m  − 1 ]  ⋅ m In our problem, we would have

ENAR

=

[ (1 + .06) 1/m  − 1 ]  ⋅ 12

= [ (1 + .06) .083333  − 1 ]  ⋅ 12

= [ 1.004868 − 1 ]  ⋅ 12

=

.0584106 or 5.84106%  (rounded)

To illustrate this concept, if we have investment A, which will provide an effective annual yield of 6 percent, and we are considering investment B, which will provide interest com- pounded monthly, we would want to know what the equivalent nominal annual rate (ENAR) of interest, compounded monthly, would have to be on investment B to provide the same effective annual yield of 6 percent. That rate would be an annual rate of 5.84106 percent, compounded monthly.

FV

=

$1 [ 1 +  0.584106 ________ 12 ]

12

=

$1.06  (rounded)

From our example, we know that the EAY is ($1.06 − $1.00)  ÷ $1.00, or 6 percent. Hence, we now know that an investment of equal risk, with returns compounded monthly, must have an annual nominal rate of interest of at least 5.84106 percent to provide us with an equivalent, effective annual yield of 6 percent. Obviously, this application can be modified for any investment with different compounding periods by altering m in the above formula.

Solution: Function:

n

=

12 months

i

=

5.84106 ÷ 12 = .486755% PV = − $1

PMT

=

0

Solve for FV

=

$1.06

FV (n, i PV, PMT )

Solving for Annual Yields with Partial Periods: An Extension Many investments produce monthly cash flows but call for investment returns to be reported as an effective annual rate. However, many investments may be sold within a year (say, after five months into a calendar year). How can monthly cash flows within a year be expressed as an annual rate of interest? Consider the following example.

An investment is made in the amount of $8,000 and is expected to be owned for two years. The contract calls for investment returns to be reported as an effective annual rate. However, the investment is sold early and monthly cash flows of $500 are received for 17 months. What is the equivalent annual return on the investment? This can be deter- mined as follows:

Final PDF to printer

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 73

bru19684_ch03_042-077.indd 73 10/31/17 06:57 PM

Therefore, this investment over a 17-month period has produced an equivalent effective annual yield (EAY) of 8.5 percent. (Note that this yield is also equivalent to a nominal annual rate, compounded monthly, which would be .682083 × 12 = 8.19 percent. )

Note on the XIRR An alternative way of calculating an effective annual rate is to calculate what is referred to as the XIRR. The XIRR has been increasingly used in performance measurement because it is included in spreadsheet programs like Excel and can handle cash flow patterns that include partial years, as in the previous example, as well as cash flow patterns that are irregular and can occur any day of the year.

The XIRR is the rate that solves the following equation ∑ P j ∕ (1 + rate) d j /365  = 0

where Pj is the jth payment that is received dj days after the starting date of the investment. Excel allows you to actually input calendar dates for each payment (cash flow), which is then converted to the number of days. The left side of the above equation simply discounts the cash flows to a present value using the effective annual rate as the discount rate. We need to find the rate that makes the PV equal to zero.

Using the previous example of $500 occurring monthly for 17 months, we assume that cash flows are now received on about the 30th of each month over the 17 months, as shown in Exhibit 3–14. Column 2 has the days as a fraction of 365. Recall that we calculated an effective annual rate of 8.5 percent in the previous example. We now prove that the XIRR cal- culation gives the same result by using 8.5 percent to see if the result is a zero present value.

Column 3 of Exhibit 3–14 uses the effective annual rate in the above XIRR formula because we want to show that this is the rate that makes the present value equal to $0, which it does, as can be seen by the sum of the final column. Each row in this final column indicates the present value of the payment received on that day of the year.

In the above example the cash flows occurred monthly. But cash flows can occur on any day of the year. In Excel, the actual date (e.g., February 12, 2012) would be used in the XIRR function to specify that a cash flow occurred on that date.

STEP 1:

Solution: Solve for monthly interest rate Function:

n

=

17 months

PMT

=

$500

PV = − $8,000 FV

=

0

Solve for i

=

.682083%

i (n, PMT, PV, FV )

STEP 2: The monthly interest rate of .682083% can now be used to determine the effective annual rate as follows:

Solution: Function:

PV

=

− $1

i =

.682083%

PMT = 0 n

=

12

Solve for FV

=

1.084991

FV (PV, i, PMT, n)

STEP 3: The effective annual rate of interest would be: (FV / PV )  − 1 = 1.084991 − 1.000 = .084991 or 8.5%  (rounded)

Final PDF to printer

74 Part 2 Mortgage Loans

bru19684_ch03_042-077.indd 74 10/31/17 06:57 PM

Rate 8.5%

(1) (2) (3) (4)

Month Days Days/365 P (1 + rate) (days/365) P/Column 3 0 0 0.000000 –8,000 1.000000 –$8,000.00 1 31 0.084932 500 1.006953 496.55 2 61 0.167123 500 1.013727 493.23 3 92 0.252055 500 1.020775 489.82 4 122 0.334247 500 1.027643 486.55 5 152 0.416438 500 1.034557 483.30 6 182 0.498630 500 1.041517 480.07 7 213 0.583562 500 1.048758 476.75 8 243 0.665753 500 1.055814 473.57 9 274 0.750685 500 1.063155 470.30

10 305 0.835616 500 1.070547 467.05 11 336 0.920548 500 1.077990 463.83 12 366 1.002740 500 1.085243 460.73 13 396 1.084932 500 1.092544 457.65 14 425 1.164384 500 1.099648 454.69 15 455 1.246575 500 1.107046 451.65 16 485 1.328767 500 1.114494 448.63 17 515 1.410959 500 1.121992 445.64

Sum .00

EXHIBIT 3–14 Proof of XIRR

annual percentage yield (APY), 46

annuity, 57 annuity due, 57 compound interest, 42 discounting, 52 effective annual yield (EAY), 45

equivalent nominal annual rate (ENAR), 72

future value (FV), 43 future value of an annuity, 57 internal rate of return

(IRR), 68 investment yield, 65

ordinary annuity, 57 present value (PV), 43 present value of an

annuity, 60 rate of return, 65 sinking-fund factor (SFF), 65 yield, 65

Key Terms

Conclusion This chapter introduced and illustrated the mathematics of compound interest in financial analysis. Although this may be a review for many readers, a thorough understanding of this topic is essential in real estate finance. The concepts and techniques introduced in this chap- ter are used throughout the remainder of this text to solve a variety of problems encountered in real estate finance. In the following two chapters, we apply the mathematics of finance to the calculation of mortgage payments and the effective cost of various alternative mortgage instruments. Later, we apply the mathematics of finance to the analysis of income prop- erty investments. This chapter illustrated the use of financial tables, interest factors, and how these tables and factors can be found using a financial calculator. These tables were included to help the reader to understand the process of compounding, discounting, and finding internal rates of return by using interest factors. The tables are not necessary to solve any of the problems in the remainder of the book. In fact, an alternative calculator solution is also provided for many of the problems. The interest factor solutions are shown only so that the readers can see the mathematics behind the calculator solutions. As we move toward more advanced material, it is assumed that readers can obtain the solutions using a financial calculator or by using a spreadsheet program on a personal computer.

Final PDF to printer

bru19684_ch03_042-077.indd 75 10/31/17 06:57 PM

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 75

1. What is the essential concept in understanding compound interest? 2. How are the interest factors (IFs) in Exhibit 3–3 developed? How may financial calculators be

used to calculate interest factors in Exhibit 3–3? 3. What general rule can be developed concerning maximum values and compounding intervals

within a year? 4. What does the time value of money (TVM) mean? 5. How does discounting, as used in determining present value, relate to compounding, as used in

determining future value? How would present value ever be used? 6. What are the interest factors in Exhibit 3–9 and how are they developed? How can financial

calculators be used to calculate interest factors in Exhibit 3–9? 7. What is an annuity? How is it defined? What is the difference between an ordinary annuity and

an annuity due? 8. How must one discount a series of uneven receipts to find present value (PV)? 9. What is the sinking-fund factor? How and why is it used? 10. What is an internal rate of return? How is it used? How does it relate to the concept of com-

pound interest?

Questions

1. Jim makes a deposit of $12,000 in a bank account. The deposit is to earn interest compounded annually at the rate of 6 percent for seven years.

a. How much will Jim have on deposit at the end of seven years? (Hint: What is future value?) b. Assuming the deposit earned a 9 percent rate of interest compounded quarterly, how much

would he have at the end of seven years? c. In comparing (a) and (b), what are the respective effective annual yields? (Hint: Consider

the future value of each deposit after one year only.) Which alternative is better? 2. Would you prefer making a $25,000 investment that will earn interest at the rate of 6 percent

compounded monthly or making the same $25,000 investment at 7 percent compounded annu- ally? (Hint: Consider one year only.)

3. Jones can deposit $5,000 at the end of each six-month period for the next 12 years and earn interest at an annual rate of 8 percent, compounded semiannually. What will the value of the investment be after 12 years? If the deposits were made at the beginning of each year, what would the value of the investment be after 12 years?

4. Suppose you deposit $1,250 at the end of each quarter in an account that will earn interest at an annual rate of 10 percent compounded quarterly. How much will you have at the end of four years?

5. Suppose you deposit $2,500 at the end of year 1, nothing at the end of year 2, $750 at the end of year 3, and $1,300 at the end of year 4. Assuming that these amounts will be compounded at an annual rate of 15 percent, how much will you have on deposit at the end of five years?

6. Suppose you have the opportunity to make an investment in a real estate venture that expects to pay investors $750 at the end of each month for the next eight years. You believe that a reason- able return on your investment should be an annual rate of 15 percent compounded monthly.

a. How much should you pay for the investment? b. What will be the total sum of cash you will receive over the next eight years? c. What do we call the difference between (a) and (b)?

Problems

Useful Websites

www.bai.org—Good source of current market rates on various financial instruments as well as discussion of ways to properly compare investments with different payment patterns. www.interest.com—This site provides the current average mortgage rates, a mortgage calculator, and basic information on home buying. www.bankrate.com—Source of interest rates for CDs and other investments.

Final PDF to printer

bru19684_ch03_042-077.indd 76 10/31/17 06:57 PM

76 Part 2 Mortgage Loans

7. An investor is considering an investment that will pay $2,150 at the end of each year for the next 10 years. He expects to earn a return of 12 percent on his investment, compounded annually. How much should he pay today for the investment? How much should he pay if the investment returns are received at the beginning of each year?

8. An investor can make an investment in a real estate development and receive an expected cash return of $45,000 at the end of six years. Based on a careful study of other investment alterna- tives, she believes that a 9 percent annual return compounded quarterly is a reasonable return to earn on this investment. How much should she pay for it today?

9. Walt is evaluating an investment that will provide the following returns at the end of each of the following years: year l, $12,500; year 2, $10,000; year 3, $7,500; year 4, $5,000; year 5, $2,500; year 6, $0; and year 7, $12,500. Walt believes that he should earn 12 percent compounded annu- ally on this investment. How much should he pay for this investment? What if he expects to earn an annual return of 9 percent compounded monthly? How much should he pay?

10. John is considering the purchase of a lot. He can buy the lot today and expects the price to rise to $15,000 at the end of 10 years. He believes that he should earn an investment yield of 8 percent compounded annually on his investment. The asking price for the lot is $7,000. Should he buy it? What is the internal rate of return compounded annually on the investment if John purchases the property for $7,000 and is able to sell it 10 years later for $15,000?

11. The Dallas Development Corporation is considering the purchase of an apartment project for $100,000. They estimate that they will receive $15,000 at the end of each year for the next 10 years. At the end of the 10th year, the apartment project will be worth nothing. If Dallas purchases the project, what will be its internal rate of return, compounded annually? If the company insists on an 8 percent return compounded annually on its investment, is this a good investment?

12. A corporation is considering the purchase of an interest in a real estate syndication at a price of $75,000. In return, the syndication promises to pay $1,000 at the end of each month for the next 25 years (300 months). If purchased, what is the expected internal rate of return, compounded monthly? How much total cash would be received on the investment? How much is profit and how much is return of capital?

13. An investment in a real estate venture will provide returns at the end of the next four years as follows: year 1, $5,500; year 2, $7,500; year 3, $9,500; and year 4, $12,500. An investor wants to earn a 12 percent return compounded annually on her investment. How much should she pay for the investment? Assuming that the investor wanted to earn an annual rate of 12 percent com- pounded monthly, how much would she pay for this investment? Why are these two amounts different?

14. A pension fund is making an investment of $100,000 today and expects to receive $1,600 at the end of each month for the next five years. At the end of the fifth year, the capital investment of $100,000 will be returned. What is the internal rate of return compounded annually on this investment?

15. A loan of $60,000 is due 10 years from today. The borrower wants to make annual payments at the end of each year into a sinking fund that will earn compound interest at an annual rate of 10 percent. What will the annual payments have to be? Suppose that the monthly payments earn 10 percent interest, compounded monthly. What would the annual payments have to be?

16. An investor has the opportunity to make an investment that will provide an effective annual yield of 12 percent. She is considering two other investments of equal risk that will provide compound interest monthly and quarterly, respectively. What must the equivalent nominal annual rate (ENAR) be for each of these two investments to ensure that an equivalent annual yield of 12 percent is earned?

17. An investment producing cash flows in the amount of $1,200 per month is undertaken for a period of 28 months. The investor pays $24,000 for the investment and the contract stipulates that investment returns must be reported on a basis equivalent with annual compounding. Given that the investment is sold after 28 months, what would be the equivalent annual compound rate

Final PDF to printer

bru19684_ch03_042-077.indd 77 10/31/17 06:57 PM

Chapter 3 Mortgage Loan Foundations: The Time Value of Money 77

of interest reported to the investor? What would be the annual rate compounded monthly for this investment?

18. An investment is expected to produce the following annual year-end cash flows:

year 1: $5,000 year 4: $5,000 year 2: $1,000 year 5: $6,000 year 3: $0 year 6: $863.65

The investment will cost $13,000 today. a. Will this investment be profitable? b. What will be the IRR (compounded annually) on this investment? c. Prove your answer in (b) by showing how much of each year’s cash flow is recovery of

the $13,000 investment and how much of the cash flow is return on investment. (Hint: See Exhibit 3–13 and Concept Box 3.2.)

Final PDF to printer

78

bru19684_ch04_078-121.indd 78 10/31/17 07:07 PM

Chapter 4 Fixed Interest Rate Mortgage Loans This chapter deals with various approaches to pricing and structuring fixed interest rate mortgage loans. By pricing a loan, we refer to the rate of interest, fees, and other terms that lenders offer and that borrowers are willing to accept when mortgage loans are made. As a part of the pricing process, we also stress the supply and demand for loanable funds, the role of inflation, and how both affect the rate of interest. As to loan structuring, we review the many innovations in mortgage payment patterns that have evolved from changes in the economic environment.

Another major objective of this chapter is to illustrate techniques for determining the yield to the lender and actual cost to the borrower when various provisions exist in loan agreements. Lenders on real estate commonly include various charges and fees in addi- tion to the interest rate as a condition of making a loan. These charges may include loan discounts, origination fees, prepayment penalties, or prepaid interest. In addition, various amortization or loan repayment schedules can be agreed upon by the borrower and lender to facilitate financing a particular real estate transaction. Because these provisions often affect the cost of borrowing, the methodology used to compute the yield to the lender (cost to the borrower) is heavily stressed.

Determinants of Mortgage Interest Rates: A Brief Overview

Changing economic conditions have forced the real estate finance industry to go through an important evolution. These changing conditions now require lenders and borrowers to have a better understanding of the sources of funds used for lending and the nature of how risk, economic growth, and inflation affect the availability and cost of mortgage funds.

When considering the determinants of interest rates on mortgage loans, we must also consider the demand and supply of mortgage funds. Most mortgage lenders are intermedi- aries, or institutions that serve as conduits linking flows of funds from savers to borrowers. Borrowers use the savings in the form of mortgage credit. The market rate of interest on mortgage loans is established by what borrowers are willing to pay for the use of funds over a specified period of time and what lenders are willing to accept in the way of com- pensation for the use of such funds. On the demand side of the market, it can be safely said

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 79

bru19684_ch04_078-121.indd 79 10/31/17 07:07 PM

that the demand for mortgage loans is a derived demand, or is determined by the demand for real estate.

When supplying funds to the mortgage market, lenders also consider returns and the associated risk of loss on alternative investments in relation to returns available on mort- gages. Hence, the mortgage market should also be thought of as part of a larger capital market, where lenders and investors evaluate returns available on mortgages and all com- peting forms of investment, such as bonds, stocks, and other alternatives, and the relative risks associated with each. Should lenders believe that a greater return can be earned by making more mortgage loans (after taking into account the costs and the risk of loss) than would be the case if they invested in corporate bonds or business loans, more funds would be allocated to mortgage loans, and vice versa. Hence, lender decisions to allocate funds to mortgages are also made relative to returns and risk on alternative loans and investment opportunities.

The Real Rate of Interest: Underlying Considerations When discussing market interest rates on mortgages, we should keep in mind that these interest rates are based on a number of considerations. We pointed out earlier that the sup- ply of funds allocated to mortgage lending in the economy is, in part, determined by the returns and risks on all possible forms of debt and investment opportunities.

One fundamental relationship that is common to investments requiring use of funds in the economy is that they earn at least the real rate of interest.1 This is the minimum rate of interest that must be earned by savers to induce them to divert the use of resources (funds) from present consumption to future consumption. To convince individuals to make this diversion, income in future periods must be expected to increase sufficiently from interest earnings to divert current income from consumption to savings. If expected returns earned on those savings are high enough to provide enough future consumption, adequate amounts of current savings will occur.

Interest Rates and Inflation Expectations In addition to the real rate of interest, a concern that all investors have when making invest- ment decisions is how inflation will affect investment returns. The rate of inflation is of particular importance to investors and lenders making or purchasing loans made at fixed rates of interest over long periods of time. Hence, when deciding whether to make such commitments, lenders and investors must be convinced that interest rate commitments are sufficiently high to compensate for any expected loss in purchasing power during the period that the investment or loan is outstanding; otherwise, an inadequate real return will be earned. Therefore, a consensus of what lenders and investors expect inflation to be during the time that their loans and investments are outstanding is also incorporated into interest rates at the time investments and loans are made.

To illustrate the relationship between the nominal interest rate, or the contract interest rate agreed on by borrowers and lenders, and real rates of interest, suppose that a $10,000 loan is made at a nominal or contract rate of 10 percent with all principal and interest due at the end of one year. At the end of the year, the lender would receive $11,000, or $10,000 plus $10,000 times (.10). If the rate of inflation during that year was 6 percent, then the $11,000 received at the end of the year would be worth about $10,377  ($11,000 ÷ 1.06) . Thus, although the nominal rate of interest is 10 percent, the real rate on the mortgage is

1 If the reader can visualize an investment portfolio containing investments in all productive activities in the economy based on the weight that any particular activity has to the total value of all productive activity in the economy, the rate of current earnings on such a portfolio would be equivalent to the real rate of interest. Such a rate would also be the rate required by economic units to save rather than consume from the current income.

Final PDF to printer

bru19684_ch04_078-121.indd 80 10/31/17 07:07 PM

80 Part 2 Mortgage Loans

just under 4 percent ($377 ÷ $10,000 = 3.77%) . Therefore, we conclude that if the lender wanted a 4 percent real rate of interest, the lender would have to charge a nominal rate of approximately 10 percent to compensate for the expected change in price levels due to inflation.2

We can summarize by saying that the nominal interest rate on any investment is par- tially determined by the real interest rate plus a premium for the expected rate of inflation. In our example, the real rate of 4 percent plus an inflation premium of 6 percent equals 10 percent. Note that this premium is based on the rate of inflation expected at the time that the loan is made. The possibility that inflation will be more or less than expected is one of many risks that lenders and investors must also consider.

We should also point out that the nominal interest rate is usually expressed as an annual rate of interest. However, depending on the type of loan, the nominal rate could be an annual rate compounded daily, monthly, quarterly, annually, or continuously. We will explore the effects of compounding, accrued interest, and payment patterns in more detail throughout this chapter.

Interest Rates and Risk In addition to expected inflation, lenders and investors are also concerned about various risks undertaken when making loans and investments. Lenders and investors are concerned about whether interest rates and returns available on various loans and investments com- pensate adequately for risk. Alternatively, will a particular loan or investment provide an adequate risk-adjusted return?

Many types of risk could be discussed for various investments, but they are beyond the scope of this book. Consequently, we will focus on risks affecting mortgage loans. Many of these risks are, however, present to greater and lesser degrees in other loans and investments.

Default Risk One major concern of lenders when making mortgage loans is the risk that borrowers will default on obligations to repay interest and principal. This is referred to as default risk, and it varies with the nature of the loan and the creditworthiness of individual borrow- ers. The possibility that default may occur means that lenders must charge a premium, or higher rate of interest, to offset possible loan losses. Default risk relates to the likelihood that a borrower’s income may fall after a loan is made, thereby jeopardizing the receipt of future mortgage payments. Similarly, a property’s value could fall below the loan balance at some future time, which could result in a borrower defaulting on payments and a loss to the lender.

Interest Rate Risk An additional complication in lending and investing arises from the uncertainty in today’s world about the future supply of savings, demand for housing, and future levels

2 Actually, the nominal rate of interest should be (1.06 × 1.04) − 1, or 10.24 percent, if a real rate of 4 percent is desired. For convenience throughout this text, we will add the real rate and premium for expected inflation as an approximation to the nominal interest rate. We should point out that the relationship of expected inflation and interest rates has long been a subject of much research. While we show a very simple, additive relationship in our discussion, there may be interaction between real interest rates and inflation. The specific relationship between the two is not known exactly. Hence, the student should treat this discussion at a conceptual or general level of interpretation.

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 81

bru19684_ch04_078-121.indd 81 10/31/17 07:07 PM

of inflation. Thus, interest rates at a given point in time can only reflect the market consensus of what these factors are expected to be. Investors and lenders also incur the risk that the interest rate charged on a particular loan may be insufficient, should economic conditions change drastically after a loan is made. The magnitude of these changes may have warranted a higher interest rate when the loan was made. The uncer- tainty about what interest rate to charge when a loan is made can be referred to as interest rate risk.

For example, anticipated inflation may have been 6 percent at the time our $10,000 loan was made. But if actual inflation turns out to be 8 percent, this means the interest rate that should have been charged is 12 percent. In this case, we say that the anticipated rate of inflation at the time the loan was made was 6 percent. However, because unanticipated inflation of 2 percent occurred, the lender will lose $200 in purchasing power (2% of $10,000) because the rate of interest was too low. This does not mean that lenders did not charge the “correct” interest rate at the time the loan was made. At that time, the inflation was expected to be 6 percent. Therefore, to be competitive, a 10 percent interest rate had to be charged. However, the additional 2 percent was unanticipated by all lenders in the market. It is unanticipated inflation that constitutes a major component of interest rate risk to all lenders.

The possibility that too low an interest rate was charged at the time the loan was made is a major source of risk to the lender. Hence, a premium for this risk must also be charged or reflected in the market rate of interest. Interest rate risk affects all loans, particularly those that are made with fixed interest rates, that is, where the interest rate is set for a lengthy period of time when the loan is made. Being averse to risk, lenders must charge a premium to incur this risk.

Prepayment Risk Some mortgage loans allow borrowers to prepay loans before the maturity date without a penalty. This, in effect, gives borrowers the option to prepay the loan, refinance, or pay off the loan balance if a property is sold. If loans are prepaid when interest rates fall, lend- ers must forgo the opportunity to earn interest income that would have been earned at the original contract rate. As funds from the prepaid loans are reinvested by lenders, a lower rate of interest will be earned. When interest rates increase, however, the loan is not as likely to be prepaid. The risk that the loan will be prepaid when interest rates fall below the loan contract rate is referred to as prepayment risk.

Other Risks There are additional risks that lenders and investors consider that may vary by type of loan or investment. For example, the liquidity or marketability of loans and investments will also affect the size of the premium that must be earned. Securities that can be easily sold and resold in well-established markets will require lower premiums than those that are more difficult to sell. This is called liquidity risk.

Legislative risk is another risk associated with mortgage lending that also may result in a premium. It can refer to changes in the regulatory environment in which markets oper- ate; for example, regulations affecting the tax status of mortgages, rent controls, state and federal laws affecting interest rates, and so on, are all possibilities that lenders face after making loans for specified periods of time. Lenders must assess the likelihood that such events may occur and be certain that they are compensated for undertaking these risks when loans are made.

Final PDF to printer

bru19684_ch04_078-121.indd 82 10/31/17 07:07 PM

82 Part 2 Mortgage Loans

A Summary of Factors Important in Mortgage Loan Pricing We can now see that the interest rate charged on a particular mortgage loan will depend on the real interest rate, anticipated inflation, interest rate risk, default risk, prepayment risk, and other risks. These relationships can be summarized in general as follows:

i = r + p + f In other words, when pricing or setting the rate of interest (i) on a mortgage loan, the lender must charge a premium ( p) sufficiently high to compensate for default and other risks and a premium ( f ) that reflects anticipated inflation to earn a real rate of interest (r) that is competitive with real returns available on other investment opportunities in the economy. If lenders systematically underestimate any of the components in the above equation, they will suffer real economic losses.

Pricing decisions by lenders are rendered complex because mortgage loans are made at fixed interest rates for long periods of time. For example, if we assume that a mortgage loan is to be made with a one-year maturity, the interest rate charged at origination should be based on what the lender expects each of the components discussed above to be during the coming year. More specifically,

i 1  =  r 1  +  p 1  +  f 1 or the mortgage interest rate (i) at origination (time t) would be based on the lender’s expectations of what the real rate of interest, the rate of inflation, and risk premiums (for risks taken in conjunction with making the mortgage loan over and above the level of risk reflected in the real rate of interest) should be for the term of the loan.

Understanding Fixed Interest Rate Mortgage (FRM) Loan Terms

As previously discussed in Chapter 2, there are many terms and options in mortgage loan agreements that are very important. We begin our analysis of fixed interest rate loans with a discussion of some of the most elementary terms: ∙ Loan amount ∙ Loan maturity date ∙ Interest rate ∙ Periodic payments

The loan amount identifies the amount borrowed and what the borrower is legally required to repay. The loan maturity date is the date by which the loan must be fully repaid. While these terms are relatively easy to understand, when analyzing and comparing vari- ous loan alternatives, the interest rate and its affect on periodic payments can be more complex and will be discussed further.

When dealing with fixed interest rate loans, in addition to the loan amount and matu- rity, lenders generally quote what is referred to as a nominal annual rate of interest. To elaborate, say a 30-year loan is made for $60,000 and the interest rate is 12 percent. That rate of interest is referred to as the nominal rate because no reference is made as to how interest is to be calculated or how frequent payments will be. If, in this case, inter- est is to be calculated monthly and payments are to be made monthly, one interpretation of the 12 percent nominal interest rate would be an annual rate of 12 percent interest compounded monthly. Recall from Chapter 3 that another way to interpret an annual rate of interest, compounded monthly, is to calculate its equivalent annual rate of inter- est. That is, a rate of interest compounded annually that would be equivalent to a loan

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 83

bru19684_ch04_078-121.indd 83 10/31/17 07:07 PM

with an annual rate of interest compounded monthly. This can be done in our example as follows:

STEP 1: Solution: Find the FV of an amount

that earns interest at an annual rate compounded monthly:

Function: FV (PV, i, n )

PV

=

− $60,000

i =

12% / 12 = 1% or .01

n

=

12

Solve for FV

=

$67,609.50

STEP 2: Find the equivalent annual interest rate compounded annually:

FV

=

$67,609.50

n

=

1

PV

=

$60,000.00

Solve for i

=

12.6825%

In Step 1, using our approach outlined in Chapter 3, we consider a $60,000 deposit made today and compounded monthly for 12 months at 12 percent, leaving an FV of $67,609.50. We then solve for the annual compound rate equivalent in Step 2 by changing the compounding period to 1. This produces i = 12.6825 percent. In other words, a loan quoted with a 12 percent annual rate of interest compounded monthly is equivalent to a loan with an annual rate of 12.6825 percent compounded annually. The difference in these rates is due to the fact that when interest on a loan is compounded monthly and paid monthly, the incremental value is greater than receiving cash flows annually.3 This is true even though the interest rate may be quoted as 12 percent in both cases. So, a loan with an annual rate of 12 percent compounded monthly is worth the equivalent of a loan with an annual rate of 12.6825 percent compounded annually. The latter can be thought of as an effective or equivalent annual rate of interest. Alternately, a loan with an annual rate of 12.6825 percent compounded annually is equivalent to a 12  percent annual rate com- pounded monthly.

So why do lenders quote nominal rates of interest (12% in our case)? If interest is to be compounded monthly (or for other periods), why not quote equivalent annual rates (12.6825% in our case)? If the latter approach was used, uniformity would be achieved because interest rates on all loans could be quoted based on an equivalent annual rate regardless of how frequently interest is calculated and payments are made (daily, monthly, quarterly, annually). The answer partially lies in the evolution of banking, financial instru- ments, simplicity when making interest calculations, and a general lack of knowledge (understanding) among people working in finance-related fields. In the discussion that follows, and throughout this book, we will follow the practice used by lenders and use the nominal rate of interest for all mortgage loan examples. In most cases, interest will be cal- culated monthly and payments will be made monthly. However, the reader should be aware that interest could be calculated and payments made over very different time periods.

3 The reader may recall that we discussed this concept with annual percentage yield (APY) in Chapter 3.

Final PDF to printer

bru19684_ch04_078-121.indd 84 10/31/17 07:07 PM

84 Part 2 Mortgage Loans

Calculating Payments and Loan Balances—Fixed Interest Rate Loans

The Importance of Accrued Interest and Loan Payments A very important concept that must be understood when calculating payments or outstand- ing loan balances for real estate loans is: (1) the relationship between accrued interest and loan payments for a given period and (2) how any differences between them will affect loan balances. For example, as discussed above, many loans require interest to be accrued monthly (i/12); that is, if a fixed interest rate mortgage (FRM) loan is made in an amount of $60,000 (PV) at a 12 percent interest rate and interest (i) is to be accrued monthly, the dollar amount of interest accrued as of the end of the first month would be calculated as

$60,000 ×  (.12 / 12)  = $600 We should also point out that (i/12) is referred to as the accrual rate. The amount of

interest accrued and owed to the lender at the end of the month will be $600. The borrower and lender may also negotiate payments (PMT). The ratio of these pay-

ments to the loan amount is referred to as the pay rate. If the borrower and lender agree that payments (PMT) to be made at the end of each month are to be equal to accrued inter- est, then the monthly pay rate and the monthly accrual rate are the same.4 This means that dollar payments (PMT) will be $600, or exactly equal to $600 accrued interest. When the monthly accrual rate and the monthly pay rate are equal, the outstanding loan balance remains unchanged. So, in our example, the loan balance would remain $60,000 at the end of the month. We should again stress at this point that, in any given period, the pay rate and accrual rate do not have to be equal.

Loan Amortization Patterns In the previous section, we emphasized the relationship between accrued interest and pay- ments on mortgage loans. We used the example of an interest-only loan which indicated that the pay rate and accrual rate were equal. When considering other loan types, we will see that the monthly accrual and pay rates are frequently not equal. There are many situa- tions when lenders and borrowers consider different loan structures and vary the pay rate and accrual rate. In these cases, loan balances will be affected and will change depending on the difference between the two.

Differences between Accrued Interest and Payments We now consider situations where the pay rate, and therefore, monthly payments are (1) greater than, (2) equal to, or (3) less than monthly accrued interest. We then consider the effect that each case has on loan balances. At this point in our discussion of constant payment mortgage (CPM) loans, we will use examples for fixed interest rate loans that are classified in four very general ways:

4 We will use monthly time periods for accrued interest and payments to limit the number of possible examples. The reader should be aware that accrual and payment periods do not have to be equal.

Type of CPM Loan Pay Rate Loan Balance at Maturity

1. Fully amortizing Greater than accrual rate Fully repaid 2. Partially amortizing Greater than accrual rate Not fully repaid 3. Interest only Equal to accrual rate Equal to amount borrowed 4. Negative amortizing Less than accrual rate Greater than amount borrowed

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 85

bru19684_ch04_078-121.indd 85 10/31/17 07:07 PM

Notice that the first loan type, which we refer to as fully amortizing, means that the pay rate will exceed the accrual rate. This means that monthly payments will exceed accrued interest by an amount sufficient to pay the accrued interest due each month and fully repay the loan by the maturity date.

The second loan type, or the partially amortizing loan, refers to the case when the borrower and lender agree that, like the fully amortizing loan, the pay rate will result in a payment that will exceed accrued interest, but not by as much as the payment for the fully amortizing loan. Therefore, the loan will not be fully repaid at maturity. It will be only partially repaid.

The third loan type, or the interest-only loan, is sometimes called a zero amor- tizing loan. As we have discussed, in this case the pay rate will equal the accrual rate. Consequently, the loan balance at the end of each month will remain the same as the origi- nal loan amount. The full, original, loan amount will have to be paid at maturity.

Finally, the fourth loan type, or the negative amortizing loan, represents the case where borrowers and lenders agree that the pay rate will be less than the accrual rate. As a result, payments will not equal the amount of interest due and the loan balance will actu- ally increase each month. At maturity, the loan balance will be greater than the original loan amount.

We will now illustrate payments for each category of loan. We also should note at this point that each category of loan will have constant, or level, monthly payments. We will discuss other monthly payment patterns later in this chapter.

Fully Amortizing, Constant Payment Mortgage (CPM) Loans The most common loan payment pattern used in real estate finance during the post- depression era, and one which is still very prevalent today, is the fully amortizing, con- stant payment mortgage (CPM). (Amortization means the process of loan repayment over time.) The CPM loan payment pattern is used most extensively in financing single family residences and, to a lesser extent, income-producing properties such as multifamily apart- ment complexes and shopping centers. This payment pattern means simply that a level, or constant, monthly payment is calculated on an original loan amount at a fixed rate of interest for a given term. Each monthly payment includes interest and some repayment of principal. At the end of the term of the CPM loan, the original loan amount, or principal, is completely repaid, or has been fully amortized. The lender has earned and the borrower has paid a fixed rate of interest on the monthly loan balance.

To illustrate how the monthly loan payment calculation is made, we turn to our previ- ous example of a $60,000 loan made at a 12 percent (nominal) rate of interest for 30 years. What are the constant monthly mortgage payments on this loan, assuming it is to be fully amortized at the end of 30 years? Based on our knowledge of discounting annuities from Chapter 3, the problem involves no more than finding the present value of an annuity and can be formulated as follows:

PV =  ∑ t=1

n

[ PM T t _ 1 +  i _ 12 ] t

where

PV

=

present value

PMT

=

payment

i =

fixed nominal, interest rate on mortgage

n

=

number of months loan will remain outstanding

Final PDF to printer

bru19684_ch04_078-121.indd 86 10/31/17 07:07 PM

86 Part 2 Mortgage Loans

because PMT is a constant, this is also equivalent to

PV = PMT ×  ∑ t=1

n

1 ______ (1 +  i __ 12 ) t

and

PMT =  PV _________ ∑ t=1

n

1 ______ (1 +  i __ 12 ) t

Solution: Function:

n

=

30 × 12 = 360

i

=

12%/ 12 = 1% or .01 PV = − $60,000

FV

=

0

Solve for PMT

=

$617.17

PMT (n, i, PV, FV )

In this case, we are interested in solving for PMT, or the constant monthly payment (annuity) that will fully repay the loan amount (PV) and earn the lender 12 percent interest compounded monthly. The required payment will be $617.17.

Consider the fully amortizing loan pattern illustrated in Exhibit 4–1. The initial, rela- tively low principal reduction, shown in column 6, results in a high portion of interest charges in the early monthly payments. Note that the ending loan balance after the first six months (column 6) is $59,894.36; thus, only $105.64 has been amortized from the original balance of $60,000 after six months. Interest paid during the same six-month period totals $3,597.38. The explanation for the high interest component in each monthly payment is

(1) (2) (3) (4) (5) (6)

Month Beginning

Loan Balance Monthly Payment

Interest (.12 ÷ 12) Amortization*

Ending Loan Balance

1 $60,000.00 $617.17 $600.00 $17.17 $59,982.83 2 59,982.83   617.17   599.83   17.34 59,965.49 3 59,965.49   617.17   599.65   17.52 59,947.97 4 59,947.97   617.17   599.48   17.69 59,930.28 5 59,930.28   617.17   599.30   17.87 59,912.41 6 59,912.41   617.17   599.12   18.05 59,894.36 . . . . . . . . . . . . . . . . . .

358 1,815.08   617.17   18.15   599.02 1,216.06 359 1,216.06   617.17   12.16   605.01 611.06 360 611.06   617.17     6.11   611.06 -0-

*Amortization increases each month by the factor 1 + i / 12 ; that is, 17.17 (1.01)  = 17.34, and so on.

EXHIBIT 4–1 Fully Amortizing Loan Pattern

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 87

bru19684_ch04_078-121.indd 87 10/31/17 07:07 PM

vthat the lender earns an annual 12 percent return (1 percent monthly) on the outstanding monthly loan balance. Because the loan is being repaid over a 30-year period, obviously the loan balance is reduced only very slightly at first and monthly interest charges are cor- respondingly high. Exhibit 4–1 also shows that the pattern of accrued interest in the early years of the loan reverses as the loan begins to mature. Note that during the last months of the loan, accrued interest declines sharply and amortization increases.

Interest, Principal, and Loan Balance Illustrated Exhibit 4–2 (panel A) illustrates the loan payment pattern over time, by indicating the rela- tive proportions of interest and principal in each monthly payment over the 30-year term of the loan. Exhibit 4–2 (panel B) shows the rate of decline in the loan balance over the same 30-year period. It is clear that the relative share of interest as a percentage of the total monthly mortgage payment declines very slowly at first. Note in panel A that halfway into the term of the mortgage, or after 15 years, interest still makes up $514.24 of the $617.17 monthly payment and principal the difference ($617.17 = $514.24 = $102.93) . Further, the loan balance after 15 years (panel B) is approximately $51,424. Total mortgage payments

EXHIBIT 4–2 Monthly Payment, Principal, Interest, and Loan Balances for a Fully Amortizing, Constant Payment Mortgage

$617.17

$514.24

$277.45

$60,000

$51,424

$27,745

Years

0 5 10 15 20 25 30

PanelA: Monthly Interest and Principal

Payment

Principal

Interest

Years

0 5 10 15 20 25 30

Panel B: Outstanding Loan Balance

Final PDF to printer

bru19684_ch04_078-121.indd 88 10/31/17 07:07 PM

Interest Rate

Years Months 9% 10% 11% 12%

  5 60 .020758 .021247 .021742 .022244 10 120 .012668 .013215 .013775 .014347 15 180 .010143 .010746 .011366 .012002 20 240 .008997 .009650 .010322 .011011 25 300 .008392 .009087 .009801 .010532 30 360 .008046 .008776 .009523 .010286

Prior to widespread use of financial calculators and spreadsheets, performing loan calcula- tions had to be done manually. Therefore, a series of tables containing what were referred to as loan constants were developed. These factors continue to be used in the vocabulary of the lending industry. Equivalent to the pay rate discussed earlier in the chapter, these con- stants are simply the present value of a monthly annuity for various interest rates and time periods. These can be applied to any FRM loan to determine the constant monthly payment.

Related to our example, if we desired we could calculate the loan constant as

Mortgage Loan Constants Fully Amortizing Loans Concept Box 4.1

Solution: Function:

PV

=

− $1

n

=

360

FV = 0 i

=

12% / 12 = 1 %  or .01

Solve for PMT

=

.01286 (or loan constant)

PMT (PV, n, FV, i )

This constant, or payment, can be applied to any fully amortizing loan made at 12 percent for 30 years (360 months) to determine the monthly payment. The term loan constant continues to be used in lending negotiations, loan agreements, and other discussions between lenders and borrowers. The loan constant can be multiplied by any beginning loan amount to obtain the monthly mortgage payments necessary to amortize the loan fully by the maturity date.

In the table above, we provide a sample of monthly mortgage loan constants (or pay rates) for various interest rates and loan maturities. Returning to our problem of finding the monthly mortgage payment for a $60,000 loan made at 12 percent for 30 years, we locate the 12 percent column and look down until we find the row corresponding to 30 years, where the loan constant is .010286 (rounded).* Loan constants are often stated on an annu- alized basis by multiplying the monthly loan constant by 12. In the above example, the annu- alized loan constant is .010286 ×  12 =  .123432, or  12.34% (rounded). Note that this is greater than the interest rate of 12 percent. The difference is how the loan gets amortized. If the annualized constant was 12 percent, it would be an interest-only loan. Note that the annualized loan constant still assumes that payments are made monthly.

88

* Because of rounding (to six decimal places), the loan constant is .010286. When we multiply $60,000 by the rounded constant, we get a monthly payment of $616.16. The more exact solution is $617.17. Hence, readers should be aware that small discrepancies between their solutions and ours may occur when financial calculators are used, because calculator solutions may be rounded off to eight or more decimal places. We have attempted to carry out solutions to at least six decimal places before rounding.

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 89

bru19684_ch04_078-121.indd 89 10/31/17 07:07 PM

of $111,090.60  ($617.17  ×  180  months) have been made through the 15th year, with approximately $8,576  (or $60,000 − $51,424) of the loan repaid at that point. This pattern reverses with time. Note in panel A that after 25 years, interest makes up only $277.45 of the monthly payment, and the loan balance (panel B) has declined sharply to $27,745.

The Effect of Maturity on Monthly Payments—Fully Amortizing Loans Exhibit 4–3 shows the effect of loan maturity on monthly payments for the base case mort- gage loan. The exhibit shows the extent to which levels of constant monthly payments decline as maturities negotiated by the lender and borrower increase. In our base case example of a $60,000, fully amortizing, 30-year loan made at 12 percent interest, monthly payments would decline from $860.83 for a maturity period of 10 years to $617.17 for a maturity of 30 years. This indicates the importance of loan maturity and its effects when negotiating a loan structure.

Partially Amortizing, Constant Payment Mortgage (CPM) Loans In many cases, loans may be structured to accomplish one or more goals. For example, the borrower may desire (1) a payment that is lower than what would be available with a fully amortizing loan and/or (2) a nonzero outstanding loan balance on the maturity date. This can be shown in the following example: A borrower and lender agree that a $60,000 loan made at 12 percent interest for 30 years will have a $40,000 balance (sometimes referred to as a balloon payment) on the maturity date. It will have constant monthly payments.

To solve for those payments, we modify the equation that was used to calculate the CPM with full amortization as follows:

PV =  ∑ t=1

n

PM T t ______ (1 +  i __ 12 ) t

 +  F V n ______ (1 +  i __ 12 ) n

The above equation differs in that the term FV is introduced and represents the desired outstanding balance (also frequently referred to as a balloon payment), at period n,  or maturity.

EXHIBIT 4–3 Relationship between Monthly Mortgage Payments and Maturity Periods: Fully Amortizing Loans

120

$617.17 $631.93

$660.65

$720.10

$860.83

180 Months

240 300 360

Final PDF to printer

bru19684_ch04_078-121.indd 90 10/31/17 07:07 PM

90 Part 2 Mortgage Loans

The calculator solution for our problem can be modified as follows:

Month Beginning

Loan Balance Monthly Payment

Interest (.12 ÷ 12) Amortization

Ending Loan Balance

1 $60,000.00 $605.72 $600.00 $     5.72 $59,994.28 2 59,994.28 605.72 599.94 5.78 59,988.50 3 59,988.50 605.72 599.88 5.84 59,982.66 4 59,982.66 605.72 599.83 5.90 59,976.76 5 59,976.76 605.72 599.77 5.95 59,970.81 6 59,970.81 605.72 599.71 6.01 59,964.79 . .       .       .       . . . .       .       .       . . . .       .       .       . .

358     40,605.03 605.72 406.05 199.67 40,405.35 359 40,405.35 605.72 404.05 201.67 40,203.69 360 40,203.69 605.72 402.04 203.69 40,000.00

EXHIBIT 4–4 Partially Amortizing Loan Pattern

Solution: Function:

n

=

360

i

=

12%/ 12 = 1% or .01 PV = − $60,000

FV

=

$60,000

Solve for PMT 

=

$600.00

PMT (n, i, FV, PV )

Solution: Function:

n

=

12 × 30 = 360

i

=

12%/ 12 = 1% or .01 PV = − $60,000

FV

=

$40,000

Solve for PMT

=

$605.72

PMT (n, i, PV, FV )

Note that the payment for the partially amortizing loan is $605.72, which is less than the $617.17 payment that we calculated for the fully amortizing loan. We should also point out that the loan constant, or pay rate, is $605.72 ÷ $60,000 =  .010095 . This is differ- ent from the loan constant that would apply if the loan was fully amortizing, which was $617.17 ÷ $60,000 = .010286.

It should be noted that the $605.72 payment also is slightly closer to the $600 accrued interest calculated earlier. This means that loan amortization will be only $5.72 at the end of month one. A more detailed schedule demonstrating the monthly relationships between payments, accrued interest, and the loan balance is shown in Exhibit 4–4.

Zero Amortizing, or Interest-Only—Constant Payment Mortgage (CPM) Loans Another pattern for fixed interest rate and constant payment loans that is frequently used in real estate finance is referred to as the interest-only loan. As the name implies, constant monthly payments will be “interest only.”

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 91

bru19684_ch04_078-121.indd 91 10/31/17 07:07 PM

Solution: Function:

n

=

360

i

=

12% / 1% or .01 PV = − $60,000

FV

=

$80,000

Solve for PMT 

=

$594.28

PMT (n, i, FV, PV )

Because the loan is interest only, the payment is simply equal to accrued interest, or 12 ÷ 12 × $60,000 = $600 . This means, of course, that the loan balance at the end of each month will remain at $60,000. The monthly pattern of accrued interest, payments, and loan balances for the interest-only loan are detailed in Exhibit 4–5.

Month Beginning

Loan Balance Monthly Payment

Interest (.12 ÷ 12) Amortization

Ending Loan Balance

1 $60,000.00 $600.00 $600.00 $0.00 $60,000.00 2 60,000.00 600.00 600.00 0.00 60,000.00 3 60,000.00 600.00 600.00 0.00 60,000.00 4 60,000.00 600.00 600.00 0.00 60,000.00 5 60,000.00 600.00 600.00 0.00 60,000.00 6 60,000.00 600.00 600.00 0.00 60,000.00 . .       .       .       .       .       . .       .       .       .       .       . .       .       .       .       .      

358     60,000.00 600.00 600.00 0.00 60,000.00 359     60,000.00 600.00 600.00 0.00 60,000.00 360     60,000.00 600.00 600.00 0.00 60,000.00

EXHIBIT 4–5 Interest-Only Loan Pattern

Negative Amortizing, Constant Payment Mortgage (CPM) Loans A final category of fixed rate, constant payment loans to be discussed in this chapter is referred to as a negative amortizing loan. This pattern may occur when: (1) the borrower and lender agree that the loan balance at maturity will be greater than the initial loan amount; that is, FV > PV or (2) payments are negotiated to be lower than the periodic interest due on the loan.

To illustrate the first case, if $60,000 is borrowed but the amount due at maturity will be $80,000, then monthly payments will be $594.28. This result can be obtained as shown in the calculator solution below.

We should also point out that the pay rate, calculated as $594.28 ÷ $60,000, is now equal to .009905. This is lower than the accrual rate, which is . 12 ÷ 12, or .010000. When the pay rate used to determine monthly payments is less than the interest rate specified in the note, also referred to as the “accrual rate,” negative amortization occurs. This is because payments are not large enough to meet monthly interest requirements. The difference between payments actually made and those that would be made on an interest-only loan is deferred and becomes additional amounts owed by the borrower to the lender. These amounts must also earn inter- est. The rate at which they earn interest is usually the same as the interest rate on the note. In this example, it would be . 12 ÷ 12, or .010000 per month. The monthly payment pattern, accrued interest, and loan balance for the negative amortizing loan are shown in Exhibit 4–6.

The second example for negative amortization loans is to set the desired payment pat- tern, and then to solve for the loan balance that will include negative amortization. For

Final PDF to printer

bru19684_ch04_078-121.indd 92 10/31/17 07:07 PM

92 Part 2 Mortgage Loans

example, in the above problem, if we assume that the loan is negotiated with monthly pay- ments preset at $400, the loan balance at the end of year five could be calculated as

Month Beginning

Loan Balance Monthly Payment

Interest (.12 ÷ 12) Amortization

Ending Loan Balance

1 $60,000.00 $594.28 $600.00 $(5.72) $60,005.72 2 60,005.72 594.28 600.06 (5.78) 60,011.50 3 60,011.50 594.28 600.12 (5.84) 60,017.34 4 60,017.34 594.28 600.17 (5.90) 60,023.24 5 60,023.24 594.28 600.23 (5.95) 60,029.19 6 60,029.19 594.28 600.29 (6.01) 60,035.21 . .       .       .       .       .       . .       .       .       .       .       . .       .       .       .       .      

358   79,394.97 594.28 793.95 (199.67) 79,594.65 359   79,594.65 594.28 795.95 (201.67) 79,796.31 360   79,796.31 594.28 797.96 (203.69) 80,000.00

EXHIBIT 4–6 Negative Amortizing Loan Pattern

Solution: Function:

PV

=

− $60,000

n

=

60

i = 12% / 12 P"#

=

$400

Solve for FV 

=

$76,333.93

FV (PV, n, i, PMT )

Note that because the monthly payments have been set at $400, which is below the $600 in monthly interest being accrued, $200 per month in interest is not being collected. Over the 60-month period, this amount must be added to the loan balance and also must earn 12 percent interest compounded monthly. This results in a total of $16,333.93 being added to the loan balance. Note that the balance outstanding at the end of year 5 is now $76,333.93. When compared to the initial loan amount of $60,000, we can see that nega- tive amortization has increased the loan balance by $16,333.93.

Summary and Comparisons: Fixed Interest Rate, Constant Payment Mortgage (CPM) Loans with Various Amortization Patterns

At this point, we have discussed four types of fixed interest rate, constant payment mort- gage (CPM) loans, categorized by amortization pattern. Exhibit 4–7 (panel A), provides a diagram showing the four distinct monthly mortgage payments for our base case example (a $60,000 loan made at 12% for 30 years). Looking at the monthly loan balance pattern for each of the four cases, the reader should begin to understand the trade-offs involved when considering these different loan types. Furthermore, the strategy and objectives of borrow- ers should be apparent. Holding all else constant, monthly payments range from the highest amount when loans are fully amortizing to the lowest amount when they are negatively amortizing.5 Moving to panel B, we can see that loan balances are highest when payments

5 Obviously, there are many combinations in between.

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 93

bru19684_ch04_078-121.indd 93 10/31/17 07:07 PM

EXHIBIT 4–7 Base Case: Summary and Comparison of Monthly Payments and Loan Balances for Selected Fixed Interest Rate, Constant Payment Mortgage (CPM) Loan Patterns

$617.17

$605.72

$600.00

$594.28

(FA)

(PA)

(IO)

(NA)

360 Month

$20,000

$30,000

$40,000

$50,000

$60,000

$70,000

$80,000

$0

(NA) = $80,000

(PA) = $40,000

(IO) = $60,000

(FA) = $0

(FA) = Fully amortizing (IO) = Interest only

(PA) = Partially amortizing (NA) = Negative amortizing

360 Month

$10,000

Panel A: Monthly Payments

Panel B: Outstanding Loan Balances

are lowest and lowest when payments are highest. Risk is also considerably different under each of the four scenarios. It should be clear that if the same property is being financed by the same borrower in each case, risk will be greatest in the case involving the negative amortizing loan.

We should emphasize that we have deliberately kept our base case example the same throughout the chapter in order to emphasize the most important aspects of mortgage loan mechanics and loan structuring. Structuring mortgage loans in real estate financing is, in many cases, critical to the success or failure of a transaction; therefore, knowledge of the relationships discussed in this chapter should prove valuable to the reader. For instance, many of these concepts will prove to be beneficial in later chapters when applications involving structuring partnerships, mortgage-backed securities, and other financing vehi- cles and arrangements are considered. Another important observation should be made regarding the interest rate in our base case example, which has been kept constant. In reality, we would expect the interest rates on loans to increase as risk increases. Finally, there are additional factors that affect risk when structuring loans. These factors include varying loan maturities and varying the amount borrowed. Changes in these factors tend to increase or decrease risk, depending upon the type of payment and loan amortization patterns chosen.

Final PDF to printer

bru19684_ch04_078-121.indd 94 10/31/17 07:07 PM

94 Part 2 Mortgage Loans

Determining Loan Balances Because most mortgage loans are repaid before they mature, mortgage lenders and real estate investors must be able to determine balances on mortgage loans at any time. As pre- viously indicated, even though most loans are made for terms of 25 or 30 years, mortgages are usually repaid from 8 to 12 years after they are made. Therefore, it is very important to know what the loan balance will be at any time when financing real estate. There are many ways to find loan balances. We will demonstrate several approaches in this section.

To illustrate one approach, let us return to our base case example of the $60,000 fully amortizing loan made at 12 percent interest for a term of 30 years. After 10 years, the borrower decides to sell the property. To do so, the existing loan must be paid off. How much will have to be repaid to the lender after 10 years? We could construct a loan balance schedule as in Exhibit 4–1; however, this is time consuming and unnecessary. Finding loan balances can be accomplished in other ways. First, one can simply find the present value of the $617.17 payments at the 12 percent contract rate of interest for the 20 years remaining until maturity. For example

Solution: Function:

n

=

20 × 12 = 240

i

=

12%/ 12 = 1% or .01 P"# = − $617.17

FV

=

0

Solve for PV

=

$56,051.02

PV (n, i, FV, PMT )

Solution: Function:

PV

=

− $60,000

n

=

10 × 12 = 120 i = 12%12 = 1% or .01

P"#

=

$617.17

Solve for FV

=

$56,050.24 (difference due to rounding of payment)

FV (PV, n, i, PMT )

The unpaid balance after 10 years is $56,051.02. This exercise also points out another interesting fact. Because the payments include interest and a reduction of principal each month, by “removing” all interest from all remaining payments, it follows that only the principal can remain. Discounting the $617.17 monthly payments at an annual rate of 12 percent compounded monthly is a process that really amounts to “removing interest” from the payments. Hence, after “removing interest” by discounting, we ascertain that the unamortized or unpaid balance must be $56,051.02.

Another way of finding a loan balance using a financial calculator is to calculate future value (FV). This may be done by entering payments (PMT), the initial loan amount as a pres- ent value (PV), the number of periods (n) (e.g., months) that the loan has been amortized, and the interest rate (i). Future value (FV) then can be calculated as the outstanding loan balance.

An alternative method for finding mortgage balances at any time in the life of the mort- gage is to divide the interest factor for the FV of $1 per period, for the year in which the balance is desired, by the FV of $1 per period factor for the original term of the mortgage, and then subtract that result from 1. The result of this computation is the loan balance expressed as a percentage of the original amount.

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 95

bru19684_ch04_078-121.indd 95 10/31/17 07:07 PM

Solution: Function: % of loan balance: FV (PV, n, i, PMT )

1 −  FV at n = 10 year ________________ FV at n = 30 year

STEP 1: FV at 10 years:

n = 120, i

=

12 %, P"# = − 1, PV = 0

Solve for FV

=

$230.03869

STEP 2: FV at 30 years:

n = 360,  i

=

12 %,  P"# = −1, PV = 0

Solve for FV

=

$3,494.9641

STEP 3: % of loan outstanding 1 −  ($230.03869 ÷ $3,494.9641)  = 93.42%

Solution:

Partial Amortizing Interest Only Negative Amortizing

PV

=

− $60,000

i =

12 % / 12

n = 120 P"#

=

$605.72

Solve for FV

=

$58,684

PV

=

− $60,000

i =

12 % / 12

n = 120 P"#

=

$600

Solve for FV

=

$60,000

PV

=

− $60,000

i =

12 % / 12

n = 120 P"#

=

$594.28

Solve for FV

=

$61,316

This is a more general formula that can be used regardless of the original dollar amount of the loan or payments because it gives a solution in percentage form. In this case, we determine that approximately 93.42 percent, or $56,052, of the original loan balance ($60,000) is still outstanding. This solution is nearly the same result that we obtained by discounting. The difference is due to rounding.

It should also be noted that many financial calculators may be purchased with a loan amortization function preprogrammed in them. Finding a loan balance becomes simply a matter of inputting the loan information and pressing an amortization key.

Finding Loan Balances—Other Amortization Patterns We now consider how to solve for loan balances when loans are prepaid at the end of 10 years for the other three CPM loan categories discussed in this section.

The reader should note that simply substituting the loan payment that we calculated pre- viously for each loan amortization pattern and solving for FV yields the appropriate loan balance at the end of 10 years.

A Note on Interest Rates, Loan Yields, and Early Payoff At this point, it is not unusual for some readers to wonder: Is the cost to borrowers or the yield6 to lenders different if the loan is repaid early or prior to maturity? It should be stressed that regardless of when loans are repaid, either at maturity or any time prior to maturity, each loan pattern discussed here will yield 12 percent compounded monthly to the lender. Similarly, the cost for the borrower also will be an annual rate of 12 percent compounded monthly, regardless of when the loan is repaid. This is the case because each

Final PDF to printer

bru19684_ch04_078-121.indd 96 10/31/17 07:07 PM

96 Part 2 Mortgage Loans

loan pattern is structured around an accrual rate of 12 percent. Thus, interest is accrued and will eventually be paid on all loan balances outstanding. This is the case for fully, partially, zero, or negative amortizing loans.

However, we also should stress that if additional financing fees are charged by the lender, the effective cost of borrowing to the borrower will usually be greater than the interest rate. Yields to the lender also will vary depending on when the loan is repaid. We now turn to the topic of loan fees and the cost of borrowing.

Loan Closing Costs and Effective Borrowing Costs Loan closing costs are incurred in many types of real estate financing, including residen- tial property, income property, construction, and land development loans. Closing costs that affect the cost of borrowing are additional finance charges levied by the lender. These charges constitute additional costs to the borrower and must be included as a part of the cost of borrowing. Generally, lenders refer to these additional charges as loan fees.

Loan fees can be classified into two categories: loan origination fees and loan discount fees. Loan origination fees are intended to cover expenses incurred by the lender for pro- cessing and underwriting loan applications, preparation of loan documentation and amor- tization schedules, obtaining credit reports, and any other expenses that the lender believes should be recovered from the borrower. Lenders usually charge these costs to borrowers when the loan is made, or “closed,” rather than charging higher interest rates. They do this because if the loan is repaid soon after closing, the additional interest earned by the lender as of the repayment date may not be enough to offset the fixed costs of loan origination. For example, assume that the prevailing interest rate on a $60,000 mortgage is 12 percent and the lender believes that expenses equal to $1,000 will be incurred to close the loan. If the lender chose to increase the interest rate to 12.25 percent to recover these origina- tion costs, an additional $150 (approximately) would be collected during the first year ($60,00 × .0025) . If the loan was repaid after the first year, the lender would not recover the full $1,000 in origination costs. This is why lenders attempt to “price” these origination costs separately

The second category of loan fees is loan discount fees, or points.7 This charge also represents an additional finance charge, but its primary purpose is to adjust the yield on a mortgage loan. In the context of real estate lending, loan discounting amounts to a bor- rower and lender negotiating the terms of a loan based on a certain loan amount. The lender then discounts the loan by charging a fee, which will be deducted from the loan funds advanced to the borrower. Payments made by the borrower, however, are based on the contract amount of the loan. For example, assume a borrower and lender agree on a $60,000 loan at 12 percent interest for 30 years. The lender actually disburses $58,200 to the borrower by including a loan discount charge of 3 percent (points), or $1,800. The bor- rower is required to repay $60,000 at 12 percent interest for 30 years. However, because the borrower actually receives $58,200 but must repay $60,000 plus interest, it is clear that the actual borrowing cost to the buyer is greater than 12 percent.

Why do pricing practices such as discounting exist? Many reasons have been advanced. One reason given by lenders is that mortgage rates tend to be somewhat “sticky” in upward and downward moves. For example, suppose that the prevailing rate is 12 percent and

6 When the term yield is used in lending it is usually referred to from the lender’s perspective, who evaluates loans on the basis of profitability. Also, in addition to interest, lenders frequently charge fees on loans and use the term yield to include interest and fees on loans that they make. 7 Lenders in some areas of the country refer to loan discounts as “discount points” or simply “points.” In conventional mortgage lending, the borrower usually pays this charge, which adds to financing costs. In this chapter, we are concerned with conventional lending situations where the borrower pays the loan discount as a part of origination fees.

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 97

bru19684_ch04_078-121.indd 97 10/31/17 07:07 PM

Contractual loan amount $60,000     Less: Loan fees     1,800 Net cash disbursed by lender $58,200 Amount to be repaid:     Based on $60,000 contractual loan amount, $617.17 for 30 years.

market pressures begin to push rates upward. However, instead of all lenders moving the rate to perhaps 12.25 percent, one or more lenders may continue to quote 12 percent as the loan rate. However, in lieu of raising the interest rate, these lenders may charge borrowers loan discount points. This practice is also referred to as the borrower “buying down the interest rate.” That is, instead of paying 12.25 percent interest, the borrower will buy down the interest rate to 12 percent by paying discount points to the lender.

Another reason points may be charged is because many mortgage loans are originated by lenders who have entered into contracts with investors to assemble, or package, then sell them a specific number, or dollar amount, of such loans. Such contracts with investors may require that loans are to be sold to yield investors a rate of interest very close to the rate that lenders expect to charge borrowers. Therefore, in order for originating lenders to earn a profit, points are charged to borrowers to provide lenders with revenue for performing origination services prior to the delivery of loans to investors.

Another situation may provide lenders with an opportunity to replace revenue in a declin- ing interest rate environment. In these cases, interest rates may begin to decline before the date that the loan is made to the borrower but after the date on which the lender and investor agree on the yield on the packaged mortgages to be sold. In this case, loans will be originated at a lower interest rate, and the lender will charge discount points in order to offset the decline in interest rates being charged to borrowers as the loans are being assembled or packaged.

A final reason for loan discount fees is that lenders believe that, in this way, they can better price the loan relative to the risk they take. For example, in the beginning of this chapter we referred to the risk premium component (p) of the interest rate. However, the risk for some individual borrowers is slightly higher than it is for others. Further, these loans may require more time and expense to process and control. In this case, instead of raising the interest rate, discount points may be charged by the lender (in addition to origi- nation fees) to compensate for the slightly higher risk.

The practice of using loan origination fees and discount points has historically prevailed throughout the lending industry. It is important to understand (1) how these charges affect borrowing costs and (2) how to include them in computing effective borrowing costs on loan alternatives when financing any real estate transaction.

Loan Fees and Borrowing Costs To illustrate loan fees and their effects on borrowing costs in more detail, consider the follow- ing problem: A borrower would like to finance a property for 30 years at 12 percent interest. The lender indicates that loan fees(origination and discount points) equal to 3 percent of the loan amount will be charged to obtain the loan. What is the actual interest cost of the loan?

We structure the problem by determining the amount of the loan fee [ .03  ×  ($60,000)   =  1,800 ] . Second, we know that the monthly mortgage payments based on $60,000 for 30 years at 12 percent will be $617.17. Now we can determine the effect of the origination fee on the interest rate being charged as follows:

In other words, the amount actually disbursed by the lender will be $58,200, but the repayment will be made on the basis of $60,000 plus interest at 12 percent compounded

Final PDF to printer

bru19684_ch04_078-121.indd 98 10/31/17 07:07 PM

98 Part 2 Mortgage Loans

monthly, in the amount of $617.17 each month. Consequently, the lender will earn a yield on the $58,200 actually disbursed, which must be greater than 12 percent.

Using a financial calculator, we can calculate the effective interest rate for the loan, assuming it is outstanding until maturity, as 12.41 percent. This yield is obviously higher than the 12 percent contract, or nominal, rate of interest specified in the note or mortgage.

Solution: Function:

n

=

30 × 12 = 360

P"#

=

− $617.17

PV

=

$58,200

FV

=

0

i (n, PMT, PV, FV )

Solve for

i (monthly)

=

1.034324 %  monthly rate

i (annualized)

=

1.034324 % × 12 = 12.41 %  effective interest rate

This computation forms the basis for a widely used rule of thumb in real estate finance; that is, for every 2 percentage points in the origination fee charged to the borrower, the effective cost to the borrower, or investment yield earned by the lender, increases by approximately one-fourth of a percent above the contract rate. Note that in our solution, we obtained an effective rate of 12.41 percent, versus 12.375 percent using the approximation. While this estimate is close to the yield calculated in one example, we have assumed that the loan remains outstanding until maturity. However, most loans on the average are “pre- paid” or paid off long before maturity. Hence, this rule of thumb, while helpful, generally provides a very rough estimate of the effective cost (yield) for most mortgage loans.8

We should point out that, in the above example, the 12.41 percent effective interest rate is an annual rate of interest, compounded monthly. Many analysts prefer to calculate the effective annual interest rate (recall that this is equivalent to an annual rate of interest, compounded annually). We can easily calculate this as follows:

8 This rule of thumb will become very inaccurate if the payoff period is very short relative to the maturity and when the level of interest rates increases.

STEP 1: Solution: Function:

i

=

12.41%

PV

=

− $60,000

n

=

12

Solve for FV

=

$67,884.47

FV (PV, i, n )

STEP 2: Solution:

FV

=

$67,884.47

n

=

1

PV

=

$60,000,00

Solve for i

=

13.14%

Final PDF to printer

99

bru19684_ch04_078-121.indd 99 10/31/17 07:07 PM

Note that because of the effects of (1) monthly compounding and (2) discount points, the effective annual interest rate is 13.14 percent, whereas the nominal interest rate is 12 percent and the effective interest cost is 12.41 percent (annual rate of interest compounded monthly) for the loan in our example.

Loan Fees and Early Repayment: Fully Amortizing Loans An important effect of loan fees and early loan repayment must now be examined in terms of the effect on interest rate. We will show in this section that when loan fees are charged and the loan is paid off before maturity, the effective interest rate of the loan increases even further than when the loan is repaid at maturity.

To demonstrate this point, we again assume our borrower obtained the $60,000 loan at 12 percent for 30 years and was charged an $1,800 (3 percent) loan origination fee. At the end of five years, the borrower decides to sell the property. The mortgage contains a due-on-sale clause; hence, the loan balance must be repaid at the time the property is sold. What will be the effective interest rate on the loan as a result of both the origination fee and early loan repayment?

To determine the effective interest rate on the loan, we first find the outstanding loan balance after five years to be $58,598.16. To solve for the yield to the lender (cost to the borrower), we proceed by finding the rate at which to discount the monthly payments of $617.17 and the lump-sum payment of $58,598.16 after five years so that the present value of both equals $58,200, or the amount actually disbursed by the lender.

This presents a new type of discounting problem. We are dealing with an annuity in the form of monthly payments for five years and a loan balance, or single lump-sum receipt of cash, at the end of five years. To find the yield on this loan, we proceed as follows:

Because of problems involving loan fees and the potential abuse by some lenders of charg- ing high fees to unwary borrowers, Congress passed the federal Truth-in-Lending Act to provide disclosure regarding the effects of loan fees to consumers purchasing residences.* As a result of this legislation, the lender must disclose to consumers the annual percent- age rate (APR) being charged on the loan. (We will deal with the APR more extensively in Chapter 8.) Calculation of the APR is generally done in the manner shown for calculating the effective interest rate, assuming that the loan is repaid at maturity. The APR in our chapter example would be disclosed to the borrower at closing as 12.41 percent. The APR, then, does reflect origination fees and discount points and treats them as additional income or yield to the lender regardless of what costs, if any, the fees are intended to cover. Other fees charged by the lender as a condition for obtaining the loan also may have to be included in the APR.†

* See Regulation Z of the Federal Reserve Board, 12 C.F.R., sec. 226, as amended.

† Generally, the APR disclosed to the borrower is the effective interest rate computed under the assumption that the loan will be outstanding until maturity. The lender may round the APR to the nearest quarter percent; however, it must fall in a range that is within one-eighth of 1 percent above or below the APR that is calculated based on federal guidelines as disclosed in Regulation Z. If the reader desires greater accuracy in these computations, consult Computational Procedures Manual for Supplement 1 to Regulation Z of the Federal Reserve Board: Calculator Instructions (Office of the Comptroller of the Currency, February 1978).

Truth-in-Lending Requirements and the Annual Percentage Rate (APR) Concept Box 4.2

Final PDF to printer

bru19684_ch04_078-121.indd 100 10/31/17 07:07 PM

100 Part 2 Mortgage Loans

This formulation simply says that we want to find the interest rate (i) that will make the present value of both the $617.17 monthly annuity and the $58,598.16 received at the end of five years equal to the amount disbursed, or $58,200. From the above analysis, we can conclude that the actual yield (or actual interest rate) that we have computed to be approxi- mately 12.82 percent is higher than both the contract interest rate of 12 percent and the 12.41 percent yield computed assuming that the loan was outstanding until maturity. This is true because the $1,800 origination fee is earned over only five years instead of 30 years, which is equivalent to earning a higher rate of compound interest on the $58,200 dis- bursed. Hence, when this additional amount earned is coupled with the 12 percent interest being earned on the monthly loan balance, this increases yield to 12.82 percent.9

Relationship between Yield and Time Based on the preceding discussion, we can make some general observations about the rela- tionship of mortgage yields and the time during which mortgages are outstanding. The first observation is that the effective interest rate on a mortgage will always be equal to the contract rate of interest when no finance charges are made at the time of loan origination or repayment. This follows because, as we saw in Exhibit 4–2, the level payment pattern assures the lender of earning only a given annual rate of interest, compounded monthly, on the monthly outstanding loan balance. Hence, the outstanding mortgage balance can be repaid at any time, and the lender’s yield (borrower’s cost) will not be affected. It will be equal to the contract rate of interest.

The second observation is that if origination or financing fees are charged to the bor- rower, the following occurs: (1) the effective yield will be higher than the contract rate of interest and (2) the yield will increase as repayment occurs sooner in the life of the mortgage. These relationships can be explained by referring to Exhibit 4–8, where the two curves, A and B, represent the mortgage yield pattern under two assumptions. Line A represents the effective yield, or cost, when no financing fees are charged to the borrower. In our previous example, the yield would remain at 12 percent, equal to the contract rate of 9 If the loan is repaid in less than one year, the yield becomes larger and approaches infinity, should the loan be repaid immediately after closing.

STEP 1: Solve for remaining balance: Solution: Function:

n = 25 × 12 = 300 i (n, PMT, FV, PV ) i = 12%/12 = 1% or .01 PMT = −$617.17 FV = 0 Solve for PV = $58,598.16 (remaining balance)

STEP 2: Next, solve for the interest payment, holding a 30-year loan, for five years, and discounted by the loan origination fee:

Solution: Function: n = 5 × 12 = 60 i (n, PMT, FV, PV )

PMT = −$617.17 PV = −$58,200

FV = −$58,598.16 Solve for i (monthly) = 1.069%

Solve for i (monthly) = 1.069% × 12 = 12.82% An Excel template is included on the Website for this book that may be used to calculate the same yield shown in this example (www.mhhe.com/bf16e).

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 101

bru19684_ch04_078-121.indd 101 10/31/17 07:07 PM

interest regardless of when the loan is repaid; hence, the horizontal line is over the range of 0 to 30 years. Curve B represents a series of loan yields computed under the assumptions that a 3 percent origination fee is charged to the borrower and that the loan is prepaid in various years prior to maturity. In our example, we note that the yield earned by the bor- rower is 15.26 percent if the loan is repaid one year after closing and that it diminishes and eventually equals 12.41 percent after 30 years. Hence, we can again conclude that if financing fees are charged to the buyer, the effective yield to the lender (cost to the bor- rower) can range from one that is extremely high if prepaid, say, after one year (the yield in that case would be approximately 15.26 percent) to a yield that would be considerably lower if repaid at maturity, or 12.41 percent. If a borrower knows when he or she expects to repay a loan, this method of computing the effective borrowing cost should be used. This is particularly important if the borrower is comparing alternative loans with different terms.

Prepayment Penalties Many borrowers mistakenly take for granted that a loan can be prepaid in part or in full any- time before the maturity date. This is not the case; if the mortgage note is silent on this matter, the borrower may have to negotiate the privilege of early repayment with the lender. In our example using the 30-year mortgage loan, the note will usually specify that 360 payments are to be made at the end of each month until the loan is repaid. Any payments made in advance of this monthly schedule, or in amounts greater than the scheduled amount are prepayments

There are numerous companies offering mortgage rate information on the Internet, such as www.bankrate.com. Find a quote for a 15-year fixed rate mortgage on a $150,000 primary residence valued at $200,000. What are the current interest rate, discount points, and other lender fees for the loan you found?

Calculate the effective cost of the mortgage over the lifetime of the loan. Calculate the effective cost of paying off the mortgage after seven years. How do these rates compare to the stated APR? What accounts for the dis- crepancy between the effective rate and the APR?

Web App

EXHIBIT 4–8 Relationship between Mortgage Yield and Financing Fees at Various Repayment Dates

15.26

12.82

12.41

12.00Y ie

ld (%

)

1 5 10 15 20 25 30

A

B

Year of prepayment

Final PDF to printer

bru19684_ch04_078-121.indd 102 10/31/17 07:07 PM

102 Part 2 Mortgage Loans

and may be subject to penalties. However, many mortgages provide explicitly that the bor- rower can pay a prepayment penalty should the borrower desire to prepay the loan.

One rationale for a prepayment penalty is that the lender may be trying to recover a por- tion of loan origination costs not charged to the borrower at closing. This may have been done by the lender to compete for the loan by making initial closing costs lower for the borrower. Another reason for prepayment penalties is that the lender has agreed to extend funds for a specified time, 30 years in our present example. Early payment from the lender’s view may represent an unanticipated inflow of funds that may or may not be readily reinvested during periods when mortgage rates are unstable or are expected to decline. However, if interest rates undergo a sustained increase over long periods of time, lenders usually welcome early repayments since they may be able to loan out funds again at higher rates of interest.

Another possible reason for prepayment penalties is that they are not included in the computation of the APR; hence, they are not included in the APR disclosure to the bor- rower. Borrowers may not be able to determine the effect of these penalties on borrow- ing costs and, therefore, the penalties represent a technique lenders use to increase yields. Some states have begun prohibiting the enforcement of prepayment penalties to individuals financing residences if the loan has been outstanding more than some specified minimum number of years. Also, in some areas where penalties are allowed, lenders may waive them if the buyer of a property agrees to originate a new loan with the same lender. Some states have passed consumer protection laws that allow for prepayment if the borrower has a job transfer to another state, joins the military, and for other unanticipated reasons. (In the case of loans on commercial real estate, prepayment penalties are common practice. Prepayment penalties may have to be paid even when the borrower wants to sell the mortgaged property. The existence and amount of penalties must be negotiated when such loans are originated.)

Because of the use of prepayment penalties, we want to know the effective mortgage loan yield (interest rate) when both a loan discount fee and a prepayment penalty are charged on the loan. To illustrate, we consider both the effects of the 3 percent loan discount and a 3 percent prepayment penalty on the outstanding loan balance for the $60,000, 30-year loan with a con- tract interest rate of 12 percent used in the preceding section. We assume the loan is the effec- tive interest rate to the borrower (yield to the lender). To solve for the yield, mortgage funds actually disbursed in this case will be $60,000 minus the origination fee of $1,800, or $58,200. Taking the loan discount fee into account, we want to find the discount rate which, when used to discount the series of monthly payments of $617.17 plus the outstanding loan balance of $58,598.16 and the prepayment penalty of $1,758 (3% of $58,598.16), or a total of $60,356, will result in a present value equal to the amount of funds actually disbursed, $58,200.

Using a financial calculator, with a 3 percent origination fee, early payment in the fifth year, and a 3 percent prepayment penalty, we see that the effective yield on the loan will increase to about 13.25 percent.

Solution: Function: n = 5 × 12 = 60 i (n, PMT, FV, PV ) PMT = −$617.17 PV = $58,200 FV = −$60,356 Solve for i (monthly) = 1.10425%

Solve for i (annually) = (1.10425% × 12) = 13.25%

In this case, the APR will still be disclosed at 12.375 percent, which reflects the loan discount only, not the prepayment penalty, and assumes the loan is repaid at the end of 30 years. The actual yield computed here of 13.25 percent is a marked difference from both the loan contract rate of 12 percent and the disclosed APR of 12.375 percent.

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 103

bru19684_ch04_078-121.indd 103 10/31/17 07:07 PM

Charging Fees to Achieve Yield, or When “Pricing” FRMs In the preceding examples, we have developed the notion of the effective borrowing costs and yield from a given set of loan terms. However, we should consider how these are determined by lenders when “pricing” a loan. As we discussed earlier in the chapter, lend- ers generally have alternatives in which they can invest funds. Hence, they will determine available yields on those alternatives for given maturities and weigh those yields and risks against yields and risks on mortgage loans. Similarly, competitive lending terms estab- lished by other lenders establish yields that managers must consider when establishing loan terms. By continually monitoring alternatives and competitive conditions, manage- ment establishes loan offer terms for various categories of loans, given established under- writing and credit standards for borrowers. Hence, a set of terms designed to achieve a competitive yield on categories of loans representing various ratios of loan-to-property value (70% loans, 80% loans, etc.) are established for borrowers who are acceptable risks. These terms are then revised as competitive conditions change.

If, based on competitive yields available on alternative investments of equal risk, man- agers of a lending institution believe that a 13 percent yield is competitive on 80 percent mortgages with terms of 30 years and expected repayment periods of 10 years, how can they set terms on all loans made in the 80 percent category to ensure a 13 percent yield? Obviously, one way is to price all loans being originated at a contract rate of 13 percent. However, management may also consider pricing loans at 12 percent interest and charging either loan fees or prepayment penalties or both to achieve the required yield. Why would lenders do this? Because (1) they have fixed origination costs to recover and (2) competi- tors may still be originating loans at a contract rate of 12 percent.

To illustrate how fees for all loans in a specific category can be set, we consider the following solution:

STEP 1: Solve for payment Solution: Function:

PV = −1 PMT (PV, i, n, FV ) i = 12%/12 = 1% or .01 n = 30 × 12 = 360 FV = 0 Solve for PMT = .010286

STEP 2: Solve for loan balance EOY10 Solution: Function:

PV = −1 FV (PV, i, n, PMT ) n = 120 i = 12%/12 PMT = .010286 Solve for PMT = .934180

STEP 3: Solve for PV, i = 13% Solution: Function:

FV = .934180 PV (FV, i, n, PMT ) i = 13%12 n = 120 PMT = .010286 Solve for PV = .9453

Final PDF to printer

bru19684_ch04_078-121.indd 104 10/31/17 07:07 PM

104 Part 2 Mortgage Loans

The result PV = .9453 means that the net disbursement at loan closing should be 94.53 percent, or 94.5 percent (rounded), of the loan amount. Therefore, if the loan is priced by offering terms of 12 percent interest and a 5.5 percent origination fee (100 %  − 94.5%) and the loan is repaid at the end of 10 years ( EOY 10 ) , management will have its 13 percent yield.

Financing Loan Fees and Other Closing Costs

In some situations, the lender may also agree to provide financing for loan fees. In our example, this would mean that the loan amount would be $61,800 or the sum of the $60,000 loan amount and the loan fees of $1,800. The borrower would not be required to pay loan fees of $1,800 at closing, however monthly payment would be higher. For example payments would be

PV = −61,800                                                  Function: I = 1% or .01                                                PMT (PV, i, n, FV) N = 360 FV = 0 Solve for PMT = $635.68

This compares to our previous payment of $617.17 if the former pays $1,800 at closing. Borrowers may prefer to make higher monthly payments in order to reduce the amounts due at closing.

W should point out that the APR will now be based on the higher loan amount and monthly payments also will be higher. In our example based on a 30 year loan we have

PV = −60,000                                                  Function: I = 1% or .01                                                 i (PV, Pmt, n, FV) N = 360 FV = 0 Pmt = 635.68 Solve for i = 12.40%

Note that when the loan fees are financed, the APR will be 12.40% as compared to 12.41% when the loan fees are paid at closing. In our example, financing loan fees has a very small impact on the APR. However, we should point out that if the loan fees were higher there could be a more significant difference. The lower APR comes about because the fees paid by the borrower at closing are being pushed into slightly higher payments fur- ther into the future which, in this case, benefits the borrower and therefore lowers the APR.

The reader should also remember that when loan fees are financed, finding loan bal- ances, and effective borrowing costs will also change as the loan amount is now $60,000 and monthly payments are $635.68.

Other FRM Loan Patterns—Declining Payments and Constant Amortization Rates

The constant amortizing mortgage (CAM) loan pattern represents yet another varia- tion that may be considered in loan structuring. Payments on CAMs are determined first by computing a constant amount of each monthly payment to be applied to principal or monthly amortization. Interest is then computed on the monthly loan balance and added to the monthly amount of amortization. The total monthly payment is determined by adding

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 105

bru19684_ch04_078-121.indd 105 10/31/17 07:07 PM

the constant amount of monthly amortization to interest on the outstanding loan balance. Consider the following example of a CAM loan. A loan was made for $60,000 for a 30-year term at 12 percent (annual rate compounded monthly); payments were to be made monthly and were to consist of both interest and amortization (or reduction of principal), so that the loan would be repaid at the end of 30 years. However, amortization is determined by divid- ing the number of months or the term of the loan (360) into the loan amount ($60,000), resulting in a reduction of principal of $166.67 per month. Interest would be computed on the outstanding loan balance and then added to amortization to determine the monthly payment. An illustration of the payment pattern and loan balance is shown in Exhibit 4–9.

The computation in Exhibit 4–9 shows that the initial monthly payment of $766.67 includes amortization of $166.67, plus interest computed on the outstanding loan balance. The total monthly payment would decline each month by a constant amount, or $1.67 (.01 × $166.67) . The loan payment and the balance patterns are shown in Exhibit 4–10. It should be kept in mind that in spite of the declining monthly payment pattern, the yield in the CAM remains at 12 percent interest. Like the fully amortizing, partially amortizing, interest only, and negative amortizing loans, the CAM is also a fixed interest rate mortgage loan. Its payments and balance pattern are simply structured differently than the loans in our previous examples.

The constant amortizing payment pattern is considered to be a very conservative loan structure because it places primary emphasis on the amortization of the loan. Nonetheless, it demonstrates yet another alternative that may be of value when structuring a loan. Or perhaps, it may be combined with another loan amortization pattern. It also demonstrates the range of alternative payment and amortization patterns available within the fixed inter- est rate class of mortgage loans.

Amortization Schedules and Callable Loans A final variation in loan structuring to be included in this section is a commonly used provi- sion in which an amortization schedule, if specified in the note, is different from the matu- rity date. For example, two parties may agree that a $100,000 fully amortizing loan will be made at 12 percent interest with monthly payments calculated based on a 30 year amortiza- tion schedule. However, both parties agree that the loan will be, or may be, callable at the lender’s option, at the end of 10 years. In this case, payments can be calculated as follows:

STEP 1: Determine payment Solution: Function:

PV = −$100,000 PMT (i, n, PV, FV ) i = 12%/12 = .01 n = 30 × 12 = 360 FV = 0

Solve for PMT = $1,028.61

STEP 2: Determine balance Solution: Function:

PV = −$100,000 FV (PV, PMT, i, n) PMT = $1,028.61 i = 12%/12 = .01 n = 12 × 10 = 120

Solve for PV = $93,418.59

Final PDF to printer

bru19684_ch04_078-121.indd 106 10/31/17 07:07 PM

106 Part 2 Mortgage Loans

If the loan is called at the end of 10 years, the amount due would be the balance at that time, or $93,418.59 (reader should verify). This loan structure is used by borrowers and lenders (1) to keep monthly loan payments lower than they would be if a fully amortizing loan was made for 10 years, (2) to keep the loan maturity relatively short at 10 years, and (3) to achieve some loan amortization even though the loan is paid after 10 years.

By now, the reader should be aware that depending on the objectives of the borrower and lender, loans can be structured to achieve many results. Loan structuring is usually described as a process of adjusting loan terms to calibrate loan payments, loan balances, amortization rates, and so on, to achieve desired results. Such results usually include lower monthly payments than would be available under a fully amortizing structure. However, it could also be that another objective is sought, such as having a desired loan balance at maturity.

“Reverse Mortgages” Reverse mortgage loans10 represent a very different type of mortgage loan. Instead of receiving the full loan proceeds at closing, the loan amount in a reverse mortgage is “taken down” as irregular periodic payments until such payments and accrued interest reach the agreed-upon loan amount. In real estate construction and development, these “take-downs” are also referred to as “draws.” In recent years, reverse mortgages have also become impor- tant to the home-owning population as they approach retirement and seek ways to supple- ment their retirement income. For example, assume that a household owns a residential property worth $500,000 today. They would like to use the value of the property to supple- ment their retirement income with a reverse mortgage. A lender agrees to make a loan in an

EXHIBIT 4–10 Declining Loan Payment and Balance Patterns (Constant Amortizing Loan)

Payment

$766.67

Balance

$60,000

30 year 30 year0 0

(1) (2) (3) (4) (3)+(4) (2)–(4)

Month Opening

Balance × Interest

( .12 ÷ 12 ) Amortization Monthly Payment

Ending Balance

1 $60,000.00 $600.00 $166.67   $766.67  $59,833.33   2 59,833.33 598.33 166.67 765.00 59,666.66 3 59,666.66 596.67 166.67 763.34 59,499.99 4 59,499.99 595.00 166.67 761.67 59,333.32 5 59,333.32 593.33 166.67 760.00 59,166.65 6 59,166.65 591.67 166.67 758.34 58,999.98 . . . . . . . . . . . . . . . . . .

360 166.67 1.67 166.67  168.34 –0–

EXHIBIT 4–9 Monthly Payments and Loan Balance (Constant Amortizing Loan)

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 107

bru19684_ch04_078-121.indd 107 10/31/17 07:07 PM

amount not to exceed $250,000 for a period of 10 years. However, instead of giving the borrower cash in the amount of $250,000, the lender agrees to let the borrower take down the loan in monthly installments over the life of the mortgage. The lender will charge an interest rate of 10 percent on the loan. What will be the maximum monthly payments that the lender will make to the borrower under these terms? We can solve for this as follows:

10 These are also known as home equity conversation mortgages (HECMs).

Solution: Function: FV = −$250,000 PMT (FV, i, n, PV ) i = 10%/12 n = 120 PV = 0

Solve for PMT = $1,220.44

Solution: Function: i = 10%/12 FV (i, n, PV, PMT ) PMT = $1220.44

n = 36 PV = 0

Solve for FV = $50,992.21

Looking at this example, note that the borrower can supplement his income by drawing $1,220.44 from the lender each month for 120 months, at the end of which time the lender will be owed a total of $250,000. If the property has retained its value of $500,000, the homeowner will have $250,000 in equity at the end of 10 years. If the borrower makes no more draws, the loan balance will continue to increase at 10 percent until the property is sold or the owner dies.

Exhibit 4–11 shows the monthly payment pattern and loan balances for our reverse mortgage example. To determine reverse mortgage loan balances, we reverse the proce- dure used in our previous FRM examples; that is, we solve for future value (FV) and not present value. As shown in the exhibit, instead of the declining loan balances that are characteristic of fully amortizing mortgage loans, reverse mortgage balances increase over time. For example, after three years our reverse mortgage loan balance would be

EXHIBIT 4–11 Reverse Mortgage Draw and Balance Patterns

Year Draw per Month Balance EOY

1 $1,220.44 $ 15,335.52 2 1,220.44 32,276.87 3 1,220.44 50,992.21 4 1,220.44 71,667.28 5 1,220.44 94,505.30 6 1,220.44 119,738.97 7 1,220.44 147,612.73 8 1,220.44 178,405.23 9 1,220.44 212,422.11 10 1,220.44 250,000.00

Final PDF to printer

108

bru19684_ch04_078-121.indd 108 10/31/17 07:07 PM

The balance at the end of any year can be determined by changing the values for n and resolving for future value.

With the baby boomers advancing in age and many having a substantial amount of equity in residential housing, reverse mortgages, also known as home equity conversion mortgages (HECMs), have been developed. These loans are designed to help seniors “unlock’’ home equity by borrowing against property value, thereby supplementing their retirement income. Most mortgage loans are federally insured and require borrowers to consult with an approved reverse mortgage counselor. Borrowers should be aware of the following general qualifications:

• Applicant must be 62 years of age or older. • The borrower must have title to the home and the home must be the borrower’s primary

residence. • Proceeds from a RM may be used to repay any existing mortgage loans on a property at

the time of closing. • Borrowers can generally qualify as follows:

—age 62, 50% of value, 10 years or expected life —age 72, 60% of value, 10 years or expected life —age 82, 70% of value, 10 years or expected life

• Draw downs may be based on a “term option” such as 10 years, or based on a “tenure option” which is based on life expectancy at the time of closing. Because loans are federally insured in either case, the borrower continues to receive monthly payments even if the loan balance eventually exceeds the market value of the residence. This could occur if the borrower out- lives his expected life at closing or if a decline in the market value of the property occurs. As is the case with other mortgage loans, reverse mortgages usually require certain up-front costs, including loan fees, mortgage insurance, loan servicing fees, an appraisal, and other closing costs.

• Draw-downs generally may be taken in one lump sum at closing, or in monthly install- ments, or through a line of credit. The latter loan pattern gives the borrower the option of making draw-downs when desired. In this event, the interest rate is floating and interest is charged at prevailing rates on the monthly outstanding balance.

• At origination, interest rates may be fixed or floating (called adjustable rate mortgages, or ARMs--to be discussed in the next chapter).

• Borrowers must continue to maintain the residence, pay property taxes and hazard insurance. • The sum of all draw-downs plus accrued interest does not have to be paid back unless

the homeowner permanently leaves the home or dies. In the latter event, title to the prop- erty would be obtained by the borrower’s heirs. Typically, the property would then be sold and the loan balance repaid ( just as would be the case without the reverse mortgage).

• Amounts received from a reverse mortgage are not subject to federal income taxes. • All interest accrued under a reverse mortgage is not deductible when determining fed-

eral income taxes until actually paid. This is usually when the loan is paid off in full.

Useful websites:

www.aarp.org/money/personal/reverse_mortgages www.reversemortgage.org www.hud.gov/buying/rvrsmort.cfm

Concept Box 4.3 Reverse Mortgages

Conclusion In this chapter, we discussed various approaches to pricing and structuring fixed interest rate mort- gage loans. We saw that the price or interest rate on the loan depends on a number of factors, includ- ing various types of risk that affect mortgage lenders. It is important to keep these risk factors in mind in future chapters as we consider alternative mortgage instruments which are often designed in

Final PDF to printer

bru19684_ch04_078-121.indd 109 10/31/17 07:07 PM

Chapter 4 Fixed Interest Rate Mortgage Loans 109

accrual rate, 84 amortization, 85 annual percentage rate

(APR), 99 anticipated inflation, 81 balloon payment, 89 buying down the interest

rate, 97 callable loans, 105 constant amortizing

mortgage, (CAM) 104 constant payment

mortgage, (CPM) 84 default risk, 80

derived demand, 79 effective annual interest

rate, 98 effective interest rate, 98 fully amortizing loan, 85 interest, 78 interest-only loan, 85 interest rate risk, 81 legislative risk, 81 liquidity risk, 81 loan closing costs, 96 loan constants, 88 loan discount fees, 96 loan origination fees, 96

loan structuring, 106 negative amortizing loan, 85 nominal interest rate, 79 partially amortizing loan, 85 pay rate, 84 points, 96 prepayment penalty, 102 prepayment risk, 81 principal, 85 real rate of interest, 79 reverse mortgage, 106 unanticipated inflation, 81 zero amortizing loan, 85

Key Terms

www.nahb.org—National Association of Home Buyers—Provides industry news, new home listings, and remodeling information. www.bankrate.com—Provides mortgage rate information from numerous national lenders. www.freddiemac.com/pmms/pmms30.htm—This is a good site for finding fixed rates and points for 30-year mortgages.

Useful Websites

1. What are the major differences between the four CPM loans discussed in this chapter? What are the advantages to borrowers and risks to lenders for each? What elements do each of the loans have in common?

2. Define amortization. List the five types discussed in this chapter. 3. Why do the monthly payments in the beginning months of a CPM loan contain a higher propor-

tion of interest than principal repayment? 4. What are loan closing costs? How can they be categorized? 5. In the absence of loan fees, does repaying a loan early ever affect the actual or true interest cost

to the borrower? 6. Why do lenders charge origination fees and loan discount fees? 7. What is the connection between the Truth-in-Lending Act and the annual percentage rate (APR)? 8. What is the effective borrowing cost? 9. What is meant by a nominal rate of interest on a mortgage loan? 10. What is the accrual rate and payment rate on a mortgage loan? What happens when the two are

equal? What happens when the accrual rate exceeds the payment rate? What if the payment rate exceeds the accrual rate?

11. An expected inflation premium is said to be part of the interest rate. What does this mean? 12. A mortgage loan is made to Mr. Jones for $30,000 at 10 percent interest for 20 years. If Mr.

Jones has a choice between either a fully amortizing CPM or a CAM, which one would result in his paying a greater amount of total interest over the life of the mortgage? Would one of these mortgages be likely to have a higher interest rate than the other? Explain your answer.

13. What is negative amortization? 14. What is partial amortization?

Questions

ways that alter risk characteristics. Although the focus of this chapter has been on residential mort- gages, the concepts and calculations are equally important for commercial mortgages, which also are discussed in later chapters. We will find that the riskiness of the mortgage is also a factor in the risk and expected rate of return for investors in real estate income properties.

Final PDF to printer

bru19684_ch04_078-121.indd 110 10/31/17 07:07 PM

110 Part 2 Mortgage Loans

1. A borrower obtains a fully amortizing CPM loan for $125,000 at 11 percent interest for 10 years. What will be the monthly payment on the loan? If this loan had a maturity of 30 years, what would be the monthly payment?

2. A fully amortizing mortgage loan is made for $80,000 at 6 percent interest for 25 years. Payments are to be made monthly. Calculate:

a. Monthly payments. b. Interest and principal payments during month 1. c. Total principal and total interest paid over 25 years. d. The outstanding loan balance if the loan is repaid at the end of year 10. e. Total monthly interest and principal payments through year 10. f. What would the breakdown of interest and principal be during month 50?

3. A fully amortizing mortgage loan is made for $100,000 at 6 percent interest for 30 years. Determine payments for each of the periods a–d below if interest is accrued

a. Monthly. b. Quarterly. c. Annually. d. Weekly.

4. Regarding Problem 3, how much total interest and principal would be paid over the entire 30-year life of the mortgage in each case? Which payment pattern would have the greatest total amount of interest over the 30-year term of the loan? Why?

5. A fully amortizing mortgage loan is made for $100,000 at 6 percent interest for 20 years. a. Calculate the monthly payment for a CPM loan. b. What will the total of payments be for the entire 20-year period? Of this total, how much will

be the interest? c. Assume the loan is repaid at the end of eight years. What will be the outstanding balance?

How much total interest will have been collected by then? d. The borrower now chooses to reduce the loan balance by $5,000 at the end of year 8.

(1) What will be the new loan maturity assuming that loan payments are not reduced? (2) Assume the loan maturity will not be reduced. What will the new payments be?

6. A 30-year fully amortizing mortgage loan was made 10 years ago for $75,000 at 6 percent inter- est. The borrower would like to prepay the mortgage balance by $10,000.

a. Assuming he can reduce his monthly mortgage payments, what is the new mortgage payment? b. Assuming the loan maturity is shortened and using the original monthly payments, what is

the new loan maturity? 7. A fully amortizing mortgage is made for $100,000 at 6.5 percent interest. If the monthly pay-

ments are $1,000 per month, when will the loan be repaid? 8. A fully amortizing mortgage is made for $80,000 for 25 years. Total monthly payments will be

$900 per month. What is the interest rate on the loan? 9. A partially amortizing mortgage is made for $60,000 for a term of 10 years. The borrower and

lender agree that a balance of $20,000 will remain and be repaid as a lump sum at that time. a. If the interest rate is 7 percent, what must monthly payments be over the 10-year period? b. If the borrower chooses to repay the loan after five years instead of at the end of year 10,

what must the loan balance be? 10. An interest-only mortgage is made for $80,000 at 10 percent interest for 10 years. The lender and

borrower agree that monthly payments will be constant and will require no loan amortization. a. What will the monthly payments be? b. What will be the loan balance after five years? c. If the loan is repaid after five years, what will be the yield to the lender? d. Instead of being repaid after five years, what will be the yield if the loan is repaid after 10

years?

Problems

Final PDF to printer

bru19684_ch04_078-121.indd 111 11/28/17 02:44 PM

Chapter 4 Fixed Interest Rate Mortgage Loans 111

11. A partially amortizing loan for $90,000 for 10 years is made at 6 percent interest. The lender and borrower agree that payments will be monthly and that a balance of $20,000 will remain and be repaid at the end of year 10. Assuming 2 points are charged by the lender, what will be the yield if the loan is repaid at the end of year 10? What must the loan balance be if it is repaid after year 4? What will be the yield to the lender if the loan is repaid at the end of year 4?

12. A loan for $50,000 is made for 10 years at 8 percent interest and no monthly payments are scheduled.

a. How much will be due at the end of 10 years? b. What will be the yield to the lender if it is repaid after eight years? (Assume monthly

compounding.) c. If 1 point is charged in (b) what will be the yield to the lender?

13. John wants to buy a property for $105,000 and wants an 80 percent loan for $84,000. A lender indicates that a fully amortizing loan can be obtained for 30 years (360 months) at 8 percent interest; however, a loan fee of $3,500 will also be necessary for John to obtain the loan.

a. How much will the lender actually disburse? b. What is the APR for the borrower, assuming that the mortgage is paid off after 30 years (full

term)? c. If John pays off the loan after five years, what is the effective interest rate? Why is it differ-

ent from the effective interest rate in (b)? d. Assume the lender also imposes a prepayment penalty of 2 percent of the outstanding loan

balance if the loan is repaid within eight years of closing. If John repays the loan after five years with the prepayment penalty, what is the effective interest rate?

14. Our borrower, John, in problem 13 wants to “roll in” or finance the loan fee of $3,500 into the loan amount which would make the loan $87,500. Answer parts (a) through (d) from problem 13 assuming that the lender agrees to allow the loan fees to be included in the loan amount.

15. A lender is considering what terms to allow on a loan. Current market terms are 9 percent interest for 25 years for a fully amortizing loan. The borrower, Rich, has requested a loan of $100,000. The lender believes that extra credit analysis and careful loan control will have to be exercised because Rich has never borrowed such a large sum before. In addition, the lender expects that market rates will move upward very soon, perhaps even before the loan is closed. To be on the safe side, the lender decides to extend to Rich a CPM loan commitment for $95,000 at 9 percent interest for 25 years; however, the lender wants to charge a loan origination fee to make the mortgage loan yield 10 percent. What origination fee should the lender charge? What fee should be charged if it is expected that the loan will be repaid after 10 years?

16. A borrower is faced with choosing between two loans. Loan A is available for $75,000 at 6 per- cent interest for 30 years, with 6 points to be included in closing costs. Loan B would be made for the same amount, but for 7 percent interest for 30 years, with 2 points to be included in the closing costs. Both loans will be fully amortizing.

a. If the loan is repaid after 20 years, which loan would be the better choice? b. If the loan is repaid after five years, which loan is the better choice?

17. A reverse mortgage is made with a balance not to exceed $300,000 on a property now valued at $700,000. The loan calls for monthly payments to be made to the borrower for 120 months at an interest rate of 11 percent.

a. What will the monthly payments be? b. What will be the loan balance at the end of year 3? c. Assume that the borrower must have monthly draws of $2,000 for the first 50 months of

the loan. Remaining draws from months 51 to 120 must be determined so that the $300,000 maximum is not exceeded in month 120. What will draws by the borrower be during months 51 to 120?

18. A borrower and a lender agree on a $200,000 loan at 10 percent interest. An amortization sched- ule of 25 years has been agreed on; however, the lender has the option to “call” the loan after five years. If called, how much will have to be paid by the borrower at the end of five years?

Final PDF to printer

bru19684_ch04_078-121.indd 112 10/31/17 07:07 PM

112 Part 2 Mortgage Loans

19. A fully amortizing CAM loan is made for $125,000 at 11 percent interest for 20 years. a. What will be the payments and balances for the first six months? b. What would payments be for a CPM loan? c. If both loans were repaid at the end of year 5, would the lender earn a higher rate of interest

on either loan? 20. A $50,000 interest-only mortgage loan is made for 30 years at a nominal interest rate of 6 per-

cent. Interest is to be accrued daily, but payments are to be made monthly. Assume 30 days each month.

a. What will the monthly payments be on such a loan? b. What will the loan balance be at the end of 30 years? b. What is the effective annual rate on this loan?

21. Comprehensive Review Problem: A mortgage loan in the amount of $100,000 is made at 12 percent interest for 20 years. Payments are to be monthly in each part of this problem.

a. What will monthly payments be if (1) The loan is fully amortizing? (2) It is partially amortizing and a balloon payment of $50,000 is scheduled at the end of

year 20? (3) It is a nonamortizing, or “interest-only” loan? (4) It is a negative amortizing loan and the loan balance will be $150,000 at the end of

year 20? b. What will the loan balance be at the end of year 5 under parts a (1) through a (4)? c. What would be the interest portion of the payment scheduled for payment at the end of

month 61 for each case (1) through (4) above? d. Assume that the lender charges 3 points to close the loans in parts a (1) through a (4). What

would be the APR for each? e. Assuming that 3 points are paid at closing and the loan is prepaid at the end of year 5, what

will be the effective rate of interest for each loan in parts a (1) through a (4) ? f. Assume conditions in a (1) except that payments will be “interest only” for the first three

years (36 months). If the loan is to fully amortize over the remaining 17 years, what must the monthly payments be from year 4 through year 20?

g. Refer to a (4) above, where the borrower and lender agree that the loan balance of $150,000 will be payable at the end of year 20:

(1) How much total interest will be paid from all payments? How much total amortization will be paid?

(2) What will be the loan balance at the end of year 3? (3) If the loan is repaid at the end of year 3, what will be the effective rate of interest? (4) If the lender charges 4 points to make this loan, what will the effective rate of interest

be if the loan is repaid at the end of year 3? 22. Excel. Refer to the “Ch4 Eff Cost” tab in the Excel Workbook provided on the website. Suppose

that another loan is available that is an 11 percent interest rate with 6 points. What is the effec- tive cost of this loan compared to the original example on the template?

23. Excel. Refer to the “Ch4 GPM” tab in the Excel Workbook provided on the website. How would the loan balance at the end of year 7 change if the payments increase by 5 percent each year instead of 7.5 percent?www.mhhe.com/bf16e

Final PDF to printer

bru19684_ch04_078-121.indd 113 10/31/17 07:07 PM

Chapter 4 Fixed Interest Rate Mortgage Loans 113

Appendix

Inflation, Mortgage Pricing, and Payment Structuring

The fully amortizing, constant payment mortgage has been the most widely used mortgage instrument in the United States for some time. In more recent times, particularly dur- ing the 1970s and early 1980s, inflation and its effect on this “standard” mortgage instrument have caused problems for both lenders and borrowers. Because of these problems, a number of different mortgage instruments have been pro- posed as alternatives to the standard mortgage instrument. In this section, we outline the problems that inflation has brought for both borrowers and lenders who have relied on the standard mortgage instrument. Also included is a detailed description of the graduated payment mortgage. This mort- gage is also a fixed interest rate mortgage and may be used in place of the constant payment mortgage, particularly during periods of rising interest rates.

Effects on Lenders and Borrowers How does inflation relate to mortgage lending and cause dif- ficulty for lenders and borrowers desiring to make constant payment loans with fixed interest rates? The answer to this question can be easily illustrated. Let us assume initially that a $60,000 loan is made at a time when no inflation is expected. The loan is expected to be outstanding for a 30-year period. Because there is no inflation, an inflation premium ( f ) is not required; hence, the lender will earn a return equiv- alent to the riskless interest rate (r), plus a premium for risk ( p) over the period of the loan.1 We assume that the interest rate charged under such assumptions would be 4 percent, rep- resenting a 3 percent real rate of interest and a risk premium of 1 percent over the period of the loan. Assuming a constant payment, fixed interest rate loan made in an inflationless environment, the lender would collect constant payments of approximately $286 per month, based on the loan constant for 4 percent and 30 years. This amount is shown in Exhibit 4A–1 as a straight line (RP) over the life of the loan and rep- resents the series of constant real payments necessary to earn the lender a 3 percent fixed real return plus a 1 percent risk premium each year that the loan is outstanding.

Now assume that the same loan is made in an inflationary environment, where a 6 percent rate of inflation is expected

1 Actually the interest rate charged will be related to the expected repayment period that may occur before maturity. However, this will not alter the concept being illustrated. The figures chosen here are arbitrary. Some studies indicate that the real rate of interest has historically been in the 1 to 3 percent range and risk premium on mortgages in the 2 to 3 percent range.

to prevail during each year that the loan is outstanding. The interest rate on the mortgage loan would now have to increase to approximately 10 percent for the lender to earn the same real return. This includes the base rate of 4 percent earned when no inflation was expected, plus an inflation premium of 6 percent.2 Given that the standard mortgage instrument is to be used, the lender must now collect approximately $527 a month (rounded). This new payment pattern is shown in Exhibit 4A–1 as the horizontal line labeled NP, represent- ing a constant series of nominal payments received over the term of the loan. Hence, included in the series of nominal payments are amounts that will provide the lender with a 4 percent basic rate of interest representing a real return and risk premium, plus a 6 percent inflation premium over the 30-year loan term.

In our example, an expected inflation rate of 6 percent caused an 84 percent rise in the monthly mortgage payments from $286 to $527, or $241 per month. Why is there such a significant increase in these monthly payments? The reason can be easily seen by again examining curve NPD in Exhibit 4A–1. This curve represents the real value of the monthly payments that the lender will receive over the 30-year loan period. It is determined by “deflating” the $527 nominal monthly payments by the rate of inflation.3 The NPD curve is important because the lender, realizing that inflation is going to occur, expects that the constant stream of $527 payments to be received over time will be worth less and less because of lost purchasing power. Hence, to receive the full 10 per- cent interest necessary to leave enough for a 4 percent real return and risk premium over the life of the loan, more “real dollars” must be collected in the early years of the loan (pay- ments collected toward the end of the life of the mortgage will be worth much less in purchasing power).

To illustrate, let us examine the deflated or real value of the $527 payments collected each month, as represented by the curve NPD. Note that for about the first 10 years of the loan life, the real value of these payments is greater than those for the 4 percent loan. However, after 10 years, the real value of these payments falls below the payments required on the 4 percent loan. However, even though the two pay- ment streams differ, the real value of the nominal payment

2 The nominal interest rate would actually be (1 + .04)(1 + .06) − 1, or 10.24 percent. However, as indicated earlier, we use 10 percent to simplify calculations. 3 Deflating an income stream is done by computing the monthly inflation factor .06 ÷ 12, or .005, and multiplying $527(1 ÷ 1.005)1 in the first month, $527(1 ÷ 1.005)2 in the second month, and so on, until the end of year 30.

Final PDF to printer

bru19684_ch04_078-121.indd 114 10/31/17 07:07 PM

114 Part 2 Mortgage Loans

stream is equal to the required real payments at 4 percent, or NPD = RP. This means that from the stream of nominal $527 monthly receipts, the lender will ultimately earn the same real value as a stream of $286 payments or 4 percent on investment after deflating the nominal payments by the infla- tion rate. However, in order to earn the same real interest rate, the real value of the payment stream (NPD) must be greater than RP in the early years, since it will fall below RP in the later years. This relationship is referred to as tilting the real payment stream in the early years to make up for the loss in purchasing power in later years.

This tilt effect also has a considerable impact on the borrower. Recall that with no inflation the borrower faced a $286 payment; however, with inflation a $527 monthly pay- ment is necessary. When the loan is first originated, the dif- ference in the two payments is about $241 per month and represents an additional amount of real or current dollars that the borrower must allocate from current real income to meet mortgage payments.

Over time, this burden moderates. For example, by the end of the first year, the real value of the $527 payments deflated by the 6 percent rate of inflation would be about $497 per month and the borrower’s real income will have increased by 3 percent, or by the real rate of growth in the economy. At that time, the borrower will have more real income to pay declining real mortgage payments. The important point is that even though the borrower’s income is increasing in both real and nominal terms each year, it is not enough to offset the tilt effect in the early years of a loan. From this analysis,

it becomes apparent from Exhibit 4A–1 why it is so difficult for first-time home buyers to qualify for constant payment, fixed interest rate loans during periods of rising inflation. With the general rate of inflation and growth in the economy, borrower incomes will grow gradually or on a year-by-year basis. However, as expected inflation increases, lenders must build estimates of the full increase into current interest rates “up front,” or when the loan is made. This causes a dramatic increase in required real monthly payments relative to the borrower’s current real income.

One final observation about the tilt effect is that, as the rate of inflation increases, the tilt effect increases. In Exhibit 4A–2, we show the effect of an increase in inflation from 6 percent in our previous example to 8 percent per year. Note that nominal monthly payments increase from $527 to $617 per month, the latter figure based on an increase in the mort- gage interest rate to 12 percent. The impact of the tilt effect on a constant payment loan when inflation is expected to be 8 percent can be seen relative to the effect when infla- tion was expected to be 6 percent. Note that when the $617 monthly payments are deflated at 8 percent (NPD @ 8%) for inflation, the burden of the real payments to be made by the borrower increases relative to the real payments required when inflation was 6 percent in the early years of the loan. The curve corresponding to monthly payments deflated at 8  percent indicates that the real value of monthly payments on the 12  percent mortgage exceeds the real value of pay- ments on the 10 percent mortgage for about the first 10 years of the loan term. This is true even though the lender will

EXHIBIT 4A–1 IRRReal and Nominal Values of Mortgage Payments

$600

550

500

450

400

350

300

250

200

150

100

50 0 5 10 15 20 25 30

NP

Years

RP

NPD

Final PDF to printer

bru19684_ch04_078-121.indd 115 10/31/17 07:07 PM

Chapter 4 Fixed Interest Rate Mortgage Loans 115

EXHIBIT 4A–2 Relationship between Real and Nominal Payments at Various Rates of Inflation

$617

527

286

0 5 10 15 20 25 30

Nominal payments at 12%

Years

Nominal payments at 10%

8% inflation rate

6% inflation rate

earn a 4 percent real return on both mortgages after inflation. Further, if we again assume that the “average” borrower’s real income will increase by 3 percent, regardless of the rate of inflation, as inflation increases from 6 percent to 8 percent, it is clear that the borrower will have to allocate even more cur- rent real income to mortgage payments. This indicates that in the early years of the mortgage, the burden of the tilt effect on borrowers increases as the rate of inflation increases. This increased burden is due solely to (1) the nature of the mort- gage instrument, that is, a constant payment, fixed interest rate mortgage and (2) the rate of inflation. Further, the tilt effect makes it even more difficult for borrowers to qualify for loans based on their current income and make payments from current income. To partially overcome the tilt effect, lenders have designed a mortgage loan that retains a fixed rate of interest but includes a series of stepped-up payments that are lower in the earlier years, thereby better matching borrowers’ incomes, and then rising over time. These loans are known as graduated payment mortgages (GPMs).

The Graduated Payment Mortgage (GPM) In an attempt to deal with the problem of inflation and its impact on mortgage interest rates and monthly payments, lenders have instituted new mortgage instruments. One such instrument is the graduated payment mortgage (GPM). The objective of a GPM is to provide for a series of mortgage payments that are lower in the initial years of the loan than they would be with a standard mortgage loan. GPM payments then gradually increase at a predetermined rate as borrower incomes are expected to rise over time. The payment pattern thus offsets the tilt effect to some extent, reducing the

4 The Federal Housing Administration initiated the first widely accepted graduated payment plan under its Section 245 program. For more detail, see the HUD Handbook’s various issues. 5 Although we discuss GPMs relative to single family lending, this type of loan also could be used to structure debt financing for income-producing properties where mortgage loan payments are designed to match income growth from rents collected over time.

burden faced by households when meeting mortgage pay- ments from current income in an inflationary environment.4

An example of the payment pattern for the graduated payment mortgage is illustrated in Exhibit 4A–3. The exhibit contains information on how payments should be structured for the 30-year, $60,000, fully amortizing loan used in our previous examples. GPMs can have a number of plans allowing for differences in initial payment levels, rates of graduation, and graduation periods. Exhibit 4A–3 contains information on one of the more popular payment plans in use today. This plan allows for a 7.5 percent rate of graduation in monthly payments over five years, after which time the payments level off for the remaining 25 years. Computing initial payments on a mortgage of this kind is complex and is illustrated at the end of this appendix.5

Looking at the information contained in Exhibit 4A–3, we see that for a standard constant payment mortgage (CPM) loan of $60,000 originated at 12 percent for 30 years, the required constant monthly payments would be $617.17. A GPM loan made for the same amount and interest rate, where the monthly payments are increased (graduated) at the end of each year at a predetermined rate of 7.5 percent,

Final PDF to printer

bru19684_ch04_078-121.indd 116 10/31/17 07:07 PM

116 Part 2 Mortgage Loans

begins with an initial payment of approximately $474.83. This initial payment will then increase by 7.5 percent per year to an amount equal to $681.67 at the beginning of year 6 and will remain constant from that point until the end of year 30. Compared with $617.17 in the constant payment mortgage, GPM payments are initially lower by $142.34 in the first year. The difference becomes smaller over time. The graduated payment level reaches approximately the same payment under the standard mortgage between the fourth and fifth years after origination. GPM payments exceed constant payments by $64.50 ($681.67 − $617.17) beginning in year 6. GPM payments then remain at the $681.67 level for the remaining 25 years of the loan term.

Exhibit 4A–4 provides a comparison of payment patterns for a graduated payment mortgage (GPM), a constant pay- ment mortgage (CPM), and a constant amortizing mortgage (CAM). GPM payments are based on the 7.5 percent gradu- ation plan. All three loans are assumed to be originated for $60,000 at 12 percent interest for 30 years. Note that the GPM is below that of the CPM for approximately five years, at which point the GPM payments begin to exceed CPM pay- ments. The reason for this pattern should be obvious. Under either payment plan, the yield to the lender must be an annual rate of 12 percent compounded monthly, assuming no origi- nation fees, penalties, and so on. Therefore, because the GPM payments are below those of the CPM in the early years,

Interest Rate

10% 11% 12% 13% 14%

Constant Payments $526.54 $571.39 $617.17 $663.72 $710.94

GPM Payments Graduated (7.5% Annually)

1 $400.22 $436.96 $474.83 $513.71 $553.51 2 430.24 469.73 510.44 552.24 595.03 3 462.51 504.96 548.72 593.66 639.65 4 497.19 542.83 589.87 638.18 687.63 5 534.48 583.55 634.11 686.04 739.20

6–30 574.57 627.31 681.67 737.50 794.64

EXHIBIT 4A–3 Comparison of GPM Payments and Constant Payments ($60,000, 30-Year Maturity, Fully Amortizing, at Various Interest Rates)

EXHIBIT 4A–4 Comparison of Mortgage Payment Patterns (Loan Amount = $60,000, Maturity = 30 Years, Interest 12% GPM Add: 7.5% Graduation Rate, 5 years)

CAM

CPM

Income

0 5 10 15 20 25 30 Years

GPM

D ol

la rs

Final PDF to printer

bru19684_ch04_078-121.indd 117 10/31/17 07:07 PM

Chapter 4 Fixed Interest Rate Mortgage Loans 117

GPM payments must eventually exceed the level payment on the CPM loan to “make up” for the lower payments on the GPM in the early years. Hence, if the borrower chooses the GPM in our example, the payments will exceed those of a standard CPM mortgage from years 6 to 30.

The advantages of the GPM program are obvious from the borrower’s standpoint. The initial payment level under the GPM plan shown in Exhibit 4A–4 is significantly lower than under the CPM plan. Further, in the early years, GPM payments correspond more closely to increases in borrower’s income. Hence, the burden of the tilt effect requiring bor- rowers to allocate more current real dollars for mortgage payments from current real income in an inflationary envi- ronment is reduced somewhat with the GPM. Based on this analysis, it is easy to conclude that the GPM significantly reduces monthly payments for borrowers in the early years of the mortgage loan, corresponds more closely to increases in borrower income, and therefore may increase the demand for mortgage credit by borrowers.

When judged relative to the CAM, the CPM and GPM clearly provide for initial payments that are far below pay- ments required for the CAM with the same terms. It is impor- tant to stress that higher rates of inflation have caused a modification in mortgage instruments over time. Even though all three mortgage instruments provide the same yield (12%),

changes in mortgage payments have clearly been structured to reduce initial payments. This has been done with the expectation that growth in real incomes and expected infla- tion will extend into the future, resulting in sufficiently high borrower incomes to repay the debt while reducing initial payments sufficiently to reduce the payment burden at the time of loan origination.

Outstanding Loan Balances: GPMs

Because the initial loan payments under GPM plans are usu- ally lower than payments necessary to cover the monthly interest, the outstanding loan balance under the GPM will increase during the initial years of the loan. It will remain higher than that of the standard CPM mortgage until full repayment occurs at maturity. A comparison of loan balances for a GPM and a standard mortgage, based on the 12 per- cent, $60,000, 30-year terms used in our previous example, is shown in Exhibit 4A–5.

Exhibit 4A–6 indicates that the mortgage balance with the GPM increases until approximately year 5, when it begins to decline until it reaches zero in year 30. Hence, if a borrower sold this property during the first four years after making a GPM loan, more would be owed than originally borrowed. The loan balance increases during the first four years after origination because the initial GPM payments are lower than

EXHIBIT 4A–5 Loan Balances for Graduated Payment and Constant Payment Mortgages as Compared with Expected Property Value

Expected property value

0 5 10 15 20 25 30

Years

$120,000

108,000

96,000

84,000

72,000

60,000

48,000

36,000

24,000

12,000

CPM

CAM

GPM

Final PDF to printer

bru19684_ch04_078-121.indd 118 10/31/17 07:07 PM

118 Part 2 Mortgage Loans

EXHIBIT 4A–6 Determining Loan Balance on a GPM ($60,000 Loan, 12%, 30 Years, 7.5 % Rate of Graduation)

Required Monthly First Change Beginning Interest GPM Month Loan in Ending Year Balance Payment Payment Amortization Balance Balance

1 $60,000.00 $600.00 $474.83 $125.17 $1,587.47 $61,587.47 2 61,587.47 615.87 510.44 105.43 1,337.12 62,924.59 3 62,924.59 629.25 548.72 80.53 1,021.32 63,945.91 4 63,945.91 639.46 589.87 49.59 628.93 64,574.84 5 64,574.84 645.75 634.11 11.64 147.62 64,722.46* 6 64,722.46 647.22 681.67 (34.45) (436.91) 64,285.55

*Maximum balance. During the sixth year, the payments ($681.67) will exceed the required interest ($647.22), and loan amortization will begin.www.mhhe.com/bf16e

the monthly interest requirements at 12 percent. Therefore, no amortization of principal occurs until payments increase in later periods. To illustrate, in our previous example, the interest requirements under a GPM after the first month of origination would be $60,000 ×  ( .12 ÷ 12 ) , or $600.00. The GPM payments during the first year of the loan are only $474.83, which are less than the monthly interest require- ment of $600.00. The difference, or $125.17, must be added to the initial loan balance of $60,000, as if that difference represented an additional amount borrowed each month. This $125.17 monthly difference is negative amortization. Further, this shortfall in interest must also accumulate interest at the rate of 12 percent compounded monthly. Hence, dur- ing the first year, $125.17 per month plus monthly com- pound interest must be added to the $60,000 loan balance. This process amounts to compounding a monthly annuity of $125.17 at 12 percent per month and adding that result to the initial loan balance to determine the balance at year-end. The amount added to the loan balance at the end of the year will be the future value (FV) of $125.17 per month, compounded monthly at 12 percent or $125.17 (12.682503)  = $1,587.47.

Solution: n = 12 i = 12% ÷ 12 = 1% PMT = $474.83 PV = −$60,000 Solve for FV = $61,587.47 (loan balance)

Alternate Solution: n = 12 i = 12% ÷ 12 = 1% PMT = $125.17 PV = 0

Solve for FV = −$1,587.47

The importance of the increasing GPM loan balance and negative amortization can be seen in relationship to the prop- erty value also (see Exhibit 4A–5). It is important to note the “margin of safety,” or difference between property value and loan balance. This margin is much lower when a GPM loan balance is compared with that of a CPM. This makes a GPM loan riskier to the lender than a CPM, because more consid- eration must be given to future market values of real estate and future borrower income. For example, let us assume that the GPM borrower decides to sell a property after five years. When compared with the CPM, the lender will have received relatively lower monthly payments up to that point. Further, because of negative amortization, the proceeds from sale of the property must be great enough to repay the loan balance that has increased relative to the original amount borrowed. In short, with a GPM, the lender must now be more concerned about trends in real estate values because resale value will con- stitute a more important source of funds for loan repayment.

GPM Mortgage Loans and Effective Borrowing Costs

A closing note in this appendix considers the question of the effective interest rate and GPMs. In the absence of origination fees and prepayment penalties, the yield on GPMs, like yields on CAMs and CPMs, is equal to the contract rate of inter- est as specified in the note because the GPM, like the CPM, is a fixed interest rate mortgage. This is true whether or not the GPM loan, like CAM and CPM loans, is repaid before maturity. However, to the extent points or origination fees are charged, the effective yield on a GPM will be greater than the contract rate of interest, and it will increase the earlier the loan is repaid. When computing yields on GPMs originated with points, the same procedure should be followed as described with the standard CPM; that is, the interest rate making the stream of GPM payments equal to the funds disbursed after deducting financing fees is the effective cost of the loan. Where origination fees are charged on GPMs, the authors have computed results that are very close to those computed for standard mortgage loans with the same terms and origina- tion fees. This is true regardless of the loan amount or rate

(addition to annual loan balance)

Final PDF to printer

bru19684_ch04_078-121.indd 119 10/31/17 07:07 PM

Chapter 4 Fixed Interest Rate Mortgage Loans 119

6 Computations for the effective interest rate on GPMs are much more difficult than those for the CPM because the amount disbursed must be set equal to a series of seven “grouped cash flows” or annuities, representing different payments for 12 periods in each of the six years, with the final annuity payment covering years 6 to 30. Similarly, when finding loan balances, we may use for GPMs the same procedure demonstrated for CPMs; that is, the remaining payment streams would be discounted at the contract rate of interest and the present value would be determined. However, determining loan balances on GPMs may involve discounting a series of one or more annuities spanning many different 12-month intervals if any remaining CPM payments differ. For an illustration of how to calculate payments for GPMs see the following section.

of graduation on the GPM. In the GPM discussed above, for example, if 3 points are charged and the loan is repaid after five years, the effective rate would be about 12.78 percent, compared with 12.82 on a CPM with the same terms.6 Is a borrower better off or worse off with a GPM or a CPM loan? Generally, if a standard loan and a GPM are originated at the same rate of interest and have the same fees, there will be little, if any, difference in their effective costs. However, because the graduated payment pattern reduces the tilt effect, the borrower is definitely better off with a GPM if it can be obtained at the same interest rate as the standard mortgage.

Would a GPM generally be available at the same inter- est rate as a standard CPM mortgage? It would appear that because of the additional risk taken by the lender—in the form of an increasing loan balance due to negative amortiza- tion in the early years of the loan and lower initial monthly cash flows received from reduced payments—the GPM lender would require a higher risk premium than the CPM lender. Hence, all things being equal, a slightly higher inter- est rate may be required on a GPM than on a CPM. This would tend to neutralize some of the positive features of the GPM compared with the CPM.

Graduated Payment Mortgages—Further Extensions As explained in the chapter, the mechanics of determin- ing monthly payment streams and loan balance are relatively straightforward for FRMs. However, when designing a GPM structure, the reader should be aware that the rate of graduation, number of years during which payments will graduate, term, and interest rate will vary, depending on the goals of the borrower and lender and the loan market that it is being designed to serve.

Perhaps, the most complex problem associated with a GPM is establishing the initial monthly payment. For exam- ple, in Exhibit 4A–3 monthly payments for various GPMs are illustrated. Each group of monthly payments was assumed to increase at the rate of 7.5 percent beginning in year 2. However, the reader may be wondering how the initial pay- ment is determined and, perhaps more importantly, how one

may go about designing a structure for payment patterns requiring a graduated or stepped up repayment schedule. For example, in the case of our 12 percent GPM mortgage, we note that the initial payment would be $474.83. How was that payment determined?

To answer this question, we provide what appears to be a difficult solution. Upon closer examination, however, we will see that it is an application of the present value formulas that we have learned. It is important to recall that for the GPM, as was the case with the CAM, the present value of all pay- ments discounted at the contract rate of interest will equal the initial loan amount. This concept is very important and must be kept in mind as we work through the problem at hand. What follows is a general formula for determining the initial monthly payment for a GPM:

PV =

[ M P 1  ⋅  ∑ t=1

12

1 _ (1 + i / 12) t

]

+ [ M P 1 (1 + g) 1  ⋅  ∑ t=1

12

1 _ (1 + i / 12) t

 ⋅  1 _ (1 + i / 12) 12

]

+ [ M P 1 (1 + g) 2  ⋅  ∑ t=1

12

1 _ (1 + i / 12) t

 ⋅  1 _ (1 + i / 12) 24

]

+ [ M P 1 (1 + g) 3  ⋅  ∑ t=1

12

1 _ (1 + i / 12) t

 ⋅  1 _ (1 + i / 12) 36

]

+ [ M P 1 (1 + g) 4  ⋅  ∑ t=1

12

1 _ (1 + i / 12) t

 ⋅  1 _ (1 + i / 12) 48

]

+ [ M P 1 (1 + g) 5  ⋅  ∑ t=1

300

1 _ (1 + i / 12) t

 ⋅  1 _ (1 + i / 12) 60

]

where

PV = loan amount

i = contract interest rate

MP1 = monthly payments during year 1

g = rate of graduation in the monthly payment

While the computation appears to be complex, a rela- tively simple solution for M P 1 is obtainable for our $60,000, 12 percent, 30-year GPM with a graduation rate of 7.5 per- cent. Note that the expressions containing the Σ’s are sim- ply the interest factors for the present value of an annuity presented in Chapters 3 and 4. The terms 1 ÷  (1 +  i / 12) 12 , 1 ÷  (1 +  i / 12) 24 , and so on are simply the factors also dis- cussed in Chapters 3 and 4. These factors correspond to vari- ous 12-month intervals during which monthly payments will be greater than the previous 12-month period. However, in any given year, monthly payments (unknown) will remain constant during that year. Hence, what we have in our base case example are six different groups of unknown monthly annuities, which, when discounted by the contract rate of

Final PDF to printer

bru19684_ch04_078-121.indd 120 10/31/17 07:07 PM

120 Part 2 Mortgage Loans

interest on the mortgage (i), must equal the initial amount of the loan. This process is usually referred to as discounting grouped cash flows and is a problem encountered frequently in real estate finance.

Essentially, our problem involves finding MP1, which is the only unknown. We know the loan amount ($60,000), the monthly interest rate (i ÷ 12 = .01) , and the term of the loan (360 months). Further, we know that MP in years 2, 3, 4, 5, and 6 will be equal to MP1, increased by (1 + g) 1 , (1 + g) 2 , (1 + g) 3 , (1 + g) 4 , and  (1 + g) 5 , respectively, where g = .075. Given this information, MP1 can be found by assembling the information as shown in Exhibit 4A–7.

Looking at Exhibit 4A–7, we see that column 1 corre- sponds to the payments for years 1 to 30. Column 2 merely indicates that payments during each year will be increased at the rate of 7.5 percent per year, which is equivalent to compounding MP1 (unknown) by 1.075 for each year’s set of payments beginning in year 2. In other words, we are solv- ing for payments in year 1 which will remain the same for 12 months, and then increase by 1.075 beginning in year 2. Hence, column 3 is simply the compound interest factor for the rate of graduation (7.5 percent) applied to M P 1 .

In Exhibit 4A–7, column 4 contains the present value of 12 payments received at the end of the month each year at 12 percent. This factor is, in effect, being used to discount the six different series of monthly payments within the interval during which they will occur. For example, in each of the first five years, 12 monthly payments will be received and must be discounted for that 12-month interval, hence the factor 11.255077. From years 6 to 30, 300 payments will be received and must be discounted for that interval, hence the factor 94.946551.

Column 5 contains the present value of column(4) received at the end of each year, which must be used to dis- count each series of monthly annuities back to time period zero or present value. In other words, column 4 discounts the 12 monthly payments within the 12-month interval. Column

5 is necessary because each series of grouped payments is not received all at once; instead, the series received during the second year has a lower present value than the series received in the first year. Hence, each series must be discounted again by the column (5) factor for one year, the third year must be discounted for two years, and so on.

Finally, column 6 is simply the product of columns 3, 4, and 5. Note that these factors are additive because we have been able to express each series of payments (M P 2 , M P 3 , M P 4 , M P 5  and M P 6−30 ) in terms of M P 1 because we know that each succeeding period’s payment will increase by the same rate of graduation (1  +  g) . Careful inspection of the equation shows that the compounding and discount rates in columns (4) and (5) and 1 + g may be factored, multiplied, and added. This is in essence what we have done in Exhibit 4A–7. Hence, the equation reduces to

M P 1 (126.362333)  = $60,000

MP = $474.83

Because we know that MP2 will be 1.075 times greater than MP, we have we have $474.83(1.075) or $510.44, and so on. The reader may now complete the calculations and verify the payments in the 12 percent column in Exhibit 4A–3.

This formula and procedure have widespread application in real estate finance whenever one is faced with a series of payments which are scheduled to increase after given time intervals at any specified rate of increase.7 The student is also encouraged to think about how the schedule and formula may change if different rates of graduation over different periods of time are desired.

EXHIBIT 4A–7 Worksheet for Solving for Initial GPM Payments

(1) (2) (3) (4) (5) (6) Present Value Present Value of 12 Payments of (Col. 4) Graduated Received at Received at Payment Payment End of Month End of Period Payment Factor Each Year Each Year (3 × 4 × 5) MP1 = MP1(1.0) 1.0 11.255077 — 11.255077 MP2 = MP1(1 + .075) 1.075000 11.255077 .887449 10.737430 MP3 = MP1(1 + .075)2 1.155625 11.255077 .787566 10.243594 MP4 = MP1(1 + .075)3 1.242297 11.255077 .698925 9.772473 MP5 = MP1(1 + .075)4 1.335469 11.255077 .620260 9.323008 MP6–30 = MP1(1 + .075)5 1.435629 94.946551 .550450 75.030751

Total 126.362333

7 This procedure can be programmed into many financial calculators and spreadsheets. An explanation can usually be found in the manual accompanying calculators and spreadsheets under graduated payment mortgages and/or discounting grouped cash flows.

www.mhhe.com/bf16e

Final PDF to printer

Chapter 4 Fixed Interest Rate Mortgage Loans 121

bru19684_ch04_078-121.indd 121 10/31/17 07:07 PM

Regarding loan balances for GPMs, once the mortgage payments are known, balances can be determined at any time by finding the present value of the remaining payments. This is done by discounting those payments by the contract rate of interest, taking into account any grouped cash flows in the remaining series, and discounting them appropriately. As for effective interest rates, any origination fees should be subtracted from the loan amount (PV). Then, given the GPM payments and balance, a new series of compounding and dis- count rates such as shown in columns (4) and (5) in Exhibit 4A–7 at a rate greater than 12 percent would be used to dis- count the payments and balances until the present value of all cash inflows equals the net amount of funds disbursed.

Key Terms: graduated payment mortgage (GPM) negative amortization tilt effect

Questions A–1. Why do level or constant monthly mortgage payments

increase so sharply during periods of inflation? What does the tilt effect have to do with this?

A–2. As inflation increases, the impact of the tilt effect is said to become even more burdensome on borrowers. Why is this so?

Problems A–1. A property is purchased for $70,000. The purchase is

financed with a GPM carrying a 12 percent interest rate. A 7.5 percent rate of graduation will be applied to monthly payments beginning each year after the loan is originated for a period of five years. The initial loan amount is $63,000 for a term of 30 years. The home- owner expects to sell the property after seven years.

a. If the initial monthly payment is $498.57, what will the payments be at the beginning of years 2, 3, 4, and 5?

b. What would the payment be if a CPM loan was available?

c. Assume the loan is originated with two discount points. What is the effective yield on the GPM?

A–2. Mr. Qualify is applying for a $100,000 GPM loan for 25 years at an interest rate of 9 percent. Payments would be designed so as to graduate at the rate of 7.5 percent for three years beginning with payments in the second year.

a. What would the monthly payments be for Mr.  Qualify in each of the first five years of the loan?

b. What would the loan balance be on the GPM at the end of year 3?

c. If the lender charged 4 points at origination, what would be the effective interest rate on this loan after five years?

A–3. Excel. Refer to the “Ch4 GPM” tab in the Excel Workbook provided on the website. How would the initial payment change if the payments increase by 5 percent each year instead of 7.5 percent?

www.mhhe.com/bf16e

Final PDF to printer

122

bru19684_ch05_122-149.indd 122 10/31/17 03:55 PM

Chapter 5 Adjustable and Floating  Rate Mortgage  Loans In the preceding chapter, we discussed fixed interest rate mortgage (FRM) instruments, giving particular attention to payment patterns. We saw how payment structures and amor- tization rates can be negotiated.

This chapter deals with a variety of mortgage loans with interest rates that are tied to a market rate, or index, and may change with market conditions. When used to finance sin- gle family residences, these loans are called adjustable rate mortgages—ARMS. When used to finance commercial properties, these mortgages frequently are called floating rate loans. Because both types of mortgages are very similar, we will not differentiate between them. In our discussion, we will use the term ARM more frequently. These instruments differ from fixed interest rate mortgages (FRMs) in that they are designed to adjust in one or more ways to changes in economic conditions. Rather than making mortgages with fixed rates of interest over long periods of time, these mortgages provide an alternative method of financing through which lenders and borrowers share the risk of interest rate changes, or interest rate risk. This enables lenders to match changes in interest costs with changes in interest revenue more effectively and thus provide borrowers with potentially lower financing costs.

In this chapter, we begin with a general discussion of the price level adjusted mort- gage (PLAM). Although not widely used, the PLAM illustrates many of the problems that must be considered by lenders and borrowers in financial decision making. We then consider ARMs and issues relative to how they are “priced.” As a part of the analysis of ARMs, we investigate the effects of limitations on (1) interest rate changes, (2) payment increases, and (3) negative amortization and the resultant effects on ARM loan yields. We also consider how these mortgages should be priced relative to FRMs and other ARMs made on different loan terms. At the conclusion of the chapter, we consider the shared appreciation mortgage (SAM), whose repayment terms are partially based on apprecia- tion in property values.

One major issue faced by lenders and borrowers with FRMs is that the interest rate is fixed on the date of origination and remains fixed until the loan is repaid. Hence, from the day of origination, lenders are underwriting the risk of any significant changes in the

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 123

bru19684_ch05_122-149.indd 123 10/31/17 03:55 PM

implicit components of mortgage interest rates, that is, the real rate of interest (r), the risk premium ( p), and the premium for expected inflation ( f ). To the extent that lenders under- estimate any or all of these components at the time of mortgage origination, they will incur a financial loss. For example, assume that a fully amortizing mortgage loan for $60,000 is made for 30 years at 10 percent interest. This mortgage would require monthly payments of about $527 (rounded). Should such a loan be made, it must follow that the consensus of lenders at the time the loan is made is that a 10 percent rate of interest is suf- ficiently high to compensate them for all forms of risk bearing expected to occur over the time that the loan is expected to be outstanding. If over that time, one or more of the com- ponents of the mortgage interest rate (i) are significantly higher than was anticipated at the time of origination, lenders will suffer a loss.1 If, for example, lenders make an inaccurate prediction of inflation and unanticipated inflation occurs, warranting a 12 percent interest rate instead of 10 percent, the magnitude of the loss to the lender over a 30-year period is determined as follows:

1 There are many reasons why lenders may inaccurately predict the components of i over the expected repayment period. Monetary growth may expand or contract, causing changes in the rate of inflation (f ). General economic activity may expand (contract), resulting in a change in the general level of investment and employment, thereby affecting real interest rates and default risk (r and p).

Solution: Function:

i

=

12% / 12

n

=

360

PMT = $527 FV

=

0

Solve for PV

=

$51,190

PV (i, n, PMT, FV )

The loss would be equal to $60,000 − $51,190 = $8,810. Hence, in this case, a 2 percent rate of unanticipated inflation would result in a financial loss of $8,810, or 14.7 percent of the loan amount. Based on this example, it should be easy to see the relationship between interest rate risk and potential losses to lenders. That there is always some additional risk because of the uncertainty about expected levels of each of the components of i is one of the reasons why a risk premium, p, is demanded by lenders. To the extent that this uncer- tainty about future levels of r and f increases, p will also increase, and vice versa.2

It should be noted that losses incurred by lenders result in gains to borrowers. Of course, one could argue that if interest rates declined, then lenders would gain. However, when this occurs, borrowers usually try to refinance their loans. This pattern implies that with fixed interest rate lending, risk bearing may not be “symmetric,” or evenly balanced; that is, lenders bear the risk of loss when interest rates increase, which may not be equally offset by gains if interest rates decline because borrowers can usually prepay loans and will do so when interest rates decline. This problem has motivated lenders and borrowers to use interest rate caps and floors, interest rate swaps, “lockout,” and/or prepayment prohibitions and/or penalties. These features and other options will be discussed in various chapters throughout this book.

2 The reader should realize that there will always be some likelihood that expected levels of r and f will not always be accurate because of unanticipated changes. During some time periods, when economic conditions are stable, the uncertainty in these estimates is likely to be less, whereas in other periods, uncertainty may be greater. Hence, the uncertainty of these estimates is what causes interest rate risk and, in turn, larger or smaller risk premiums.

Final PDF to printer

124 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 124 10/31/17 03:55 PM

The Price Level Adjusted Mortgage (PLAM)

One concept that has been discussed as a remedy for the uncertainty problem for lenders is the price level adjusted mortgage (PLAM). Recalling from the discus- sion in the previous chapter on the determinants of mortgage interest rates, i (where r = expected real rate of interest ; p = risk premium ; and f = expected inflation ), we dis- played the following equation:

i = r + p + f We also indicated that perhaps the most difficult variable in the equation to predict was a premium for expected inflation ( f ). To help reduce interest rate risk, or the uncertainty of inflation and its effect on interest rates, it has been suggested that lenders should originate mortgages at interest rates that reflect expectations of the real interest rate plus a risk pre- mium for the likelihood of loss due to default on a given mortgage loan, or r + p .

After estimating initial values for r and p, the PLAM loan balance would be adjusted up or down by a price index. Payments would then be based on a new loan balance, adjusted for inflation. This would shift the risk of changes in market interest rates brought about by inflation ( f ) to borrowers and relieve lenders of the difficult task of forecasting future interest movements when originating loans. The lender would still bear the risk of any unanticipated change in r or p.3

PLAM: Payment Mechanics An example of a PLAM loan would have payments based on a rate of interest consist- ing only of expectations for r and p for an expected maturity period. Payments would be adjusted periodically, based on the indexed value of the mortgage balance for the remain- ing loan term. To illustrate, assume that a mortgage is made for $60,000 for 30 years at an interest rate of 4 percent, or a lender’s estimate of r + p The lender and borrower may agree that the loan balance will be indexed to the consumer price index (CPI) and adjusted annually. Initial monthly payments would be based on $60,000 at 4 percent for 30 years, or approximately $286. After one year, the loan balance, based on a 30-year amortization schedule for the 4 percent interest rate, would be about $58,943. If it is assumed that the CPI increased by 6 percent during the first year of the loan, the loan balance at the end of year 1 would become $58,943 (1.06) or $62,480. This balance would be repaid over 29 remaining years. Monthly payments, beginning in the second year, would be based on the higher-indexed loan balance of $62,480 at the same 4 percent interest rate for 29 years or $304 per month. This process would continue each year thereafter: (1) computing the loan balance using an amortization schedule based on a 4 percent interest rate for the remaining term, (2) increasing the balance by the change in the CPI during the next year, and (3) computing the new payment over the remaining loan term.

Assuming inflation continued at an annual rate of 6 percent for the remaining loan term, Exhibit 5–1 shows the nominal payment and loan balance pattern every year for the PLAM loan. There are many patterns that should be pointed out in Exhibit 5–1. Note that 3 Although we are treating each of these variables making up i as independent and additive, they may not be independent and may well interact with one another. For example, the risk premium (p) is partially dependent on the likelihood that a borrower’s income and wealth will rise or fall, which may depend on changes in the economy and, hence, the underlying real rate of interest (r). Changes in income would affect the likelihood of default on a loan because of payments rising relative to income (which may rise or fall) or the loan balance exceeding the market value of the house. Similarly, we do not fully understand the relationship between inflation (f ) and real growth (r) and the possible interaction between them. Hence, the reader should be aware that we are dealing with these influences in a conceptual way to illustrate the importance of each component, but we do not mean to imply that the specification of i is this simplistic.

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 125

bru19684_ch05_122-149.indd 125 10/31/17 03:55 PM

the PLAM payments shown in panel A increase at approximately the same rate as the change in the price level, or 6 percent over the life of the loan. This increase in payments continues over the life of the loan even though loan amortization begins to occur as the number of remaining years to maturity declines (see panel B). This pattern of rising pay- ments occurs (1) because of the effect of the increasing price index on the loan balance and (2) because each succeeding year’s payment is computed over a shorter remaining loan term.4 It is also interesting to compare the payments on this PLAM to a $60,000, constant payment FRM made at 10 percent for 30 years. Payments on the FRM would be approximately $527, as compared to the initial PLAM payment of $286. Thus, it would appear that many more households could qualify to purchase housing with PLAMs when compared to CPMs.

The PLAM is not without problems, however. Panel B in Exhibit 5–1 shows that the loan balance on the PLAM increases to about 155 percent of the original loan amount, or from $60,000 to approximately $93,000, after 15 years. Housing is only one of many components making up the CPI. Hence, should prices of other goods represented in the CPI increase faster than house prices, or if house prices declined, indexing loan balances to the CPI could result in loan balances increasing faster than property values. When this occurs, borrowers have an incentive to default. This possibility would place a consider- able burden on lenders because now, instead of dealing with inflation and fixed interest rate loans, they would have to establish adequate down payment levels for all borrowers, forecast future housing prices, and be assured that the value of the property that serves as collateral for the mortgage would always be greater than the outstanding loan bal- ance. Hence, it is questionable whether the CPI is the proper index to use when adjusting PLAM balances.

A second problem with PLAMs has to do with the relationship between mortgage payments and borrower incomes. It would appear that the tilt problem, discussed in the appendix to Chapter 4, would be greatly reduced, because payments would be matched more closely with borrower incomes. However, this assumes that both the CPI, which is used to index the PLAM, and borrower incomes change in the same way. A desired ratio

4 The reader should realize that the process of adjustments occurring at the end of each year can be viewed as an annual series of new mortgage loan originations. As such, payments may be modified based on different rates of interest or maturities, with the outstanding loan balance always representing the new amount being borrowed. Hence, it is possible for changes in interest rates or maturities to be renegotiated or varied by the lender and borrower at any time to moderate or increase monthly payments.

EXHIBIT 5–1 Payments and Loan Balance Patterns, $60,000 PLAM, 4%, Inflation = 6% per Year, versus $60,000 CPM, 10% Interest, 30 Years

5 10 15 20 25 30

PLAM

CPM

Panel A: Monthly payments

$120

100

80

60

40

20

Panel B: Outstanding loan balances ($000s)

$1,800

1,500

1,200

900

600

300

5 10 15 20 25 30

PLAM

CPM

Final PDF to printer

126 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 126 10/31/17 03:55 PM

between mortgage payments and borrower incomes may be easy to maintain as long as incomes keep pace with increases in the CPI. Over the long run, this relationship may be possible as increases in income and mortgage payments “balance out.” However, if inflation increases sharply, it is not likely that borrower incomes would increase at the same rate in the short run. During such periods, the payment burden may increase and households may find it more difficult to make mortgage payments. Because of this pos- sibility and the need to develop a desired relationship to mortgage payments, lenders would have to estimate future income for households in different occupational categories and the relationship of that income to inflation. The problems of rising loan balances and payments just discussed make estimating the risk premium ( p) that lenders must charge extremely difficult.

A third problem with PLAMs is that the price level chosen for indexation is usually measured on a historical, or ex post facto, basis. In other words, the index is based on data collected in the previous period but published currently. In as much as mortgage payments are to be made in the future, historic prices may not be an accurate indication of future prices. To illustrate, the change in the CPI may have been 10 percent during the past year (published currently). This figure would be used to index the outstanding mortgage bal- ance, which will determine payments during the next year. If the rate of increase in the CPI subsequently slowed to 2 percent during the next year, it is easy to see that mortgage pay- ments would be rising at a faster rate (10%) than current prices (2%) and, perhaps, faster than borrower incomes. Although borrower incomes may have increased by 10 percent in the previous year, the lag between realization of income in one period and higher payments in the next still presents a problem. This lag problem could become even more distorted in our example if the CPI were to decline and then increase. For this reason, many observers believe that if the PLAM programs were adopted extensively, the time intervals between payment adjustment periods would have to be shortened considerably. This time is called an adjustment interval.

In spite of the practical problems with implementing PLAMs, many PLAM features form the framework for understanding adjustable rate mortgages (ARMs). We now turn our attention to ARMs, which will be our focus for the remainder of this chapter.

ARMs and Floating Rate Loans: An Overview Rather than using changes in the price level as a mechanism to adjust mortgage interest rates and payments, lenders are choosing a variety of mortgages with interest rates that are indexed to other market interest rates. By choosing indexes based on interest rates rather than on a price index, lenders partially avoid having to estimate real interest rates and risk premiums for the entire period that loans are expected to be outstanding. With ARMs, lenders are, in effect, making a loan, with terms that are updated to current interest rate levels at the end of each adjustment period. By using an interest rate index instead of an ex post measure of inflation based on the CPI or any other price index, lenders earn expected yields based on expected future values for r, p, and f over a future period of time. Because interest rates are a reflection of lender and borrower expectations of r, p, and f over specific future periods of time, revisions in ARM payments are always based on future expecta- tions. Therefore, by tying the terms of a mortgage to an index of interest rates, payments are updated frequently. Hence, an ARM provides for adjustments that are more timely for lenders than a PLAM because values for r, p, and f are revised at specific time intervals to reflect market expectations of future values for each component of i between adjust- ment dates. For example, the value for f, or expected inflation, is based on an estimate of future prices rather than a past measure as exemplified in the CPI or other price indexes. Similarly, values for r and p are based on the market’s current assessment of risks in the prospective economic environment between adjustment dates.

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 127

bru19684_ch05_122-149.indd 127 10/31/17 03:55 PM

Payment Basics Illustrated We can begin to illustrate ARM mechanics with a simple example. An ARM for $60,000 with an initial interest rate of 10 percent is originated with a term of 30 years, but its payments are to be reset at the end of one year based on an interest rate determined by a specified index at that time. Based on these initial loan terms, monthly payments would be approximately $527 per month for the first year, and the balance at the end of the year would be $59,666. If the market index were to rise at the end of one year and change the interest rate on the ARM to 12 percent, payments would be determined based on the out- standing loan balance for 29 years as follows:

STEP A: Function: Solution: Find loan balance at end of year 1: FV (PV, n, i, PMT )

n

=

12

PMT

=

$527

PV = $60,000 i

=

10% / 12

Solve for FV

=

$59,666

STEP B: Solution: Find new payments at 12%: Function:

n

=

29 × 12 = 348

i

=

12%/12 = 1% PV = $59,666

FV

=

0

Solve for PMT

=

$616

PMT (n, i, FV, PV )

Hence, the new 12 percent interest rate on the ARM at the end of the first year is an updated estimate of the components of i for the coming year, and payments will increase from $527 to $616 per month.

At least three general observations should be made concerning our simple example. 1. The use of ARMs does not completely eliminate the possibility of lenders realizing

losses because of interest rate risk. In our first example, the yield to the lender on the ARM during the first year was 10 percent. If market rates move to 12 percent the day after the ARM is originated, the lender would sustain a 2 percent loss for the remain- ing 12-month period during year 1. Obviously, this loss would be eliminated if the adjustment period was reduced to one day, or the loss could be reduced to the extent the adjustment period was less than one year.

2. The longer the payment adjustment interval, the greater the interest rate risk to the lender is. Hence, the expected yield to the lender on such a mortgage should be greater. This idea will be elaborated later in the chapter.

3. Finally, as the lender assumes less interest rate risk, the borrower incurs more interest rate risk, depending on the nature of the index chosen and the frequency of payment adjustments. This point can be appreciated if one compares an FRM, where the lender assumes that the full risk of future interest rate changes to an ARM with payments

Final PDF to printer

128 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 128 10/31/17 03:55 PM

adjusting freely with market conditions. Clearly, in the latter case the borrower would be assuming more interest rate risk and the lender less. Because the borrower assumes more risk, the initial interest rate, or start rate, on an ARM should generally be less than that on an FRM. Further, because the lender is shifting interest rate risk to the bor- rower, the lender should also expect, at the time of loan amortization, to earn a lower yield on an ARM over the term of the loan. These three factors are obviously considered by both lenders and borrowers as they negotiate such loans.

Other ARM Characteristics The following list contains a description of some of the more important terms used when dealing with adjustable rate mortgages: ∙ Index. The index is the interest rate series (such as one from the list below) agreed on

by both the borrower and the lender and over which the lender has no control. This index may be very short or long term in nature and will be used to reset the interest rate on an ARM on the reset date. Some commonly used indexes are: — Interest rates on one-year Treasury securities or Treasury indexes with a specific

maturity (6 months, 10 years, etc.). —The average cost-of-funds index (COFI) for the 11th FHLB District. —The London Interbank Offered Rate (LIBOR) for various loan periods.

∙ Margin. A premium in addition to the index chosen for an ARM is known as the margin, or spread.

∙ Composite rate. The sum of the interest rate based on the index chosen plus the margin used to establish the new rate of interest on each reset date is called the composite rate. It can differ from the initial interest rate on the origination date.

∙ Reset date. The point in time when mortgage payments will be adjusted is called the reset date. This time period is usually six months or one year. However, it could be as long as every three to five years, or it could be as short as one month or less.

∙ Negative amortization. To the extent accrued interest in a given period exceeds the periodic payment, the difference may be compounded at current rates and added to the outstanding loan balance. When additions to the outstanding loan balance are allowed in the loan agreement, such amounts are referred to as negative amortization (see the discussion in the previous chapter).

∙ Caps. Maximum increases allowed in payments, interest rates, maturity extensions, and negative amortization (or loan balances) on reset dates are called caps.

∙ Floors. Maximum reductions in payments or interest rates on reset dates are called floors.

∙ Assumability. The ability of the borrower to allow a subsequent purchaser of a property to assume a loan under the existing terms is called assumability.

∙ Discount points. As with FRMs, these points or fees are also used with ARMs to increase the lender’s yield.

∙ Prepayment privilege. Most residential borrowers usually have the option to prepay without penalty. However, because prepayment is a privilege and not a right, lenders may charge penalties if a loan is prepaid within a certain period of time.

∙ Lockouts. Many commercial mortgage loans prohibit repayment for a specified number of years. In these cases, should a borrower wish to prepay, a prepayment fee may have to be negotiated with the lender.

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 129

bru19684_ch05_122-149.indd 129 10/31/17 03:55 PM

∙ Conversion option. The right of an ARM borrower to convert to an FRM. Depending on the agreement, this conversion option may be exercised by the borrower at will or only after a specific period of time. Lenders also may charge a fee for this option.

Clearly, many other combinations of the above provisions could be used to allocate interest rate risk between the lender and borrower.5 Space does not allow for an in-depth analysis of all of these combinations. What we will provide, however, is a framework which should provide the necessary tools that can be used to analyze any given set of ARM or floating rate provisions.

Variations: ARM and Floating Rate Loans

3/1, 5/1, and 7/1 “Hybrid Loans” Another frequently used category of ARMs is sometimes referred to as hybrid ARMs. This category combines elements of FRMs for periods of three, five, or seven years, after which interest rates are reset and the loan becomes an ARM. Subsequent payments are usually reset every year for the remaining maturity period. For example, a 3/1 hybrid would mean a three-year fixed rate after which the interest rate would become adjustable, tied to an index, and would be reset each year thereafter. ARM payments on such a loan, with a 30-year maturity and an initial rate of 6 percent, would begin with fully amortizing monthly payments like an FRM made for a period of 30 years. For the first three years, payments would be

5 In residential lending, there are three additional terms that are commonly negotiated by borrowers and lenders. These include:

• Expected start rate. The expected start rate is based on the index chosen plus the margin on the loan closing date. Because the lender is assuming less interest rate risk than the borrower, it will almost always be lower than rates on FRMs.

• Actual start rate, or initial interest rate. The actual start rate is determined by competitive market conditions among lenders at the time ARM loan commitments are made. It may be the same as or lower than the expected start rate. When the initial, or actual, start rate is lower than the expected start rate, it is sometimes referred to as a “teaser rate.”

• Teaser rate. When the actual start rate is very low when compared to the expected start rate, it is usually an indication that lenders are actively competing and are willing to offer a lower initial rate of interest (teaser rate) in order to attract borrowers. One additional issue that borrowers must determine is whether they are getting a true discount or whether the lower rate of interest will be deferred interest which will be added to the loan balance.

Solution: Function: Years 1–3: PMT (PV, i, n, FV )

PV

=

− $100,000

i =

6% / 12

n = 360 FV

=

0

Solve for PMT

=

$599.55

Final PDF to printer

130 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 130 10/31/17 03:55 PM

On the reset date at the end of three years, the reset rate would be based on the prevailing index and margin agreed on by the borrower and the lender. For example, at the end of three years, if the ARM rate has risen to 6.5 percent, payments for the first year thereafter (year 4) would be based on the balance at the end of year 3, or $96,084.

Solution: Function: Beginning of year 4 through year 30 PMT (PV, i, n, FV )

PV

=

− $96,084

i =

6.5% / 12

n = 324 FV

=

0

Solve for PMT

=

$629.88

In this example, for the first three years, payments would be the same as a $100,000 FRM made at 6 percent for 30 years, or $599.55. At the end of three years, the loan balance would be $96,084, the interest rate would be reset at 6.5 percent (assumption), and pay- ments during year 4 would become $629.88. Payments would be recalculated on the reset date every year thereafter.

As discussed above, possible variations on a hybrid loan could consist of the payments in years 1 to 3 being interest only, with payments beginning in year 4 being based on the ARM index at the end of year 3. Because payments would be interest only, the loan bal- ance beginning in year 4 would remain at $100,000. Payments beginning in year 4 would be recalculated based on the prevailing interest rate plus amortization of loan principal over 27 years. Payments would then be recalculated on each reset date at the beginning of each of the remaining 27 years.

Interest-Only ARM and Floating Rate Loans Many floating rate loans are used to finance commercial properties. The interest-only ARM or floating rate loan requires that the borrower pay interest monthly. Interest pay- ments vary in accordance with the underlying index and margin. For example, a $100,000 loan with an initial rate of 6 percent for 30 years and a one-year reset period would require monthly interest-only payments as follows:

Monthly payment

=

Loan amount ·  (Interest rate ÷ 12)

= $100,000 ·  (.06 ÷ 12)

= $500

If, at the beginning of the next year (the reset date), the index has increased and the new interest rate becomes 8 percent, the new monthly payment becomes:

=

$100,000 ·  (.08 ÷ 12)

=

$666.67

Note that in both cases, payments are interest only and do not include any amortization of principal. Now, consider the event that at the end of year 1, the borrower begins to make

Final PDF to printer

bru19684_ch05_122-149.indd 131 10/31/17 03:55 PM

As has been pointed out, interest rates and monthly payments on ARMs are reset after expiration of a specific time interval (commonly one year). As has also been pointed out, the interest rate on the reset date will be based on the index chosen by the borrower plus a fixed margin. However, it is important to understand what is referred to as the teaser rate.

The initial rate of interest on an ARM is effective on the day that the ARM closes and is used to calculate monthly payments during the first year. To illustrate: On the date of closing the ARM loan, if one year treasuries are 4 percent and the margin is 2 percent, it would be logical to assume that the expected initial, or start, rate used to compute mort- gage payments would be 6 percent. However, the initial rate does not necessarily have to be 6 percent. This is because at the point of origination, lenders are free to compete with other lenders by offering borrowers different initial interest rate points, other financing fees, and the like. For this reason, when the initial interest rate quoted on an ARM is below the prevailing market index rate plus the margin, it is sometimes referred to as a “teaser rate.” Lenders use teaser rates to attract borrowers and compete for business with other lenders. However, the teaser rate will usually prevail only from the date of loan origination until the first reset date. On that date, the teaser rate ceases to exist and the interest rate and pay- ments will be calculated based on the prevailing index plus the margin. Interest rates and payments will be reset each year thereafter based on the index plus margin for the remain- ing life of the loan.

In our example, if we assume that when the ARM is closed (with interest at the prevailing market rate of 6%), a teaser rate of 1.5 percent is offered by the lender, monthly payments for the first year would be

Importance of the “Teaser Rate” Concept Box 5.1 on ARMs—Residential Loans

Solution: Payments Based on Teaser Rate: Function:

PV

=

− $100,000

i =

1.5% / 12

n = 30 × 12 FV

=

0

Solve for PMT

=

$345.12

PMT (PV, i, n, FV )

This payment is far lower than would be the case if the loan was originated at 6 percent interest. For example, “interest-only” payments would be $500 at 6 percent interest. Or, if the payment was based on a fully amortizing 30-year-loan schedule, it would be $607.32.

THE TEASER RATE AND THE ACCRUAL RATE

Recall in the above example that the teaser rate was set at 1.5 percent when the prevailing rate on one-year treasuries (4%) plus the margin would indicate that prevailing interest rates, or the expected start rate, should be in the range of 6 percent. It is also possible that the loan agreement may specify that during the first year, interest will accrue at 6 percent even though payments may be based on the teaser rate of 1.5 percent. If this is the case, the dif- ference between the teaser rate and the accrual rate will be included in the loan balance with interest. Therefore, on the reset date, payments will be based on the outstanding loan balance which will have this difference, plus interest, added to the loan balance (negative amortization).

131

Final PDF to printer

bru19684_ch05_122-149.indd 132 10/31/17 03:55 PM

Importance of the “Teaser Rate” Concept Box 5.1 on ARMs—Residential Loans (Continued)

STEP 1:

Solution: Loan Balance EOY 1: Function:

PMT

=

$345.12

i

=

6%

n = 12 mos. PV

=

− $100,000

Solve for FV

=

$101,910.53 (balance)

FV (PMT, i, n, PV )

STEP 2:

Solution: New Payment on Reset Date at 6.5% Interest: Function:

PV

=

− $101,910.53

i =

6.5%

n = 29 years FV

=

0

Solve for PMT

=

$651.43

PMT (PV, i, n, FV )

132

Note that if the loan agreement specifies that the difference between what the initial rate on the ARM would have been if payments were based on the market rate of 6 percent (the accrual rate) and the teaser rate of 1.5 percent will be accrued in the loan balance, then the loan balance on the reset date ($101,910.53) will be greater than the initial amount of the loan ($100,000.00) because of negative amortization. (This addition to the loan balance may be calculated as the difference in monthly interest accrued at 6 percent, or $500, less the amount paid, $345.12, or $154.88 compounded monthly at 6%.) This results in $1,910.53 being added to the loan balance. This provision may become even more important if the reset date is scheduled for two, three, or more years after the origination date. In this event, the loan balance may increase by an even greater amount because of more accrued interest (negative amortization).

PAYMENT SHOCK

In the above example we determined that when the ARM is originated at a 1.5 percent teaser rate, monthly payments are $345.12. As shown in our example, at the beginning of year 2, payments could increase to $651.43. This amounts to over an 80 percent increase in monthly payments. An increase of this magnitude is sometimes referred to as payment shock. This can occur if large increases in monthly payments occur on the reset date. This can happen when the index to which the ARM interest rate is tied has increased con- siderably. Payment shock can be even more serious for ARMs originated at teaser rates. Depending on the borrower’s income, other assets, and the value of the property on the reset date, this shock could result in financial difficulty and force the borrower to default. For this reason, use of a very low teaser rate to qualify a borrower based on their current ability to make monthly payments may create future problems when it is time for interest rates to be reset.

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 133

bru19684_ch05_122-149.indd 133 10/31/17 03:55 PM

payments which will fully amortize the loan balance over the remaining 29 years. Now, instead of “interest-only” payments of $666.67, the new payments become

Solution: Function:

PV

=

−$100,000

n

=

29 × 12 = 348

i = 8% FV

=

0

Solve for PMT

=

$739.95

PMT (PV, n, i, FV )

The payment at the beginning of year 2 would be $739.95, of which $73.27 would be applied to reduce principal. When monthly compound interest is applied to $73.27 at 8 percent, the loan amortization for the year is $912.20. (This can be seen by calculat- ing PMT = $73.27 , n = 12 i = 8%, and FV = $912.20. ) When this amount is subtracted from $100,000, it produces a loan balance at the end of year 2 of $99,087.79. It should be pointed out that with a floating rate loan (ARM), lenders and borrowers may choose to begin a full or partial amortization schedule at specified times. For example, at the end of year 3, “interest-only” monthly payments must stop and all further payments must begin to include principal so as to fully or partially amortize the loan balance at maturity.

Risk Premiums, Interest Rate Risk, and Default Risk It is very difficult to determine how expected yields will vary among ARMs containing dif- ferent repayment characteristics. However, for any given class of borrowers, the expected yield (cost) of borrowing with an ARM generally depends on the ARM provisions described in detail earlier: (1) the initial interest rate, (2) the index to which the interest rate is tied, (3) the margin, or spread, over the index chosen for a given ARM, (4) discount points charged at origination, (5) the frequency of payment adjustments, and (6) the inclusion of caps or floors on the interest rate, payments, or loan balances. The loan amount and each of the six characteristics listed will determine the cash outflow or amount loaned, expected monthly payments, and the expected loan balance for an expected time period from which an expected yield (internal rate of return) can be computed. In addition to understanding how each of the above relationships is likely to affect the expected yield (or cost of borrow- ing), further complications include understanding how combinations of these terms may interact over time and possibly amplify or reduce default risk to the lender.

While much has been said about benefits to lenders from shifting interest rate risk to bor- rowers, there are added risks that lenders must assume with ARMs. The combination of the six characteristics also affects default risk either (1) by interfering with the ability of the bor- rower to make mortgage payments or (2) by increasing the loan balance so that it is too high in relation to the value of the house, assuming that negative amortization is allowed. While we discuss lender underwriting standards used to gauge default risk in more detail in a later chapter, we also want to stress the importance of default risk in our present discussion.

A useful way to approach the relationships between interest rate risk and default risk for an individual and lender is to examine panel A of Exhibit 5–2. The exhibit shows the risk premium ( p) demanded by the lender on the vertical axis and interest rate risk assumed by the lender on the horizontal axis. Looking at line A–B in the exhibit, we see that as more interest rate risk is assumed by the lender (less by the borrower), the lender will demand a higher risk premium. Hence, the interest rate risk curve is positively sloped. In the extreme, if the lender assumes all interest rate risk (point B), this would be equivalent to the amount

Final PDF to printer

134 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 134 10/31/17 03:55 PM

EXHIBIT 5–2 The Relationship between Interest Rate Risk, Default Risk, and Risk Premiums

Interest rate risk to lender

AR M

Interest rate risk to lender

FRM

Panel A Panel B

(A)

(B)

In te

re st

ra te

ri sk

p re

m iu

m

D ef

au lt

ri sk

p re

m iu

m

ARM

FRM

(C)

(D)

Interest rate risk to lender

FRM Panel C

(E)

To ta

l r isk

p re

m iu

m Total risk

ARM interest rate risk premium

Default risk premium}

FRM borrower #1 Panel D

To ta

l r isk

p re

m iu

m ARM interest rate risk premium}

FRM borrower #2

}Defaultriskpremiums Interest rate risk to lender

AR M b

orr owe

r #1

AR M b

orr owe

r #2

of interest rate risk assumed with an FRM. Note that when the lender assumes no interest rate risk, the borrower is assuming all interest rate risk. This is represented by the intersec- tion of the interest rate risk line at the origin of the diagram (point A).

When interest rate risk assumed by the borrower increases (as would be the case with an ARM with no cap on payments or the interest rate), default risk assumed by the lender increases (see panel B). Default risk is greatest at point C, where there are no restric- tions on ARM interest rates or payments, because the borrower faces a greater likelihood that unanticipated changes in interest rates may cause significant increases in payments (“payment shock”) relative to income. Hence, the likelihood of default is greater when the borrower assumes all interest rate risk. However, as more interest rate risk is assumed by the lender, we should note in panel B that risk of borrower default declines because pay- ment shock to the borrower is restricted when caps on payments or interest rates are used. In essence, by assuming more interest rate risk, the lender absorbs more shock, thereby reducing borrower default risk. This pattern is exhibited in panel B where the default risk curve is shown as negatively related to the risk premium demanded by the lender as inter- est rate risk to the lender increases. However, the level of default risk never declines below the risk assumed by the lender on a fixed rate mortgage (point D), which is also coincident with the lender’s assumption of all interest rate risk (point B in panel A).

The total risk curve (see panel C of Exhibit 5–2) establishes the risk premium demanded by the lender for both risks (interest rate risk and default risk) assumed under various ARM terms. The total amount of risk assumed by the lender corresponds to various combinations of ARM terms, ranging from the assumption of all interest rate risk by the borrower (panel A, point A) to the assumption of all interest rate risk by the lender (panel A, point B),

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 135

bru19684_ch05_122-149.indd 135 10/31/17 03:55 PM

coupled with the amount of default risk incurred by the lender given different levels of interest rate risk (panel B). Hence, panel C shows the total risk premium the lender should earn, given levels of interest rate risk and default risk that correspond to various levels of interest rate risk. However, the total risk premium should not exceed the total premium that would be earned on an FRM (panel C, point E).

Panel D in Exhibit 5–2 shows the relationship between total risk and the risk premium demanded by the lender for different borrowers. Note that the amount of interest rate risk remains the same for each borrower; however, default risk differs. Hence, the premium charged by the lender on ARMs will vary, depending on the amount of default risk being assumed for each borrower, (1) or (2), and how that default risk interacts with expected changes in interest rate risk. We should point out that many other non-interest-rate factors can cause default such as loss of employment, divorce, and so on. We focus here only on how default risk changes with fluctuations in interest rates.

Exhibit 5–2 is appropriate only for specific borrowers, however. To date, the exact rela- tionship between default risk and interest rate risk for many different classes of borrowers has not been studied extensively. Hence, you cannot generalize the example shown to all borrowers and lenders in the mortgage market. However, it is safe to say that ARM loans will only be made to an individual borrower as long as the expected benefits to the lender from shifting interest rate risk exceed the potential default losses. Similarly, as long as a given borrower is willing to undertake interest rate risk in exchange for paying a lower risk premium to a lender, the ARM will be acceptable to the borrower.

While Exhibit 5–2 graphically portrays the risk/return trade-off faced by lenders and borrowers, ARM terms may be structured in many ways to provide a trade-off between interest rate and default risk that is satisfactory to both. These terms could include many possible combinations of initial interest rates, margin, points, the index chosen, frequency of payment adjustments, caps on payments, and so on. We will explore various combina- tions of ARM terms later in this chapter.

From the above discussion, then, mortgage lending (borrowing) can be viewed as a process of pricing risk, with the expected yield being the return received (paid) by lenders (borrowers) for making loans with terms under which lenders and borrowers bear various amounts of risk. The terms utilized in construction of an ARM (e.g., initial rate, index, adjustment period, caps) are simply the “tools” at the disposal of borrowers and lenders to negotiate and allocate the amounts of interest rate and default risk being shared.6

Expected Yield Relationships and Interest Rate Risk While the contracting process used by lenders and borrowers to allocate risk is a compli- cated one, there are some general relationships regarding interest rate risk and yields that can be employed in this process. The following general relationships regarding interest rate risk may be useful when comparing ARMs with FRMs and comparing ARMs contain- ing different loan provisions with one another. The relationships focus on the effects of interest rate risk on ARM yields, given the conclusion that an ARM will never be made unless the expected benefit to a lender from shifting interest rate risk to a borrower exceeds expected losses from default risk. Proceeding with this assumption when evaluating ARM terms, interest rate risk, and expected yields to lenders, we should consider the following relationships: 1. At the time of origination, the expected yield on an ARM should be less than the

expected yield on an FRM, to the extent that benefits to lenders from shifting interest

6 If risk could be quantified, or reduced to some unit quantity such as dollars, an agreement could be devised that would specify exactly how much risk was being shared. However, because risk is an abstract concept, this is not possible. This is the reason why borrowers and lenders include various provisions in contracts to share risk under any set of unknown future economic conditions.

Final PDF to printer

136 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 136 10/31/17 03:55 PM

rate risk exceed increases in default risk to borrowers. Otherwise, the borrower and lender will always prefer an FRM. Coincident with the lower expected ARM yield, the initial interest rate on an ARM will usually be less than that of an FRM.7

2. Adjustable rate mortgages tied to short-term indexes are generally riskier to borrowers than ARMs tied to long-term indexes because the former are generally more variable than long-term interest rates. Therefore, the more risk-averse ARM borrowers will gen- erally prefer ARMs tied to a longer-term index and they should be willing to pay more (a higher risk premium and expected yield to the lender). Less risk-averse borrowers will prefer a shorter-term index and will expect to pay less for taking additional interest rate risk. Borrowers who prefer no interest rate risk will choose a fixed rate mortgage and will pay the highest total risk premium to the lender.

3. Coincidentally with (2), ARMs with shorter time intervals between adjustments in pay- ments are generally riskier to borrowers than those with longer time periods because, although an ARM may be tied to a short-term index, the adjustment period may not coincide with the index. For example, an ARM may be adjusted every three years based on the value of the one-year index at the time of adjustment. Hence, the more frequent the adjustment interval, the lower the interest rate risk to lenders because ARM pay- ments will reflect current market conditions irrespective of the index chosen. Borrowers preferring no adjustment in payments will choose FRMs.

4. To the extent ARMs contain maximum caps on interest rate adjustments, the interest rate risk incurred by borrowers will be lower. Hence, the expected yield realized by lenders should be higher than if no restrictions were present. The expected yield will vary with the size of the limitations. When floors are used, the risk to the borrower is greater because of the limit placed on the decline in the interest rate used to compute ARM payments in any given year. Borrowers who prefer certainty in payments and interest rates will choose an FRM, which will always provide the highest expected yield to the lender.

5. If an ARM has negative amortization due to a payment cap, then the effect of changes in interest rates will not materially reduce interest rate risk to borrowers or the expected yield to lenders because any interest forgone because of limitations or caps will be deferred and become a part of the loan balance. Any amounts of negative amortization will also accrue compound interest and must be eventually paid by borrowers.

More Complex Features In the preceding section, we described some general relationships regarding ARM loan terms, risk bearing, and what lenders (borrowers) should expect to yield (pay) over the life of the ARM contract, or repayment period. We must point out, however, that lend- ers and borrowers also negotiate certain initial loan provisions that (1) will be known at the point of origination and (2) will affect expected yields. Once the index frequency of payment adjustments, rates of payments, and negative amortization have been negotiated, the magnitude of the effect on lenders and borrowers will be determined solely by future market conditions. However, the initial terms on ARMs, or the loan amount, maturity, ini- tial interest rate, margin, and discount points, are quantifiable and can be negotiated with complete certainty at the time the loan is made. These initial loan terms will reflect the net effect of (1) the amount of interest rate risk assumed by the lender as determined by the 7 Although the initial interest rate on an ARM should generally be less than that of an FRM, in cases where short-term interest rates are greater than long-term rates and an ARM is tied to a short-term rate, it is possible that the initial rate on an ARM may be greater than an initial interest rate on an FRM. However, the expected yield on an ARM should be lower because yields are computed to maturity, which includes expected future interest rate patterns.

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 137

bru19684_ch05_122-149.indd 137 10/31/17 03:55 PM

index chosen, adjustment period, any caps or negative amortization and (2) the amount of default risk assumed by the lender as determined by the amount of interest rate risk shifted to a specific borrower. Exhibit 5–3 contains a summary of hypothetical loan terms being quoted on three ARMs and one FRM.

A careful review of these loans reveals considerable differences in terms. We note that the initial interest rate for ARM I is 8 percent, for ARM II it is 9 percent, and for ARM III it is 11 percent, while the fixed interest rate mortgage (FRM) is quoted at 14 percent. Why is this?

A quick review of the terms for ARM I shows that it has the same terms (b) to ( f ) as ARMs II and III; however, characteristics (g) to (i) reveal that future payments and interest rates are unrestricted since there are no caps on payments or interest rates. These terms may now be compared with ARM II, which has a cap of 7.5 percent between any adjustment period plus a provision for negative amortization. ARM III has an interest rate cap of 2 percent between adjustment periods and 5 percent over the life of the loan. When all three ARMs are compared, it is clear that the borrower is assuming more inter- est rate risk with ARM I than with any of the other ARMs. Hence, the expected yield on ARM I to the lender should be less, when compared with other ARMs, for an otherwise qualified borrower (i.e., a borrower with an acceptable level of default risk under all three ARM choices).

Because the expected yield should be less for ARM I, the initial interest rate will also generally be lower than each of the initial rates shown for the other ARM alternatives. Given that all ARMs are tied to the same index and have the same margin and discount points, the only way to “price” ARM I to achieve a lower expected yield is to reduce the initial interest rate relative to the other ARMs. ARM I should also have the largest dis- count, or spread, relative to the interest rate on the FRM. This would be expected because the borrower is bearing all interest rate risk; hence, the lender should expect to earn a lower risk premium and therefore a lower yield on ARM I when compared with the FRM (again, default risk is assumed to be acceptable for this borrower if ARM I is made).

Using a lower initial rate as an inducement for borrowers to accept more interest rate risk and unrestricted payments in the future is obviously only one of many combinations of terms that may be used to differentiate ARM I from ARMs II and III and from the FRM. For example, the lender could keep the initial rate on ARM I the same as that offered on ARM II, but reduce the margin on ARM I or charge fewer discount points, or both. Other terms, such as the choice of index, payment adjustment intervals, and so on, could also be varied with these three terms to accomplish the same objectives.

Moving to ARMs II and III in Exhibit 5–3, we note that both have initial interest rates that are greater than the initial rate on ARM I. The interest rate on ARM II is greater than that of ARM I because ARM II has a cap on payments that reduces payment uncertainty for the borrower.

Contents ARM I ARM II ARM III FRM

(a) Initial interest rate, or start rate 8% 9% 11% 14% (b) Loan maturity 30 30 30 30 (c) Maturity of instruments making up index 1 year 1 year 1 year — (d) Percent margin above index 2% 2% 2% — (e) Adjustment interval, or reset date 1 year 1 year 1 year — (f) Points 2% 2% 2% 2% (g) Payment cap None 7.5% — — (h) Interest rate cap None None 2%, 5%* — (i) Negative amortization — Yes — —

*2 percent maximum annual increase, 5 percent total increase over the loan term.

EXHIBIT 5–3 Comparison of Hypothetical Loan Terms

Final PDF to printer

138 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 138 10/31/17 03:55 PM

When ARM III is compared to ARMs I and II, the interest rate risk assumed by the lender is clearly greater because payments are limited by interest rate caps. In this case, should market interest rates rise, the interest rate cap would restrict interest payments and not allow the lender to recover any lost interest. When compared with ARMs I and II, ARM III provides that more interest rate risk will be borne by the lender. Hence, it should be originated at a higher initial rate of interest.

Important note should be taken of other possibilities in Exhibit 5–3. If other terms, such as the index and adjustment interval, were to be changed, we would also expect changes in the initial loan terms. Suppose that in ARM I an index based on securities with longer maturities were to be chosen or payment intervals were longer than those shown. We would then expect either or all of the initial rate, index, or points to increase because of lower interest rate risk to the borrower; the risk is less because indexes tied to securities based on longer maturities are not as volatile as those based on shorter maturities. Obviously, the same would hold true for the other ARMs if a longer-term index and payment interval were used. Indeed, if such changes were made to the other ARMs, they would become more like an FRM. If longer-term indexes and lower caps were used on ARMs II and III, interest rate risk bearing would become greater for the lender; hence, the expected yield earned by the lender should approach that of an FRM as of the date of origination.

ARM Payment Mechanics To illustrate how payment adjustments and loan balances are determined over the term for the ARMs in Exhibit 5–3, consider the example of a loan amount of $60,000 with a term of 30 years. We assume that the ARM interest rate will be adjusted annually. Hence, the first adjustment will occur at the beginning of the second year. At that time, the composite rate on the loan will be determined by the index of one-year U.S. Treasury securities, plus a 2 percent margin. If we assume (1) that the index of one-year Treasury securities takes on a pattern of 10, 13, 15, and 10 percent for the next four years, based on forward rates in existence at the time each ARM is originated and (2) that monthly payment and interest rate adjustments are made annually, what would payment adjustments, loan balances, and expected yields be for an ARM with these assumed characteristics?

No Caps or Limitations on Payments or Interest Rates The first case to consider is ARM I, where payments are unrestricted or allowed to move up or down with the index without limit. What would be the payment pattern on such an ARM given that the expected distribution of future interest rates actually occurred? This unrestricted case, where no limitations apply to payments or interest, is straightforward to deal with.

The first four columns of Exhibit 5–4 contain the data needed for our computations. Note that we assume that the initial interest rate is 8 percent for the first year, but after the first year the index plus the 2 percent margin establish what the payment will be. From the

(1) (2) (3) (4) (5) (6)

Year Index + Margin = Interest

Rate Payments Balance†

1 8%* $440.26 $59,499 2 10% 2% 12 614.25 59,255 3 13 2 15 752.27 59,106 4 15 2 17 846.21 58,990 5 10 2 12 617.60 58,639

*Initial rate. †Rounded.

EXHIBIT 5–4 Summary Data and Results: ARM I (Unrestricted Case)

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 139

bru19684_ch05_122-149.indd 139 10/31/17 03:55 PM

beginning of year 2 through the beginning of year 5, the interest rates used to determine payments are 12, 15, 17, and 12, respectively, based on our assumptions. As previously pointed out, ARMs tied to the same index may vary with respect to the initial rate of inter- est, the margin, and, perhaps, discount points offered by lenders. These components are usually set by competitive conditions in the lending area and are the primary variables (along with caps or other restrictions) with which lenders compete when pricing loans. Lenders have no control over the index and, therefore, must rely on other components with which to compete when pricing the loan.

The payments column of Exhibit 5–4 is based on a series of relatively simple compu- tations. They are carried out as though a new loan is originated at the end of each year based on a new rate of interest, as determined by the index plus the margin, applied to the outstanding loan balance.

The process of (1) computing the loan balance, based on the interest rate applicable dur- ing the year for which the balance is desired and (2) computing the new payment, based on any change in the index at the end of the appropriate adjustment interval, would continue after each adjustment interval over the remaining life of the loan.

STEP 1:

Solution: Determine First Year Payment: Function:

n

=

30 × 12 = 360

i

=

8% / 12 = .66666% PV = $60,000

FV

=

0

Solve for !"T

=

− $440.26

PMT (n, i, PV, FV )

STEP 2:

Solution: Determine First Year Mortgage Balance: Function:

n

=

29 × 12 = 348

i

=

8% / 12 = .66666% PMT = − $440.26

FV

=

0

Solve for PV

=

$59,499

PMT (n, i, PMT, FV )

STEP 3:

Solution: Determine Second Year Payment: Function:

n

=

29 × 12 = 348

i

=

12% / 12 = 1% PV = $59,499

FV

=

0

Solve for PMT

=

− $614.25

PMT (n, i, PV, FV )

STEP 4:

Solution: Determine Second Year Mortgage Balance: Function:

n

=

28 × 12 = 336

i

=

12% / 12 = 1% PMT = − $614.25

FV

=

0

Solve for PV

=

$59,255

PV (n, i, PMT, FV )

Final PDF to printer

140 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 140 10/31/17 03:55 PM

Looking again at Exhibit 5–4, we carry out the computations using the hypothetical interest rate pattern. Assuming no restrictions or caps on interest rates or payments, we see considerable variation in monthly payments. Depending on interest rate changes, pay- ments increase by over 39.5 percent and decline by as much as 27 percent during the first five years. For borrowers who have a strong aversion to interest rate risk and the coincident variability in payments, the unrestricted ARM, tied to a short-term instrument, may not be desirable. One final pattern should be noted in Exhibit 5–4: regardless of the interest rate pattern chosen, the loan is amortizing. The rate of amortization will differ, however, depending on the rate of interest in effect at each adjustment interval.

The default risk associated with ARM I should also be clear from Exhibit 5–4. Note that although the initial payment level is low, the variation in payments over the five-year period is great. Clearly, for a borrower to take this risk, the lender must view the borrow- er’s future income or present and future wealth as sufficient to cover significant changes in monthly payments.

Payment Caps and Negative Amortization We now consider ARM II where the lender and borrower have agreed that to moderate possible interest rate fluctuations in the future, there will be a payment cap, or a maximum rate at which payments can increase between adjustment intervals. This maximum rate of increase will be 7.5 percent per year. In this case, however, any difference between pay- ments and interest that should be earned, based on unrestricted changes in interest rates, will be added to the loan balance. As previously discussed, this type of ARM contains both a payment cap and negative amortization.

Because this ARM allows for a payment cap and negative amortization, the receipt of more cash flow is pushed further into the future than in the unrestricted case. Therefore, interest rate risk to the lender is somewhat greater than with ARM I, so we assume that the initial rate on the mortgage is quoted to be 9 percent, while the margin will remain at 2 percent. Exhibit 5–5 contains computations of the payment and loan balance patterns for the ARM just described. As shown in the exhibit, based on an unrestricted change in our hypothetical pattern of interest rates, monthly payments in the second year would be $615.18, or 27.4 percent higher than the $482.77 payment required during the first year. A payment of $615.18 would obviously be greater than the 7.5 percent maximum allowable increase; hence, the payment would be capped at $518.98, or 7.5 percent more than $482.77. However, because this ARM requires negative amortization, the difference between interest charged during year 2, or 12 percent, and the amount actually paid will be added to the outstanding loan balance plus compound interest.

Negative amortization is computed by using the method shown for the graduated pay- ment mortgage (GPM) in Chapter 4. Exhibit 5–5 contains a breakdown of interest and amortization for ARM II. Note that during the first year when loan payments are computed at 9 percent interest, monthly amortization occurs and the loan balance is reduced. After the first year, monthly payments must be computed first based on the unrestricted interest rate (column 3) to determine whether payments will increase at a rate greater than 7.5  percent. If uncapped payments would exceed 7.5 percent, then the payment cap (col- umn 4) becomes operative and actual payments will be restricted to a 7.5 percent increase. The monthly interest that is accruing on the loan balance at the unrestricted rate is (.12 ÷ 12) $59,590 = $595.90 (column 6). However, the payment that will actually be made is $518.98. The difference, $76.92 (column 7), must be added to the loan balance with compound interest. Hence, the difference in year 2, $76.92 per month, is compounded at 1  percent per month (column 8), resulting in an increase of $975.54 in the loan balance.8

8 Using a calculator: PV = 0, PMT = $76.92, i = 12% ÷ 12, n = 12: solve for  FV = $975.54.

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 141

bru19684_ch05_122-149.indd 141 10/31/17 03:55 PM

Year Index Margin Interest

Rate

Beginning of Year

Balances Payments

Less: Annual

Amortization

End of Year Loan Balances

1 — — 9%* $60,000 $482.77 409.87 $59,590 2 10% 2% 12 59,590 518.98 (975.54) 60,566 3 13 2 15 60,566 557.90 (2,561.53) 63,128 4 15 2 17 63,128 599.74 (3,823.69) 66,952 5 10 2 12 66,952 644.72 (314.53) 67,267

*Origination rate.

EXHIBIT 5–6 ARM II: Loan Balances When Payments Are Capped at 7.5 Percent Annually (Negative Amortization Allowed)

(1) (2) (3) (4)

Beginning of Year

Balance (Rounded)

Uncapped Payment

Payment Capped at 7.5 Percent

1 $60,000 $482.77 $482.77 2 59,590 615.18 518.98 3 60,566 768.91 557.90 4 63,128 903.79 599.74 5 66,952 700.96 644.72

(5) (6) (7) (8) (9) Monthly Interest

Rate

Monthly Interest (5)  ×  (2)

Monthly Amortization

(4)  −  (6)

Compounded Monthly Rate

(End Year) from (5)

Annual Amortization

(7)  ×  (8)

.09 ÷ 12 $450.00 $32.77 12.507596 $409.87 .12 ÷ 12 595.90 (76.92) 12.682503 (975.54) .15 ÷ 12 757.08 (199.18) 12.860378 (2,561.53) .17 ÷ 12 894.31 (294.57) 12.980582  (3,823.69) .12 ÷ 12 669.52 (24.80) 12.682503 (314.53)

EXHIBIT 5–5 Determination of Payment Limits ( Negative  Amortization:  ARM II, with  Payment Cap = 7.5 Percent Annually)

Payments in the third year of the ARM are determined by again establishing whether uncapped payments would increase by more than 7.5 percent. To determine this, we find that the loan balance, which includes the previous year’s negative amortization, is $59,590 + $975.54 = $60,566 (rounded). The unrestricted interest rate of 15 percent for the remaining 336 months is used to compute the uncapped payment. Uncapped payments based on the unrestricted rate of 15 percent would be $768.91. This is a 48 percent increase from $518.98; hence, the payment will again be capped at a 7.5 percent increase, and nega- tive amortization will be computed on the interest shortfall, compounded at 15 percent monthly, and added to the loan balance. This process is repeated for each adjustment inter- val over the life of the loan.9 Actual loan balances with payments capped at 7.5 percent are shown in Exhibit 5–6.

Another observation regarding ARM II (see Exhibit 5–5) has to do with the increase in both the payment and loan balance during year 5 even though there is a significant decline in the interest index from 17 to 12 percent. This occurs because the loan balance has

9 ARMs with negative amortization provisions usually limit increases in the loan balance during the life of the loan because it is possible for the loan balance to increase to a level that exceeds the value of the property serving as security for the loan. Consequently, lenders and borrowers must agree that if a prespecified maximum is reached, the lender must either forgo further accumulation of interest in the loan balance or require that monthly payments be increased at that time.

Final PDF to printer

142 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 142 10/31/17 03:55 PM

increased, due to past negative amortization, to $66,952 at the end of year 4. Even though the interest rate declines to 12 percent, monthly interest will be $669.52, which is in excess of the maximum 7.5 percent increase from the $599.74 payment in the preceding year. Hence, payments would increase by 7.5 percent, even though interest rates have declined.

An alternative method that may be used to find loan balances for the ARM illustrated in Exhibits 5–5 and 5–6 is shown in the calculator sequence described below. Note in step 4 that even though payments due in year 2 have been increased by 7.5 percent to $518.98, they remain lower than the interest due which is $595.90 (the accrued rate of 12% ÷ 12, or 1% × $59,590.08 ). Furthermore, when the interest rate of 12 percent is used for i in the calculator sequence and the future value (FV ) is solved for, the loan balance increases to $60,566 (rounded). When compared to the loan balance of $59,590 at the end of year 1, negative amortization of $975 (rounded) has occurred. This coincides with the amount shown in Exhibit 5–5 (column 9) during year 2 and consists of $76.92 per month com- pounded at a monthly rate of 12 percent (or 12% ÷ 12 = .01) . The reader should read both Exhibits 5–5 and 5–6 and review the process involved to better understand the results from the alternative calculator solution shown below.

STEP 1:

Solution: Determine Monthly Payments for Year (1): Function:

PV

=

$60,000

n

=

30 × 12 = 360

i = 9% / 12 = .75% FV

=

0

Solve for PMT

=

$482.77

PMT (PV, n, i, FV )

STEP 2:

Solution: Determine Balance at the End of First Year: Function:

PV

=

$60,000 (from above)

PMT

=

$482.77 (from above)

i = 9% / 12 = .75% (from above) n

=

1 × 12 = 12

Solve for FV

=

$59,590.08

FV (PV, PMT, i, n)

STEP 3:

Solution: Determine Monthly Payments for Year (2): PMT = $482.77 × 1.075 = $518.98

STEP 4:

Solution: Determine Balance at the End of Second Year: Function: FV (PV, PMT, i, n)

Repeat steps 2 through 4 for the remaining years.

PV = $59,590.08 (balance at end of first year calculated above) PMT = $518.98 (from above) i = 12%/12 = 1% n = 1 × 12 = 12 Solve for FV = $60,565.61

Alternative Solution for Determining Loan Balances and Negative Amortization for ARM in Exhibits 5–5 and 5–6:

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 143

bru19684_ch05_122-149.indd 143 10/31/17 03:55 PM

Interest Rate Caps The final case that we consider with ARMs is a common pattern in which interest rates are capped or limited (see Exhibit 5–7). In ARM III, the increase in interest rates is limited to 2 percent during any one adjustment interval (year in our example) and to a total of 5  percent over the life of the loan. If interest rates ever exceed these caps, payments are limited. Hence, the interest rate cap also acts as a payment cap because the maximum increase in interest rate determines the maximum increase in mortgage payments. This means that if the index plus the margin exceeds these caps, the lender will lose any amount of interest above the capped rates.10 Exhibit 5–7 illustrates the payment mechanics of ARM III, where the interest rate quoted at origination, 11 percent, is higher than it is with ARMs I and II because the latter two have unrestricted interest rates, while ARM III has interest rate caps. Therefore, the lender is taking more interest rate risk with ARM III because of the possibility that the cap will be exceeded and interest will be lost. To compensate for this possibility, the lender will charge a higher initial interest rate and should expect to earn a higher expected yield.

The payment patterns shown in Exhibit 5–7 are determined from the loan balance estab- lished at the end of each adjustment interval. Payments are then computed based on the indicated rate of interest for the remaining term. Results of computations show that, com- pared with ARM I (the unrestricted case), payments on ARM III are higher initially, and then remain generally lower than payments on ARM I for the remaining term. Hence, borrowers would have to have more income to qualify for ARM III and default risk to the lender should be lower. The loan balances for both ARMs are about the same in year 5. ARM III payments begin at a higher level than those of ARM II, because of the higher initial rate of interest, and remain higher over the term of the loan. However, because of negative amortization, loan balances over time for ARM II are significantly higher than for ARM III.

Expected Yields on ARMs: A Comparison In the preceding sections, we examined three kinds of ARMs with provisions commonly used in real estate lending. Other considerations are also important to lenders and borrow- ers. One important issue is the yield to lenders, or cost to borrowers, for each category of loan. Given the changes in interest rates, payments, and loan balances, it is not obvious what these yields (costs) will be.

10 In many cases, ARMs may contain floors as well as a cap. In our example, this would mean that a maximum reduction of 2 percent in the mortgage rate would be allowed, regardless of the decline in the index. These floors have limited effectiveness, however, because if a significant decline in the index occurs and the loan agreement allows for prepayment, borrowers may refinance with a new mortgage loan at a rate that is lower than the floor would allow.

Year Index

+ Margin Capped

Interest Rate Payments Balance

1 11% $571.39 $59,730 2 12% 12 616.63 59,485 3 15 14 708.37 59,301 4 17 16 801.65 59,159 5 12 12 619.37 58,807

EXHIBIT 5–7 Summary Data and Results: ARM III Interest Rates Capped at 2 Percent, 5 Percent (No Negative Amortization Allowed)

Final PDF to printer

144 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 144 10/31/17 03:55 PM

Computing Yields on ARMs To compare yields on ARMs, the yield (cost) to the lender (borrower) must be computed for each alternative by solving for the internal rate of return (IRR), or the rate of discount. This rate makes the present value of all expected mortgage payments and the loan balance in the year of repayment equal to the initial loan amount less discount points (or $58,800) for each alternative. To illustrate, consider the case of the unrestricted ARM I which is paid off in year 5. Using data from Exhibit 5–4, we compute the internal rate of return (or yield) as shown in Exhibit 5–8.

From the computations shown in Exhibit 5–8, we see that the solution is approximately 13.0 percent.11 This means that even though the initial rate of interest was 8 percent and the forward rates of interest are expected to range from 8 to 17 percent over the five-year period, the expected yield (cost) is 13.0 percent. Hence, by computing the internal rate of return we have a result that can be compared among alternative ARMs.

Before comparing the results for each ARM considered, we examine the computational procedure used in Exhibit 5–8. Essentially, we are discounting a series of grouped cash flows. In the present case, we are dealing with five groups of monthly cash flows and a single receipt (the loan balance). Note that we discount each group of monthly cash flows by using the present value of a monthly annuity factor of 13 percent (column 3). However, this procedure gives us a present value for a one-year group of 12 monthly payments and does not take into account that the cash flows occurring from years 2 through 5 are not received during year 1. Hence, each of the grouped cash flows must be discounted again by the present value of $1 factor to recognize that the present value of each group of cash flows is not received at the same time. This is carried out in column 4. The loan balance, or $58,639, is then discounted as a lump sum.

Summary Observations: ARMs, Borrower, Lender, and Market Behavior Recalling the graphic analysis of the risk premium and the relationship between interest rate and default risk in Exhibit 5–2, we now show how risk premiums demanded for ARMs I to III would fall on the total risk curve in Exhibit 5–9. This diagram basically indicates that in moving from ARMs I to III, interest rate risk to the lender increases. However, based on panel B in Exhibit 5–2, we recall that as interest rate risk increases to the lender,

11 Using a financial calculator yields a solution of 13.0 percent. Also see Concept Box 3.2 in Chapter 3 for solving for the IRR. We will rely on this result in our discussion.

(1) (2) (3) (4) (5)

Year Monthly

Payments PV Monthly Annuity 13%, 12 Months

PV of $1 per Year, 13%, Years 1–5 PV †

1 $440.26  × 11.196042 × — = $  4,929.39  2 614.25 × 11.196042 × .878710 = 6,043.53 3 752.27 × 11.196042 × .772130 = 6,503.22 4 846.21 × 11.196042 × .678478 = 6,428.04 5 617.60 × 11.196042 × .596185 = 4,122.43 5 $58,639.00 × — × .523874 =   30,719.45

$58,746.06*

*Desired PV = $58,800 : IRR approximately 13 percent. †Rounded.

EXHIBIT 5–8 Computing the IRR for an Unrestricted ARM, Payoff at End of Year 5

Final PDF to printer

Chapter 5 Adjustable and Floating Rate Mortgage Loans 145

bru19684_ch05_122-149.indd 145 10/31/17 03:55 PM

EXHIBIT 5–9 Ranking ARMs Based on Total Risk

Risk to lender

FRM

To ta

l r isk

p re

m iu

m

Total risk premium

Interest rate risk premium

Default risk premium}

ARM I

ARM II

ARM III

Many lenders offer mortgage rate information online. Use a search engine like www.yahoo.com or www.google .com to find a lender offering an adjustable rate mort- gage (ARM). Find out as many things as you can about how the mortgage works (e.g., What is the initial rate?

What index is used for the adjustments? What is the mar- gin over the index? How often does it adjust? What is the term of the loan? Are there any caps or floors on the loan? How does the rate on this ARM compare to the rate for a fixed rate mortgage? Which would you choose?)

Web App

default risk for a specific borrower declines due to interest rate changes. Following the market rule that benefits to the lender (from shifting interest rate risk to the borrower) must exceed expected default risk for the ARM to be originated, we see in Exhibit 5–9 that the total risk premium, and hence the expected yield to the lender, increases as we move from ARMs I to III. All expected ARM yields remain below that of the FRM, as they should.

We also know that, in general, the initial interest rate and expected yield for all ARMs should be lower than that of an FRM on the day of origination. The extent to which the ini- tial rate and expected yield on an ARM will be lower than that on an FRM or another ARM depends on the terms relative to payments, caps, and so on. Terms that are more unre- stricted and shift more interest rate risk to the borrower will generally have initial interest rates that are discounted furthest from FRMs. They will also be discounted from ARMs containing caps on payment and interest rate increases. Hence, when a borrower is faced with selecting from a given set of ARMs with different terms and expectations of forward

Final PDF to printer

146 Part 2 Mortgage Loans

bru19684_ch05_122-149.indd 146 10/31/17 03:55 PM

interest rates, an expected yield must be calculated before a comparison among adjustable rate mortgages and a fixed rate mortgage can be accomplished. While there is no guarantee that the expected yield calculated at origination will be the actual yield or cost of funds over the term of the ARM, the expected yield represents the best estimate of the cost of an ARM based on the information available at the time of origination.

actual start rate, 129 adjustable rate mortgage

(ARM), 122 adjustment interval, 127 assumability, 128 caps, 128 composite rate, 128 expected start rate, 129

floating rate loans, 122 floors, 128 index, 128 interest-only ARM, 130 interest rate risk, 122 margin, 128 negative amortization, 128

payment shock, 132 price level adjusted mortgage

(PLAM), 124 reset date, 128 spread, 128 teaser rate, 129 unanticipated inflation, 123

Key Terms

Useful Websites

www.hud.gov—Department of Housing and Urban Development. www.va.gov—Veterans Association website. www.freddiemac.com—Federal Home Loan Mortgage Corporation. www.mbaa.org—Mortgage Bankers Association of America. www.aba.com—America Banker Association. www.pueblo.gsa.gov/cic_text/housing/handbook/handbook.htm—Provided by U.S. Federal Reserve’s Office of Thrift Supervision. Answers frequently asked questions about adjustable rate mortgages, describes how ARMs work, and provides a means of comparing two different loans. www.fanniemae.com/homebuyers/index.html—Provided by Fannie Mae. Information, tools, and resources for consumers on getting a mortgage, buying, or refinancing a home. www.freddiemac.com/pmms/pmmsarm.htm—This is a good site for finding monthly average commitment rate and points on a one-year adjustable rate mortgage.

Questions 1. In the previous chapter, significant problems about the ability of borrowers to meet mortgage payments and the evolution of fixed interest rate mortgages with various payment patterns were discussed. Why did not this evolution address problems faced by lenders? What have lenders done in recent years to overcome these problems?

2. How do inflationary expectations influence interest rates on mortgage loans?

Conclusion In this chapter, we have shown how mortgage loan terms can be modified to incorporate variable interest rates. Loans with adjustable interest rates become necessary from time to time, depending on the rate of economic expansion and expected rates of inflation. In many situations, when the expected rate of inflation accelerates and becomes more uncertain, questions arise as to whether borrowers or lenders will bear the risk of future interest rate changes. During these times, fixed interest rate lend- ing becomes very costly to borrowers because fixed interest rates and mortgage payments increase at a greater rate than borrower incomes. This imbalance between loan payments and borrower incomes motivates both borrowers and lenders to seek ways to modify loan agreements so that real estate pur- chases can be financed at loan payment levels that are commensurate with current borrower incomes. Adjustable rate mortgage (ARM) loans provide one solution to the imbalance problem. Through a variety of options, including the benchmark index chosen for ARM interest rates, the volatility of the index, frequency of payment adjustment, annual and over-the-loan-life interest rate caps, and negative amortization and other features, lenders and borrowers can negotiate loans and payment structures that result in interest rate risk-sharing agreements that are satisfactory to all parties.

Final PDF to printer

bru19684_ch05_122-149.indd 147 10/31/17 03:55 PM

Chapter 5 Adjustable and Floating Rate Mortgage Loans 147

3. How does the price level adjusted mortgage (PLAM) address the problem of uncertainty in infla- tionary expectations? What are some of the practical limitations in implementing a PLAM program?

4. Why do adjustable rate mortgages (ARMs) seem to be a more suitable alternative for mortgage lending than PLAMs?

5. List each of the main terms likely to be negotiated in an ARM. What does pricing an ARM using these terms mean?

6. What is the difference between interest rate risk and default risk? How do combinations of terms in ARMs affect the allocation of risk between borrowers and lenders?

7. Which of the following two ARMs is likely to be priced higher, that is, offered with a higher initial interest rate? ARM A has a margin of 3 percent and is tied to a three-year index with payments adjustable every two years; payments cannot increase by more than 10 percent from the preceding period; the term is 30 years and no assumption or points will be allowed. ARM B has a margin of 3 percent and is tied to a one-year index with payments to be adjusted each year; payments cannot increase by more than 10 percent from the preceding period; the term is 30 years and no assumption or points are allowed.

8. What are forward rates of interest? How are they determined? What do they have to do with indexes used to adjust ARM payments?

9. Distinguish between the initial rate of interest and expected yield on an ARM. What is the gen- eral relationship between the two? How do they generally reflect ARM terms?

10. If an ARM is priced with an initial interest rate of 8 percent and a margin of 2 percent (when the ARM index is also 8% at origination) and a fixed rate mortgage (FRM) with constant payment is available at 11 percent, what does this imply about inflation and the forward rates in the yield curve at the time of origination? What is implied if an FRM were available at 10 percent? 12 percent?

Problems 1. A price level adjusted mortgage (PLAM) is made with the following terms:

Amount = $95,000

Initial interest rate = 4 percent

Term = 30 years

Points = 6 percent

Payments to be reset at the beginning of each year. Assuming inflation is expected to increase at the rate of 6 percent per year for the next

five years: a. Compute the payments at the beginning of each year (BOY ). b. What is the loan balance at the end of the fifth year? c. What is the yield to the lender on such a mortgage?

2. A basic ARM is made for $200,000 at an initial interest rate of 6 percent for 30 years with an annual reset date. The borrower believes that the interest rate at the beginning of year (BOY ) 2 will increase to 7 percent.

a. Assuming that a fully amortizing loan is made, what will the monthly payments be during year 1?

b. Based on (a) what will the loan balance be at the end of year (EOY ) 1? c. Given that the interest rate is expected to be 7 percent at the beginning of year 2, what will

the monthly payments be during year 2? d. What will be the loan balance at the EOY 2? e. What would be the monthly payments in year 1 if they are to be interest only?

3. A 3/1 ARM is made for $150,000 at 7 percent with a 30-year maturity. a. Assuming that fixed payments are to be made monthly for three years and that the loan is fully

amortizing, what will be the monthly payments? What will be the loan balance after three years?

Final PDF to printer

bru19684_ch05_122-149.indd 148 10/31/17 03:55 PM

148 Part 2 Mortgage Loans

b. What would new payments be beginning in year 4 if the interest rate fell to 6 percent and the loan continued to be fully amortizing?

c. In (a) what would monthly payments be during year 1 if they were interest only? What would payments be beginning in year 4 if interest rates fell to 6 percent and the loan became fully amortizing?

4. An ARM for $100,000 is made at a time when the expected start rate is 5 percent. The loan will be made with a teaser rate of 2 percent for the first year, after which the rate will be reset. The loan is fully amortizing, has a maturity of 25 years, and payments will be made monthly.

a. What will be the payments during the first year? b. Assuming that the reset rate is 6 percent at the beginning of year (BOY ) 2, what will the pay-

ments be? c. By what percentage will the monthly payments increase? d. What if the reset date is three years after loan origination and the reset rate is 6 percent, what

will the loan payments be beginning in year 4 through year 25? 5. An interest-only ARM is made for $200,000 for 30 years. The start rate is 5 percent and the bor-

rower will (1) make monthly interest-only payments for three years. Payments thereafter must be sufficient to fully amortize the loan at maturity.

a. If the borrower makes interest-only payments for three years, what will the payments be? b. Assume that at the end of year 3, the reset rate is 6 percent. The borrower must now make

payments so as to fully amortize the loan. What will the payments be? 6. A borrower has been analyzing different adjustable rate mortgage (ARM) alternatives for the

purchase of a property. The borrower anticipates owning the property for five years. The lender first offers a $150,000, 30-year fully amortizing ARM with the following terms:

Initial interest rate = 6 percent

Index = 1−year Treasuries

Payments reset each year

Margin = 2 percent

Interest rate cap = None

Payment cap = None

Negative amortization = Not allowed

Discount points = 2 percent

Based on estimated forward rates, the index to which the ARM is tied is forecasted as fol- lows: Beginning of year (BOY )  2 = 7 percent; BOY 3 = 8.5 percent;  (BOY )  4 = 9.5 percent; (BOY )  5 = 11 percent.

Compute the payments, loan balances, and yield for the unrestricted ARM for the five-year period.

7. An ARM is made for $150,000 for 30 years with the following terms:

Initial interest rate = 7 percent

Index = 1−year Treasuries

Payments reset each year

Margin = 2 percent Interest rate cap = None

Payment cap = 5 percent increase in any year

Discount points = 2 percent

Fully amortizing; however, negative amortization allowed if payment cap reached Based on estimated forward rates, the index to which the ARM is tied is forecasted as fol-

lows: Beginning of year  (BOY )  2 = 7 percent ;   (BOY )  3 = 8.5 percent ;   (BOY )  4 = 9.5 percent ;   (BOY )  5 = 11 percent.

Compute the payments, loan balances, and yield for the ARM for the five-year period.

Final PDF to printer

bru19684_ch05_122-149.indd 149 10/31/17 03:55 PM

Chapter 5 Adjustable and Floating Rate Mortgage Loans 149

8. Assume that a lender offers a 30-year, $150,000 adjustable rate mortgage (ARM) with the fol- lowing terms:

Initial interest rate = 7.5 percent

Index = one-year Treasuries

Payments reset each year

Margin = 2 percent

Interest rate cap = 1 percent annually; 3 percent lifetime

Discount points = 2 percent

Fully amortizing; however, negative amortization allowed if interest rate caps reached Based on estimated forward rates, the index to which the ARM is tied is forecasted as fol-

lows: Beginning of year (BOY )  2 = 7 percent;  (BOY )  3 = 8.5 percent;  (BOY )  4 = 9.5 percent;  (EOY )  5 = 11 percent.

Compute the payments, loan balances, and yield for the ARM for the five-year period. 9. MakeNu Mortgage Company is offering a new mortgage instrument called the Stable Mortgage.

This mortgage is composed of both a fixed rate and an adjustable rate component. Mrs. Maria Perez is interested in financing a property, which costs $100,000, and is to be financed by Stable Home Mortgages (SHM) on the following terms:

a. The SHM requires a 5 percent down payment, costs the borrower 2 discount points, and allows 75 percent of the mortgage to be fixed and 25 percent to be adjustable. The fixed portion of the loan is for 30 years at an annual interest rate of 10.5 percent. Having neither an interest rate nor payment cap, the adjustable portion is also for 30 years with the following terms:

Initial interest rate = 9 percent

Index = one-year Treasuries

Payments reset each year

Margin = 2 percent

Interest rate cap = None

Payment cap = None

The projected one-year U.S. Treasury-bill index, to which the ARM is tied, is as follows: (BOY )  2 = 10 percent;  (BOY )  3 = 11 percent;  (BOY )  4 = 8 percent;  (BOY )  5 = 12 percent.

Calculate Mrs. Perez’s total monthly payments and end-of-year loan balances for the first five years. Calculate the lender’s yield, assuming Mrs. Perez repays the loan after five years.

b. Repeat part (a) under the assumption that the initial interest rate is 9.5 percent and there is an annual interest rate cap of 1 percent.

10. A floating rate mortgage loan is made for $100,000 for a 30-year period at an initial rate of 12 percent interest. However, the borrower and lender have negotiated a monthly payment of $800.

a. What will be the loan balance at the end of year 1? b. What if the interest rate increases to 13 percent at the end of year 1? How much interest will

be accrued as negative amortization in year 1 if the payment remains at $800? Year 5? 11. Excel. Refer to the “Ch5 ARM No Caps” tab in the Excel Workbook provided on the website.

Suppose that the index goes to 18 percent in year 5. What is the effective cost of the unrestricted ARM?

12. Excel. Refer to the “Ch5 ARM Int Cap” tab in the Excel Workbook provided on the website. Suppose that the index goes to 18 percent in year 5. What is the effective cost of this ARM? What cap affected the rate in year 5?

13. Excel. Refer to the “Ch5 ARM Pmt Cap” tab in the Excel Workbook provided on the website. Suppose that the index goes to 18 percent in year 5. What is the effective cost of the ARM? Does the payment cap keep the effective cost from rising?

www.mhhe.com/bf16e

Final PDF to printer

150

bru19684_ch06_150-184.indd 150 11/01/17 02:54 PM

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications In previous chapters, we have considered the analytics of various types of mortgages used in real estate finance. This chapter extends those concepts to various questions related to the analysis of mortgage financing. Questions raised include how to compare two loans with different loan terms (e.g., amount of loan, interest rate), how to decide whether to refinance or prepay a loan, and whether a loan assumption is desirable. We will also evaluate the effect of below-market financing on the sale price of a property. This is important because one must often pay a higher price for a property that appears to have favorable financing.

Incremental Borrowing Cost

We begin by considering how to evaluate two loan alternatives, where one alternative involves borrowing additional funds relative to the other. For example, assume a borrower is purchasing a property for $100,000 and faces two possible loan alternatives. A lender is willing to make an 80 percent first mortgage loan, or $80,000, for 25 years at 12 percent interest. The same lender is also willing to lend 90 percent, or $90,000, for 25 years at 13 percent. Both loans will have fixed interest rates and constant payment mortgages. How should the borrower compare these alternatives?

To analyze this problem, emphasis should be placed on a basic concept called the marginal, or incremental, cost of borrowing. Based on the material presented in earlier chapters, we know how to compute the effective cost of borrowing for one specific loan. However, it is equally important in real estate finance to be able to compare financing alternatives, whereby the borrower can finance the purchase of real estate in more than one way or under different lending terms.

In the problem at hand, we are considering differences in the amount of the loan and the interest rate. A loan can be made for $80,000 for 25 years at 12 percent, or $90,000 can be borrowed for 25 years at 13 percent interest. Because there are no origination fees, we know from Chapter 4 that the effective interest cost for the two loans will be 12 percent and 13 percent, respectively. However, an important cost that the borrower should compute is the cost to acquire the incremental or additional $10,000, should he choose to take the $90,000 loan over the $80,000 loan. At first glance, you may think that because the interest rate on the $90,000 loan is 13 percent, the cost of acquiring the additional $10,000 is also

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 151

bru19684_ch06_150-184.indd 151 11/01/17 02:54 PM

13 percent. This is not so. Careful analysis of the two loans reveals that if the borrower wants to borrow the additional $10,000 available with the $90,000 loan at 13 percent, he also must pay an additional 1 percent interest on the first $80,000 borrowed. This increases the cost of obtaining the additional $10,000 considerably. The $90,000 loan has a larger payment due not only to the additional $10,000 being borrowed but also to the higher inter- est rate being charged on the entire amount. To determine the cost of the additional $10,000, we must consider how much the additional payment will be on the $90,000 loan compared with the $80,000 loan.1 This difference should then be compared with the addi- tional $10,000 borrowed. This can be done as follows:2

1 Although we use an $80,000 and a $90,000 loan in our example, the calculation can be generalized to other loans that are the same percentage of the property value. 2 For single family residential properties, when loan amounts exceed 80 percent of the property value, private mortgage insurance is usually required by lenders. The cost of this insurance will affect the incremental borrowing costs and must be considered in the calculations. More will be said about private mortgage insurance in Chapter 8.

Loan Amount

Loan Constant

Monthly Payments

Alt. II at 13% $90,000 × .0112784 = $1,015.05 Alt. I at 12%   80,000 × .0105322 =       842.58  Difference $10,000 Difference $   172.47

Solution: Function: n = 25 × 12 = 300 i (n, PV, FV, PMT )

PV = –$10,000 PMT = $172.47

FV = 0 Solve for i = 20.57% (annual)

We want to find the annual rate of interest, compounded monthly, that makes the present value of the difference in mortgage payments, or $172.47, equal to $10,000, or the incre- mental amount of loan proceeds received. Solving for i, we find

A financial calculator indicates that the answer is 20.57 percent. Hence, if our borrower desires to borrow the additional $10,000 with the $90,000 loan, the cost of doing so will be more than 20 percent, a rate considerably higher than 13 percent. This cost is referred to as the marginal, or incremental, cost of borrowing. The 13 percent rate on the $90,000 loan can be thought of as a weighted average of the 12 percent rate on the $80,000 loan and the 20.57 percent rate on the additional $10,000. That is,

[ 80,000 ______ 90,000  × 12% ]  +  [ 10,000 ______ 90,000  × 20.57% ]  = 12.95% or 13%  (rounded) The borrower must consider this cost when evaluating whether the additional

$10,000 should be borrowed. If the borrower has sufficient funds so that the $10,000 would not have to be borrowed, it tells the borrower what rate of interest must be earned on funds not invested in a property because of the larger amount borrowed. In other

Final PDF to printer

bru19684_ch06_150-184.indd 152 11/01/17 02:54 PM

152 Part 2 Mortgage Loans

words, by obtaining a larger loan ($90,000 vs $80,000), the borrower’s down payment will be $10,000 less than it would have been on the $80,000 loan. Hence, unless the bor- rower can earn 20.57 percent interest or more on a $10,000 investment of equal risk on funds not invested in the property, he or she would be better off with the smaller loan of $80,000.

If the borrower does not have enough funds for a down payment to combine with the $80,000 loan and must borrow $90,000, the incremental borrowing cost is the cost of obtaining the extra $10,000. There may be alternative ways of obtaining the extra $10,000. For example, if the borrower could obtain a second mortgage for $10,000 at a rate less than 20.57 percent, this may be a better alternative than a $90,000 loan.3 Therefore, the mar- ginal cost concept is also an opportunity cost concept in that it tells the borrower the mini- mum rate of interest that must be earned, or the maximum amount that should be paid, on any additional amounts borrowed.

It should be noted that the 20.57 percent figure we calculated also represents the return that the lender earns on the additional $10,000 loaned to the borrower; that is, the cost of a loan to the borrower will reflect the return on the loan to the lender. Of course, keep in mind that the figures we are calculating do not take federal income tax considerations into account, which are also important in determining returns and costs (see the appendix to this chapter). For example, if the borrower is in a higher tax bracket than the lender, the after-tax cost to the borrower will be less than the after-tax return to the lender.

Early Repayment We should also note that in this example, the incremental cost of borrowing will depend on when the loan is repaid. For example, if the loan is repaid after five years instead of being held for the entire loan term, the incremental borrowing cost increases from 20.57 percent to 20.83 percent. To see this, we modify the above analysis to consider that if the loan is repaid after five years, the amount that would be repaid on the $80,000 loan will differ from the amount that would be repaid on the $90,000 loan. Thus, in addition to consider- ing the difference in payments between the two loans, we must also consider the difference in the loan balances at the time the loan is repaid. We can find the incremental borrowing cost as follows:

3 A lower effective cost for a second mortgage means that the borrower pays less interest each month. However, if the second mortgage has a term less than 25 years, the total monthly payments will be higher with the $80,000 first mortgage and a $10,000 second mortgage than with a $90,000 first mortgage. Thus, some borrowers may prefer to choose a higher effective borrowing cost to have lower monthly payments.

Loan Amount

Loan Constant

Monthly Payments

Loan Balance after Five Years

Alt. II at 13% $90,000 ×  .0112784 = $1,015.05 $86,639.88 Alt. I at 12%   80,000 ×  .0105322 =    842.58    76,522.56

Difference $10,000 Difference $  172.47 $10,117.32

To find the answer, we must find the interest rate that makes the present value of the monthly annuity of $172.47 and the differences in loan balances equal to $10,000. We can verify that the incremental borrowing cost is now 20.83 percent, the result of early repay- ment. As we will see in the next section, the impact of early payment may be greater when points are also involved on one or both of the loans.

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 153

bru19684_ch06_150-184.indd 153 11/01/17 02:54 PM

Origination Fees It should be apparent that the concept of incremental borrowing cost is extremely impor- tant when deciding how much should be borrowed to finance a given transaction. In the preceding section, the two alternatives considered were fairly straightforward; the only differences between them were the interest rate and the amount borrowed. In most cases, financing alternatives under consideration will have different interest rates as the amount borrowed increases and, possibly, different loan maturities. Also, loan origination fees will usually be charged on the loan alternatives. This section considers differences in loan fees on two loan alternatives. We will consider differences in loan maturities later.

The first case is the incremental cost of borrowing when loan origination fees are charged on two 25-year loan alternatives. For example, if a $1,600 origination fee (2 points) is charged on the $80,000 loan and a $2,700 fee (3 points) is charged on the $90,000 loan, how does this affect the incremental cost of borrowing? These differences can be easily included in the cost computation as follows.

Differences in amounts borrowed and payments:

Loan – Fees = Net Amount Disbursed Loan

Loan Constant

Monthly Payments

Alt. II at 13% $90,000 – $2,700 = $87,300 $90,000 ×  .0112784 = $1,015.05 Alt. I at 12%  80,000 – 1,600 =   78,400  80,000 ×  .0105322 =    842.58

Difference =  $  8,900  Difference = $  172.47

Solution: Function: n = 25 × 12 = 300 i (n, PV, FV, PMT )

PV = –$8,900 PMT = $172.47

FV = 0 Solve for i = 1.9316 × 12 = 23.18% (annually)

Solution: Function: n = 5 × 12 = 60 i (n, PV, PMT, FV )

PV = –$10,000 PMT = $172.47

FV = 10,117.32 Solve for i = 1.7360 (monthly) Solve for i = 1.7360 × 12 = 20.83% (annual)

We want to find an annual rate of interest, compounded monthly, that makes the present value of the difference in mortgage payments, or $172.47, equal to $8,900, or the incre- mental amount of loan proceeds received. Using a financial calculator, we find that the exact answer is 23.18 percent. Hence, the marginal cost increases to about 23.2 percent when the effects of an additional $1,100 in origination fees charged on the $90,000 loan are included in the analysis. Thus, the borrower only benefits from an additional $8,900 instead of $10,000.

Final PDF to printer

bru19684_ch06_150-184.indd 154 11/01/17 02:54 PM

154 Part 2 Mortgage Loans

As before, the marginal or incremental cost of borrowing increases if the loan is repaid before maturity. For example, if the loan in the above problem were repaid after five years, the incremental cost would increase to about 24.67 percent.

Incremental Borrowing Cost versus a Second Mortgage The incremental borrowing cost obviously depends on how much the interest rate increases with the loan-to-value ratio. In the examples considered previously, the interest rate increased from 12 percent to 13 percent (a differential of 1%) when the loan-to-value ratio increased from 80 percent to 90 percent. When no points were charged and the loan was held until maturity, the incremental borrowing cost was 20.57 percent. The incremental borrowing cost would increase if the differential between the rate on the 80 percent loan and the 90 percent loan were greater than 1 percent. Conversely, the incremental borrow- ing cost would decrease if the differential were less than 1 percent.

Because borrowers have a choice between obtaining a 90 percent loan or an 80 percent loan plus a second mortgage for the remaining 10 percent, we would expect the incre- mental borrowing cost to be competitive with the rate on a second mortgage with the same maturity. In the example, if a second mortgage with a maturity of 25 years can be obtained with an effective borrowing cost that is much less than 20.57 percent, then the 90 percent loan is not competitive; it implies that the 1 percent yield differential between the 90 percent loan and the 80 percent loan is too great. Lenders would have to adjust the differential (or the second mortgage rate) so that the incremental borrowing cost is about the same as the effective cost of a second mortgage.

In Exhibit 6–1, we calculate the incremental borrowing cost for the alternatives dis- cussed earlier, which assume that the loan is prepaid after five years. The exhibit shows how the incremental borrowing cost is affected by the interest rate differential on the 90 percent loan and the 80 percent loan. A 0 percent interest rate differential means that the contract interest rate, which is 12 percent, is the same for both loans. A 1 percent differen- tial means the contract rate is 1 percent higher (e.g., 13% for the 90% loan).

When the interest rate differential is zero, the incremental cost is the same as the effective cost of the loan. For example, with no points the incremental cost is exactly 12  percent, the same as the interest rate for the 80 percent loan. As the interest rate differ- ential increases, the incremental borrowing cost increases. The incremental cost increases by about the same rate for each loan.

Suppose that a second mortgage for 10 percent of the purchase price (on top of an 80% first mortgage) can be obtained with an effective cost of 20 percent with a 25-year matu- rity. This is added to Exhibit 6–1.4 This implies that, to be competitive, the 90 percent loan should be priced so that its incremental cost over an 80 percent loan is 20 percent. Suppose that lenders expect the loan to be prepaid on average after five years and that they want to charge 2 points on an 80 percent loan and 3 points on a 90 percent loan as we have assumed in the previous examples. This implies that the interest rate differential should be about .50 percent or 50 basis points (see Exhibit 6–1). Alternatively, if lenders do not want to charge any points on either loan, the interest rate differential would have to be about 90 basis points.

Relationship between the Incremental Cost and the Loan-to-Value Ratio In the previous section, we illustrated the calculation of the incremental borrowing cost for a 90 percent loan ($90,000) with a 13 percent interest rate versus an 80 percent loan

4 To compare this rate with the incremental borrowing cost, this must be the effective cost of the loan, considering any points and the effect of prepayment.

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 155

bru19684_ch06_150-184.indd 155 11/01/17 02:54 PM

($80,000) with a 12 percent interest rate. Where there were no points and the loan was held until maturity, the incremental cost was 20.57 percent. The incremental borrowing cost is the amount that lenders require on the amount added to the loan that increases the loan- to-value ratio from 80 percent to 90 percent. As discussed previously, this incremental return should be competitive with the return required for a second mortgage for 10 percent of value. The incremental borrowing cost represents the return that lenders require at the margin for lending additional funds, that is, increasing the loan-to-value ratio, whether this is done with a larger first mortgage or a second mortgage.

In the previous examples, we used the difference in interest rates for the entire loan amount (e.g., the rate on an 80% loan vs. the rate on a 90% loan) to calculate the implied cost of the incremental 10 percent loan. In theory, however, it is the incremental cost of the extra amount loaned that must reflect the equilibrium required rate of return for the level of default risk associated with the additional amount loaned. As the loan-to-value ratio increases, the level of default risk also increases. Thus, we would expect the incremental borrowing cost to rise with the loan-to-value ratio. This, in turn, pulls up the average cost of the entire loan. Exhibit 6–2 shows the relationship between the rate for the incremental amount borrowed (incremental borrowing cost) and the average rate for the entire loan (effective rate for a loan with a particular loan-to-value ratio). To compare the results with the previous examples, the calculations in the exhibit are based on a loan term of 25 years, the assumption that the loan is held until maturity, and no points. Loans are assumed to be made in increments of 10 percent of value. The average and incremental rates are the same for a loan-to-value ratio of 10 percent because this is the first incremental loan amount. The incremental rate then increases as the loan-to-value ratio increases. The incre- mental rate rises faster than the average rate for the entire loan because the average rate for the entire loan is a weighted average of the incremental cost of each of the previous

EXHIBIT 6–1 Incremental Borrowing Cost versus Interest Rate Differential

40

35

30

25

20

15

10

No points Points

Interest rate differential (%)

In cr

em en

ta l b

or ro

w in

g co

st (%

)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25

Second mortgage

Final PDF to printer

bru19684_ch06_150-184.indd 156 11/01/17 02:54 PM

156 Part 2 Mortgage Loans

incremental costs. This is the familiar relationship between marginal and average costs; that is, the marginal cost pulls up the average cost as long as the marginal cost is greater than the average cost.

The exhibit indicates, for example, that the average cost for an 80 percent loan is 12  percent. The marginal cost of a 90 percent loan is about 21 percent. This implies that the average cost of a 90 percent loan can be approximated as a weighted average as follows:

Average cost of 90% loan = ( 80 / 90 × 12% )  +  ( 10 / 90 × 21% ) Average cost of 90% loan = 13%

Note that these are the same numbers (rounded) as calculated in the previous section for the same loan when the loan had no points and was held until maturity.5

Because the incremental borrowing cost must be competitive with the rate for a second mortgage, the rate for the incremental amount borrowed shown in Exhibit 6–2 should also approximate the market rate for a second mortgage. Because it is inefficient for lenders to make loans with low loan-to-value ratios,6 however, we may not actually observe quotes for loans at the lower end of the loan-to-value range; that is, a borrower may have to pay the same rate for any loan that is less than 60 percent of value. This means that the incre- mental cost and average cost might not actually begin to rise until the loan-to-value ratio exceeds 60 percent.

5 This formula is an approximation because the relative weight of each loan actually changes slightly over time as the loans are amortized. Because each loan is amortized over 25 years, the loan-to-value ratio of the 80 percent loan must drop much faster than that of the 10 percent loan because both loan- to-value ratios must be zero at loan maturity. 6 The transactions cost would be the same as loans with a higher loan-to-value ratio.

EXHIBIT 6–2 Effect of Loan-to-Value Ratio on Loan Cost

25

20

15

10

5

Rate for incremental amount borrowed Average rate for entire loan

Loan-to-value ratio (%)

Yi el

d ra

te (%

)

0 10 20 30 40 50 60 70 80 90 100

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 157

bru19684_ch06_150-184.indd 157 11/01/17 02:54 PM

Differences in Maturities In the previous examples, the loan alternatives considered had the same maturities (25 years). How does one determine the incremental cost of alternatives that have different maturities as well as different interest rates? Do differences in maturities materially change results? We examine these questions by changing our previous example and assuming that the $90,000 alternative has a 30-year maturity and a higher interest rate. How would the analysis be changed? We first must compute the following information:

Private mortgage insurance is a way of getting a loan that is greater than an 80 percent loan-to-value ratio. Companies like Mortgage Guarantee Insurance Corporation (www.mgic.com) offer such loans. Paying for the insurance to get the additional loan (more than 80%) is analogous to paying a higher interest rate to get

a higher loan-to-value ratio as discussed in the chapter. Go to the MGIC website and find out more about how private mortgage insurance works and the typical cost. How would you determine the incremental cost of a loan with private mortgage insurance versus one that did not require insurance?

Web App

Loan Payments

Years 1–25 Payments

Years 26–30

Alt. III at 13%, 30 years $90,000 $995.58 $995.58 Alt. I at 12%, 25 years   80,000   842.58     –0–    

Difference $10,000 $153.00 $995.58

Solution: Requires cash flow analysis:

Function: IRR (CF1, CF2, . . . CFn)

CF0 = –$10,000 CFj = $153.00

nj = 300 (years 1–25) CFj = $995.58

nj = 60 (years 26–30) Solve for IRR: (monthly) = 1.5719% (annualized) = 18.86%

In this case, we compute the monthly payment for a $90,000, 30-year loan at 13 percent interest, which is $995.58. However, there are two differences in the series of monthly pay- ments relevant to our example. For the first 25 years, the borrower will pay an additional $153.00 per month for alternative III. For the final five-year period, years 26 through 30, the difference between payments will be the full $995.58 payment on alternative III because the $80,000 loan would be repaid after 25 years. In the above formulation, the sec- ond annuity of $995.58 runs for five years, but it is not received until the end of year 25 and therefore must also be discounted for 25 years. We cannot solve directly for the solution because there are two unknowns. Thus, we must use the procedures outlined in Concept Box 3.2 in Chapter 3 to calculate the yield (cost).

Final PDF to printer

bru19684_ch06_150-184.indd 158 11/01/17 02:54 PM

158 Part 2 Mortgage Loans

Because the desired present value is $10,000, the answer must be slightly less than 19  percent. Using a calculator7 that can solve for an IRR with uneven, or grouped, cash flows, we find the solution is 18.86 percent. Hence, the marginal or incremental cost of borrowing the additional $10,000 given that (1) the interest rate increases from 12 percent to 13 percent and (2) the loan term increases from 25 years to 30 years will be about 18.86 percent. Compare this with the incremental cost of 20.57 percent in the first exam- ple, where no fees were charged but both maturities were 25 years. The reason the marginal cost is lower in this case is that although a higher rate must be paid on the $90,000 loan, it will be repaid over a longer maturity period, 30 years. Even though the borrower pays a higher rate for the $90,000 loan, there is a benefit to having a longer amortization period (and thus lower monthly payments) on the $90,000 loan.

Note that if the borrower expects to repay the loan before maturity, both the differ- ences in monthly payments and loan balances in the year of repayment must be taken into account when computing the marginal borrowing cost. Also, should any origination fees be charged, the incremental funds disbursed by the lender should be reduced accordingly.

Loan Refinancing

On occasion, an opportunity may arise for an individual to refinance a mortgage loan at a reduced rate of interest. The fundamental relationships to know in any loan refinancing decision include at least three ingredients: (1) terms on the present outstanding loan, (2)  new loan terms being considered, and (3) any fees associated with paying off the existing loan or acquiring the new loan (e.g., prepayment penalties on the existing loan or origination and closing fees on the new loan). To illustrate, assume a borrower made a mortgage loan five years ago for $80,000 at 15 percent interest for 30 years (monthly payment). After five years, interest rates fall, and a new mortgage loan is available at 14  percent for 25 years. The loan balance on the existing loan is $78,976.50. Suppose that the prepayment penalty of 2 percent must be paid on the existing loan, and the lender who is making the new loan available also requires an origination fee of $2,500 plus $25 for incidental closing costs if the new loan is made. Should the borrower refinance?

In answering this question, we must analyze the costs associated with refinancing and the benefits or savings that accrue because of the reduction in interest charges, should the borrower choose to refinance. The costs associated with refinancing are as follows:

7 Unlike the problems involving constant payments, this calculation requires a calculator that can accommodate inputs of various cash flows over time.

Cost to refinance: Prepayment penalty: (2% × $78,976.50) $1,580 Origination fees and discount points, new loan    2,500 Recording, etc., new loan         25

 $4,105

Benefits from refinancing are obviously the interest savings that result from a lower inter- est rate. Hence, if refinancing occurs, the monthly mortgage payment under the new loan terms will be lower than payments under the existing mortgage. Monthly benefits would be $60.87 as shown:

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 159

bru19684_ch06_150-184.indd 159 11/01/17 02:54 PM

Monthly savings due to refinancing:   Monthly payments, existing loan, $80,000, 15%, 30 years $1,011.56    Less: Monthly payments, new loan, $78,976.50, 14%, 25 years    –950.69    Difference in monthly payments  $     60.87   

It is useful to know that total cash savings for the 25-year (300-month) period would be $60.87 × 300 or $18,261, which is greater than the $4,105 in refinancing costs. However, the $18,261 in savings will not be received immediately, so we must ask whether it is worth “investing,” or paying out, $4,105 (charges for refinancing) to save $60.87 per month over the term of the loan. Perhaps, the $4,105 could be invested in a more profitable alternative? What rate of interest, compounded monthly, would an alternative investment have to earn in order to be equivalent to spending $4,105 to refinance? To analyze this question, we should determine what rate of return is earned on the investment of $4,105 for 25 years, given that $60.87 per month represents a savings. Using a financial calculator, we find that the yield on our $4,105 investment, with savings of $60.87 per month over 25 years, is equivalent to earning an annual rate of 17.57 percent compounded monthly. If another alternative equal in risk, which provides a 17.57 percent annual return, cannot be found, the refinancing should be undertaken. This return appears to be attractive because it is higher than the market rate of 14 percent that must be paid on the new loan. Thus, refinanc- ing is probably desirable.

Solution: Function: PV = $4,105 i (PV, n, FV, PMT ) n = 300

FV = 0 PMT = $60.87

Solve for i = 17.57%

Loan balance, 15th year—existing loan* $72,275 Loan balance, 10th year—new loan†    71,386 Difference $     889

*Based on $80,000, 15 percent, 30 years prepaid after 15 years. †Based on $78,976, 14 percent, 25 years, prepaid after 10 years.

Early Repayment: Loan Refinancing If the property is not held for the full 25 years, the monthly savings of $60.87 do not occur for the entire 25-year term, and therefore the refinancing is not as attractive. If we assume that the borrower plans to hold the property for only 10 more years after refinancing, is refinancing still worthwhile? To analyze this alternative, note that the $4,105 cost will not change, should the refinancing be undertaken; however, the benefits (savings) will change. The $60.87 monthly benefits will be realized for only 10 years. In addition, since the borrower expects to repay the refinanced loan after 10 years, there will be a difference between loan balances on the existing loan and the new loan due to different amortization rates. We assume that there will be no prepayment penalty on either loan if they are prepaid 10 years from now.

Final PDF to printer

bru19684_ch06_150-184.indd 160 11/01/17 02:54 PM

160 Part 2 Mortgage Loans

Because the loan is repaid early and the monthly savings of $60.87 will not be received over the full 25-year period, the yield is below the 17.57 percent yield computed in the previous example. The yield earned due to refinancing will be 14.21 percent per year for the 10-year period.

Obviously, this return is lower than the 17.57 percent computed under the assumption that the loan will be repaid after 25 years. This is true because the refinancing cost of $4,105 remained the same, while the savings stream of $60.87 was shortened from 25 years to 10 years. Although an additional $889 was saved because of differences in loan bal- ances, it did not offset the reduction in monthly savings that would have occurred from year 10 through year 25. The relationship between the IRR and the number of years the loan is held after refinancing is illustrated in Exhibit 6–3. Note that the returns from

Solution: Function: n = 10 × 12 = 120 i (n, PV, FV, PMT)

PV = –$4,105 PMT = $60.87

FV = $889 Solve for i = 14.21%

EXHIBIT 6–3 IRR from Savings When Refinancing

20

15

10

5

0

–5

Years held after refinancing

0 5 10 15 20 25 30

In te

rn al

ra te

o f r

et ur

n (%

)

The new calculation comparing loan balances under the existing loan and the new loan terms, should the new loan be made, shows that if refinancing occurs the amount saved with the lower loan balance will be $889. Hence, total savings with refinancing will be $60.87 per month for 10 years, plus $889 at the end of 10 years. Do these savings justify an outlay of $4,105 in refinancing costs? To answer this question, we compute the return on the $4,105 outlay as follows:

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 161

bru19684_ch06_150-184.indd 161 11/01/17 02:54 PM

refinancing are negative if the loan is held for only five years after prepayment. The return rises sharply for each additional year the loan is held after prepayment until it is held for about 15 additional years. In analyzing refinancing decisions, then, we must compare not only costs and benefits (savings), but also the time period one expects to hold a property.8

Effective Cost of Refinancing The refinancing problem can also be analyzed by using an extension of the effective cost concept discussed earlier. We know that points increase the effective cost of a loan. In our problem, the borrower would be making a new loan for $78,976.50 but must pay $4,105 in “fees” to do so. Although these fees include the prepayment penalty on the old loan, this can be thought of as a cost of making a new loan by refinancing, or the effective cost of refinancing. Thus, the borrower in effect receives $78,976.50 less $4,105, or $74,871.50. Payments on the new loan when made at 14 percent for 25 years would be $950.69. To find the effective cost where the loan is held to maturity, or 25 years, we proceed as follows:

8 Obviously, the shorter the time period is that the borrower expects to hold the property after refinancing, the lower the return will be on “investing” in refinancing. In fact if the period of time is relatively short, the return could be negative. Hence, if a borrower expects to sell a property within a short time after refinancing, it will be difficult to justify refinancing.

Solution: Function: n = 25 × 12 = 300 i (n, PV, PMT, FV)

PV = –$74,871.50 PMT = $950.69

FV = 0 Solve for i = 14.86%

Using a financial calculator, we obtain an interest rate of 14.86 percent. This can be interpreted as the effective cost of obtaining the new loan by refinancing. Since this cost is less than the rate on the old loan (15%), refinancing would seem to be desirable.9 Thus, we arrive at the same conclusion we got when calculating the return on investing in refinancing.

Borrowing the Refinancing Costs In the above analysis, we assumed that the borrower had to pay (as a cash outlay) the refi- nancing costs of $4,105. However, it is likely that if the borrower is going to the trouble of refinancing, he or she may also be able to borrow the refinancing costs.10 How does this affect our analysis?

The borrower now gets a loan for the loan balance of $78,976.50 plus the fees of $4,105.00 for a total of $83,081.50. Payments at the 14 percent rate (assuming the interest rate is still the same) would be $1,000.10.11 What do we compare this to now that the

9 Any points that had been paid on the old loan would not be relevant since they are a “sunk cost”; that is, they have already been paid and are not affected by refinancing. Thus, only the current interest rate on the old loan should be compared with the effective cost of the new loan. 10 The borrower will probably have sufficient equity in the property to do so since, if the old loan was held for several years, the borrower has reduced the balance on the old loan and the property may have increased in value. 11 If this approach were used to analyze the case where the loan was to be repaid early, the additional loan balance on the refinanced loan would have to be considered. This would reduce the benefit of the lower payments.

Final PDF to printer

bru19684_ch06_150-184.indd 162 11/01/17 02:54 PM

162 Part 2 Mortgage Loans

Solving for the effective interest rate, we obtain an answer of 14.81 percent, which is virtu- ally the same as we obtained in the previous section. The only reason the answer is slightly lower is that the origination fee on the new loan was assumed to remain at $2,500 even though the amount of the loan was increased to cover the refinancing costs.

Note that whether we calculate a return on investing in refinancing or the effective cost of refinancing, we arrive at the same conclusion. Often there are many ways of considering a problem that lead to similar conclusions. It is informative to look at a problem in several ways to gain skill in handling the wide variety of financial alternatives one may encounter. Knowing alternative ways of analyzing a problem also reduces the chance of applying an incorrect technique to solve it.

Other Considerations

Biweekly Payment Patterns—Interest Savings and Early Payoff Generally speaking, when repaying mortgage loans, most borrowers prefer to make monthly payments. However, some borrowers consider biweekly payments which may (1) lower the amount of interest over the life of the loan and (2) repay the loan sooner. For example, if a borrower makes a fully amortizing $80,000 loan at 6 percent for 30 years and is considering a monthly versus a biweekly payment pattern, a comparison of payments would be as follows:

Solution: Function: n = 25 × 12 = 300 i (n, PV, PMT, FV )

PV = –$78,976.50 PMT = $1000.10

FV = 0 Solve for i = 14.81%

Solution:

Monthly Payments (360) Biweekly Payments (26 per year)

PV = –$80,000 $479.60 ÷ 2    i = 6%

n = 360 PMT = $239.80 FV = 0

Solve for PMT = $479.60

borrower has no cash outlay when refinancing? The answer is simple. These payments are still less than those on the old loan ($1,011.56). Given that the borrower has lower pay- ments ($11.46) for 300 months without any cash outlay, it is desirable to refinance.12

We could, of course, also compute the effective cost of refinancing as we did in the previous section. In this case, the total amount of the loan is $83,081.50; however, the borrower, in effect, only benefits from $78,976.50 (the loan amount less the refinancing costs). Using the payment of $1,000.10 and assuming the new loan is held for the full loan term, we can calculate the effective cost as follows:

12 If the interest rate was higher, then we would also want to consider the incremental cost of the additional $4,105, as considered earlier in the chapter.

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 163

bru19684_ch06_150-184.indd 163 11/01/17 02:54 PM

The following table shows (1) the number of payments needed to repay the biweekly loan, (2) the approximate number of years to maturity, and (3) approximate total interest savings over the life of the loan.

Solution:

Biweekly Mortgage Loan Payoff Period: Total Interest Savings:

PV = –$80,000 Total monthly payments   $172,656 PMT = $239.80 Total biweekly payments  –152,752

i = 6%/26* Total interest savings    $  19,904 FV = 0

Solve for n = 637 payments (rounded) (approx. 24.5 years)

*Annual rate of 6% compounded biweekly.

Solution: Function:

Loan Balance EOY 5: PV (PMT, i, n, FV ) PMT = $479.64

i = 6% n = 360 months

FV = 0 Solve for PV = $74,443

These calculations show that by choosing the biweekly payment pattern, the maturity period would be shortened from 30 years to about 24.5 years and total interest saved would be about $19,904. While it is clear that the borrower would definitely save by making biweekly payments, this does not always mean this would be the best choice. 

One way to think about this choice is to consider whether an alternative investment is available that is of equal risk and that will provide the borrower a return in excess of a 6 percent rate of interest, compounded biweekly (i ÷ 26). However, if such an alterna- tive investment is unavailable, the borrower/investor would be better off “saving interest’’ by reducing interest costs and making the biweekly payments of $239.80. It should also be stressed that this analysis assumes that the borrower has sufficient cash flow to make either choice, that is, the biweekly or monthly loan payments. Unless enough cash flow is available to the borrower every two weeks, the biweekly payment pattern may not be a viable option to begin with.

Early Loan Payoffs Another question that many borrowers ask is whether loans should be paid off early, or prior to maturity. For example, we assume that a borrower makes a fully amortizing loan for $80,000 at 6 percent interest for 30 years. He makes monthly payments for five years and suddenly receives a large amount of cash (e.g., inheritance) such that he may be able to repay the entire loan balance early. The question is should he do so? This question may be considered as follows:

Final PDF to printer

bru19684_ch06_150-184.indd 164 11/01/17 02:54 PM

164 Part 2 Mortgage Loans

Assuming that $74,443 becomes available to the borrower with which to repay this loan early, the question is should it be repaid? One issue to consider is the interest savings. This would be

1. Total payments equal $479.64 × 300 = $143,892 2. Less loan balance EOY 5  –74,443 3. Interest saved by early repayment $  69,449

However, related questions would be whether or not the $74,443 available to repay the loan at the end of year 5 may be reinvested elsewhere and, if so, at what rate of interest. By paying off a loan early that has a 6 percent interest rate, the borrower is in effect “earning” a 6 percent return on the funds used to repay the loan. 1. Reinvesting at a rate greater than 6 percent. If this is possible, the borrower would be

better off not paying off the loan. If the $74,443 available for early payment could be invested elsewhere, say at 7%, the borrower should not pay off the loan early. This way, a spread of 7 percent minus 6 percent, or 1 percent, could be earned on the $74,443.

2. Reinvesting at a rate below 6 percent. If this is the case, the borrower would obvi- ously be better off repaying the loan at the end of year 5. For example, if interest rates have fallen to 5 percent, the borrower may repay the loan thereby saving 6 percent. Alternatively, he may choose to refinance the loan at 5 percent. This would provide savings based on a spread of 6 percent minus 5 percent, or 1 percent. However, even this choice would be preferable only if alternative investments are available to invest the $74,443 at rates in excess of 5 percent.

Early Loan Repayment: Lender Inducements

After a period of rising interest rates, borrowers may have a loan that has an interest rate below the market rate. Earlier, we considered the situation where interest rates have fallen. In such cases, the borrower may find it beneficial to refinance at a lower interest rate even if additional fees and penalties have to be paid to the lender. Where interest rates have risen considerably, the situation may be the opposite. Lenders and other entities that have issued debt in earlier periods may be willing to “pay” borrowers to induce them to repay the loan early. That is, a lender may offer a borrower a discount to pay off the balance of a below- market-interest-rate loan.13 How much of a discount should be offered?

Suppose a borrower has a loan that was made 10 years ago. The original loan amount was $75,000 to be amortized over 15 years at 8 percent interest. The balance of the loan is now $35,348, and the payments are $716.74 per month. If the current market interest rate has increased to 12 percent, then the lender would like to have the loan paid off early so that funds could be loaned to someone else at the market rate. However, the borrower has no incentive to prepay the loan even if he or she has $35,348 available to do so. In this case, the bank may be willing to offer the borrower a discount to prepay the loan. Suppose the lender discounts the loan by $2,000, so that only $33,348 must be paid to the lender. Is this attractive to the borrower?

By accepting the discount, the borrower, in effect, earns a return on the funds used to repay the loan; that is, by making a payment of $33,348 to the lender, the borrower saves $716.74 per month. To calculate the return earned by prepaying the loan, we have 13 An analogy in corporate finance would include a corporation buying back its debt or “calling it” at market value.

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 165

bru19684_ch06_150-184.indd 165 11/01/17 02:54 PM

Using a financial calculator, we find the return to be about 10.5 percent. Thus, the interest savings represent a 10.5 percent return on the “investment” made to repay the loan.14 Whether this represents an attractive proposition for the borrower depends on what alterna- tives he or she has for investing the $33,348.

In the preceding example, we assumed that the borrower had the funds ($33,348) to prepay the below-market-rate loan. Several other possibilities could be considered. One is that the borrower could refinance some or all of the loan at the market rate. Another is that the borrower wants to increase the loan balance by refinancing. In either case, the lender may still be willing to provide an inducement for the borrower to refinance since the exist- ing loan is at a below-market rate. However, the approach taken to analyze the problem depends on whether, on balance, the borrower gives funds to the lender to reduce the loan balance in exchange for the lower payments or the borrower receives additional funds in exchange for an additional loan payment.

Market Value of a Loan

We have considered several problems in which the balance of a loan was determined after payments had been made for a number of years. The balance of the loan represents the amount that the borrower must repay the lender to satisfy the loan contract. (Any prepay- ment penalties must be added to the loan balance.) The loan balance may be interpreted as the “contract” or “book value” of the loan. However, if interest rates have changed since the origination of the loan, the loan balance will probably not represent the “market” value of the loan.

The market value of a loan is the amount that a new lender or investor would pay to receive the remaining payments on the loan. It can be thought of as the amount that could be loaned so that the remaining payments on the loan would give the lender a return equal to the current market rate of interest.

To find the market value of a loan, you simply calculate the present value of the remain- ing payments at the market rate of interest. For example, suppose that a loan was made five years ago for $80,000 with an interest rate of 10 percent and monthly payments over a 20-year loan term. Payments on the loan are $772.02 per month. To calculate the market value of the loan, we must find the present value of the remaining monthly payments of

14 The above analysis does not consider the impact of federal income taxes. The IRS has ruled that when a lender discounts a loan such that the borrower does not have to repay the contract loan balance, the discount represents “loan forgiveness” and as such is considered taxable income. Thus, the borrower would have to pay taxes on the $2,000 discount. For an investor in the 40 percent tax bracket, the taxes would be $800. Thus, the net result is as if the borrower only received a discount of $2,000 – $800 = $1,200. This clearly reduces the benefit to the borrower to repay the loan. This forgiveness rule may also apply in cases where lenders accept a deed in lieu of foreclosure or take title to a property from a borrower when the loan balance outstanding exceeds the value of the property.

Solution: Function: n = 5 × 12 = 60 i (n, PV, FV, PMT)

PV = –$33,348 PMT = $716.74

FV = 0 Solve for i = 10.50%

Final PDF to printer

bru19684_ch06_150-184.indd 166 11/01/17 02:54 PM

166 Part 2 Mortgage Loans

STEP 1: Calculate present value of the remaining payments. Solution: Function:

i = 15% PV (i, FV, PMT, n) n = 180

PMT = $772.02 FV = 0

Solve for PV = $55.161 STEP 2: Calculate loan balance to determine % discount. Solution: Function:

PMT = $772.02 FV (i, PV, PMT, n) i = 10%

PV = $80.000 n = 60

Solve for FV = $71.842

$772.02 by discounting at the market rate of interest, which we assume to be 15 percent. We do this in two steps:

Thus, the market value of the loan is $55,161, compared to a loan balance of $71,842. The $55,161 is the amount that the lender would receive if the loan were sold to another lender, investor, or the secondary market.15 We could say that the above loan is selling at a “discount.” The amount of the difference in this case would be $71,842 – $55,161 = $16,681. We could also say that the mortgage is selling at a discount of 23 percent of its “face” value.

The market value of the loan is lower than the contract loan balance in this example because interest rates have risen relative to the interest rate (10%) at which the loan was originated 10 years ago. However, the borrower is required to make payments based on 10 percent even though market rates have risen to 15 percent. This is one reason why adjustable rate mortgages have become more attractive to lenders (see Chapter 5). With an adjustable rate mortgage, the market value of the outstanding loan will not differ as much as a new loan originated at market rates of interest. Indeed, if the interest rate on the outstanding loan could be adjusted at each payment interval and there were no limitations (caps) on the amount of the adjustment, the contract rate on the loan would always equal the market rate. In this event, the loan balance and market value for such a loan would always be equal because future payments would be based on current rates of interest.

Effective Cost of Two or More Loans

Many situations exist when an investor may be considering a combination of two or more loans (e.g., a first and a second mortgage). One situation is the assumption of a loan that has a favorable rate of interest.16 However, the amount of cash necessary for the 15 It is informative to look at an alternative approach that yields the same answer. Suppose that we were to make a loan for $71,842 at the market rate of 15 percent for the remaining loan term of 15 years. The payment would be $1,005.49. This is $233.47 higher than the contract payment. If we discount this difference in payments for the 15-year period at the market rate, we get a present value of $16,681. Subtracting this difference from the loan balance results in the market value of the loan. 16 Depending on negotiations between borrowers and lenders, it may be possible for properties to be sold on assumption. However, the right to sell on assumption may be precluded explicitly in the mortgage or by the lender not approving the new buyer. Lending practices vary widely, depending on the tradition and the economic conditions in a given area.

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 167

bru19684_ch06_150-184.indd 167 11/01/17 02:54 PM

buyer to assume a mortgage may be prohibitive. This can occur when the seller has already paid down the balance of the loan and when the property has appreciated in value since it was originally financed by the seller. Thus, the buyer must use a second mortgage to bridge the gap between the amount available from the loan assumption and the desired total loan amount.

Suppose that an individual bought a $100,000 property and made a mortgage loan five years ago for $80,000 at 10 percent interest for a term of 25 years. Due to price appre- ciation, the market value of the property has risen in value over the past five years to $115,000. The amount of cash equity required by the buyer to assume the seller’s loan would be $39,669, determined as follows:

Purchase price $115,000 Seller’s mortgage balance ($80,000, 10%, 25 years after 5 years)     75,331

Cash equity required to assume seller’s loan $  39,669

Monthly payment, assumed loan* $726.96 Monthly payment, second mortgage loan†    207.28

$934.24

*Based on original $80,000 loan, at 10 percent, for 25 years. †Based on second mortgage loan of $16,669, at 14 percent, for 20 years.

Solution: Function: n = 20 × 12 = 240 i (n, PV, PMT, FV )

PV = –$92,000 PMT = $934.24

FV = 0 Solve for i = 10.75%

If the buyer does not have $39,669 in cash, even though he or she desires an assumption, the transaction may not be completed. One alternative open to the buyer unable to make the large cash outlay may be to obtain a second mortgage. However, using a second mort- gage will be justified in this case only if the terms of the second mortgage, when combined with the terms on the assumed mortgage, are such that the borrower is as well or better off than if the entire purchase had been financed with a new mortgage. If the entire purchase can be financed with a new $92,000 loan (80% of value) at 12 percent for 20 years, we must know how to combine a second mortgage with the assumed mortgage that determine whether the assumption would be as attractive as the new mortgage loan. Suppose a second mortgage for $16,669 ($92,000 – $75,331) could be obtained at a 14 percent rate for a 20-year term. To analyze this problem, we compute the combined mortgage payments on the assumed loan, and a second mortgage loan made for 20 years at 14 percent.

The combined monthly payments equal $934.24. We now want to compute the effective cost of the combined payments that are made on the combined loan of $92,000.

Final PDF to printer

bru19684_ch06_150-184.indd 168 11/01/17 02:54 PM

168 Part 2 Mortgage Loans

Using a financial calculator, we find an answer of 10.75 percent. This is the cost of obtain- ing $92,000 with the loan assumption and second mortgage. Since this is less than the cost of obtaining $92,000 with a new first mortgage at a rate of 12 percent, the borrower is still better off with the loan assumption and a second mortgage.17 It is important to note, how- ever, that the preceding analysis does not consider the fact that the seller may have raised the price of the property to capture the benefit of the assumable below-market-rate loan. Later in the chapter, we will consider this in our analysis.

Second Mortgages and Shorter Maturities In most cases, second mortgages may not be available for a 20-year period. If a five-year term were available on a second mortgage loan at 14 percent interest, would the borrower still be better off by assuming the existing mortgage and taking a second mortgage? To answer this question, we must determine the combined interest cost on the assumed mort- gage, which carries a rate of 10 percent for 20 remaining years, and the second mortgage, which would carry a rate of 14 percent for five years. This combined rate can then be com- pared with the current 12 percent rate for 20 years presently available, should the property be financed with an entirely new mortgage loan.

To combine terms on the assumable mortgage and second mortgage, we add monthly payments together as follows:

17 It should be apparent that such a high interest rate can be paid on the second mortgage because $75,331, the amount assumed, carries a 10 percent rate and represents about 82 percent of the $92,000 to be financed, while the second mortgage of $16,669 represents only 18 percent. When weighted together by the respective interest rates, the total rate paid on the combined amounts is influenced more by the amount assumed at 10 percent. As an approximation of the average “blended” rate for the two loans, we have (.82 times 10%) + (.18 times 14%) = 10.72%, which is approximately the same as the answer we found using the present value factors above.

Monthly Payments

Assumed loan* $   726.96 Second mortgage†      387.86

Total $1,114.82

*Based on original terms: $80,000, at 10 percent, for 25 years. †Based on $16,669, at 14 percent, for five years.

The sum of the two monthly payments is equal to $1,114.82. However, the combined $1,114.82 monthly payments will be made for only five years. After five years, the second mortgage will be completely repaid, and only the $726.96 payments on the assumed loan will be made through the 20th year.

Whether the combined mortgages should be used by the borrower can now be deter- mined by again solving for the combined cost of borrowing. This cost is based on the monthly payments under both the assumed loan and second mortgage, for the respective number of months payments must be made, in relation to the $92,000 amount being financed. These costs are easily seen as the monthly payments of $387.86 on the second mortgage for five years and the monthly payments of $726.96 on the assumed mort- gage for 20 years, both discounted by an interest rate that results in the present value of $92,000.

We must find the interest rate that makes the present value of the combined monthly mortgage payments (grouped cash flows) equal to $92,000. Using a financial calculator, we find that the combined interest cost on the existing mortgage assumed for 20 years and

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 169

bru19684_ch06_150-184.indd 169 11/01/17 02:54 PM

the second mortgage for five years is 10.29 percent. This combined package of financing must again be compared to the 12 percent interest rate currently available on an $80,000 mortgage for 20 years. Because the effective cost of the two combined loans is less than the market rate, this is the best alternative. It should be noted, however, that for the first five  years the combined monthly payments of $1,114.82, should the assumption and second mortgage combination be made, would be higher than the payments with a new mortgage for $92,000 at 12 percent for 20 years, which would be $1,013.00 per month. Although this is offset by the lower $726.96 payments after five years, the borrower must decide which pattern of monthly loan payments fits his or her income pattern, in addition to simply choosing the loan alternative with the lower effective borrowing cost. A bor- rower may be willing to pay a higher effective cost for a loan (or combination of loans) that has lower monthly payments.

Solution: Alternative Solution:

Requires cash flow analysis: CF0 = $92,000 Initial flow = –$92,000 CFj = $1,114.82

Flow 1 = $1,114.82 Nj = 60 Number of times = 60 (year 1–5) CFj = $726.96

Flow 2 = $726.96 Nj = 180 Number of times = 180 (year 6–20)

Solve for IRR: Solve for i = 0.8573% (monthly) IRR (monthly) = 0.8573% = 10.29% (annually)

IRR (annualized) = 10.29%

In recent years, there have been many new loans that combine features of second mortgage lending, consumer lending, and credit card debt. These are described in Concept Box 6.1.

Effect of Below-Market Financing on Property Prices

In many situations, an investor may have an opportunity to purchase a property and obtain financing at a below-market interest rate. We have previously discussed one case where the seller had a below-market-rate loan that could be assumed by the buyer. Below-market financing might also be provided by the seller with a purchase money mortgage. In this case, the seller provides some or all of the financing to the buyer at an interest rate lower than the current market rate. Indeed, this type of financing is common during periods of tight credit and high interest rates.

Obviously, below-market-rate loans have value to the buyer. However, because the informed seller also recognizes the value of this type of financing, we would expect the seller to increase the price of the property to reflect it. That is, the “price” of the property would be higher with below-market financing than with market rate financing.

We now consider how a buyer would analyze whether to purchase a property with below-market financing if the price is higher than that of an otherwise comparable property that does not have below-market financing. Suppose that a property can be purchased for $105,000 subject to an assumable loan at a 9 percent interest rate with a 15-year remaining term, a balance of $70,000, and payments of $709.99 per month. A comparable property without any special financing costs $100,000, and a loan for $70,000 can be obtained at a market rate of 11 percent with a 15-year term. Which alternative is best for the buyer? Note that we are assuming that the two loan amounts are the same. In analyzing this problem,

Final PDF to printer

bru19684_ch06_150-184.indd 170 11/01/17 02:54 PM

Many types of second mortgage loans are used by residential property owners to borrow additional funds after a property has been owned for some time and has appreciated in value. These loans are generally classified as home equity loans (HELs). Borrowers would want to consider these alternatives relative to refinancing existing loans. Generally, lenders usually require that borrower-homeowners have accumulated approximately 20 percent of equity in their properties in order to qualify for home equity loans. Borrowers must also qual- ify for financing based on income and credit history. Two of the more popular loans currently in use are home equity loans (HELs) and home equity lines of credit (HELOCs).

In the cases of both HELs and HELOCs:

1. Amounts received at closing are not taxable. Such amounts are increases in indebted- ness and not a “taxable event” as may be the case if a property was sold at a gain.

2. Interest payments are generally tax deductible as long as the lender acquires a lien on the property.

HOME EQUITY LOANS

These loans usually provide borrowers with a lump sum amount at closing. In addition to the borrower’s personal liability on the note, lenders also acquire a second mortgage lien on the property. Owner’s equity is measured as the difference between the appraised value of the property at the time that the HEL is applied for, minus any loan balance owed on the first lien. For example, if a property is currently appraised to be worth $100,000 and it has an existing first lien in an amount of $40,000, the owner’s equity would be $60,000. This $60,000 of equity serves as security for the home equity loan. In practice, because the security provided by sec- ond liens is inferior to first liens, HELs are riskier to lenders and will carry a higher rate of interest than that available for first-lien financing. Other characteristics of home equity loans are these:

1. Interest rates may be fixed or adjustable. 2. The loan agreement will specify a maturity period. 3. Payments are usually made monthly. 4. Loan payments may be fully amortizing, partially amortizing, or interest only. In the case of

the latter two options, payments will be made for a specified number of months, at which point the loan must become either fully amortizing or the remaining balance at maturity must be repaid.

HOME EQUITY LINES OF CREDIT

Not to be confused with HELs, home equity lines of credit (HELOCs) are also available to borrowers. These loans have many characteristics that are similar to consumer credit loans. Although HELOCs also are secured by second liens, there are many features of HELOCs that differentiate them from HELs. For example:

1. Although the loan will be made for a specific maximum amount, that amount is not neces- sarily disbursed as a lump sum. Funds may be borrowed (drawn down) against the line as the consumer-borrower desires. However, when the loan balance reaches a maximum amount, no further draws may be made.

2. Like credit card payments, borrowers generally have some flexibility as to the amount of monthly payment that they choose to make. However, lenders will usually insist that monthly payments be at least some minimum amount. To the extent that borrowers choose to make payments that are less than the monthly interest due, the loan balance will increase (negative amortization). Any payments greater than monthly interest due will reduce the loan balance.

3. Interest rates are usually adjustable and, like ARM rates, are usually tied to a well-known interest rate index (e.g., the prime rate).

Home Equity Loans and Concept Box 6.1 Home Equity Lines of Credit

170

Final PDF to printer

171

bru19684_ch06_150-184.indd 171 11/01/17 02:54 PM

4. Like consumer credit card accounts, amounts borrowed and monthly loan payments will determine the loan balance, which may increase or decrease from month to month.

Although HELOCs are similar to many consumer credit loans, because of the added security provided by second liens, HELOCs should be available at interest rates below those of credit card debt. This is because credit card debit is usually unsecured and is totally dependent on a borrower’s personal credit and capacity to repay.

In addition to the interest rate, HELOC borrowers should consider the following issues:

1. Early termination fees. Because these loans are more like a combination of consumer credit and an ARM, the interest rate is likely to be tied to an index. Consequently, at some future time, interest rates could increase dramatically and borrowers may want to switch to a fixed rate loan. In anticipation of this possibility, HELOC lenders may include a termi- nation fee (similar to a prepayment penalty) in the loan agreement.

2. Inactivity fees. Because this loan may be used as a line of credit, if borrowers do not use the line or if they attempt to keep only a small loan balance without terminating the account to avoid the penalty described in (1) (while switching their financing to another lender), a monthly inactivity fee also may be included in the loan agreement. Also, like many credit card loans, there may be an annual renewal or administrative fee associated with this type of loan.

Solution: Function: n = 15 × 12 = 180 i (n, PV, PMT, FV )

PV = –$5,000 PMT = $85.63

FV = 0 Solve for i = 1.6177% per month

= 19.41% per year

Home Equity Loans and Concept Box 6.1 Home Equity Lines of Credit (Continued)

Down Payment Payment

Market rate loan $30,000 $795.62 Loan assumption   35,000   709.99

Difference $  5,000 $  85.63

we must consider whether it is desirable for the buyer to pay an additional $5,000 in cash (additional equity invested) to receive the benefit of lower payments on the below-market loan. The calculations are as follows:

Using a financial calculator, we find that making the additional $5,000 down payment would result in earning the equivalent of 19.41 percent because of the lower monthly loan payments. Alternatively, should the buyer decide not to pay the additional $5,000, he or she would have to find a return of 19.41 percent on the $5,000 in an investment with com- parable risk. Because the 19.41 percent rate is higher than the 11 percent market rate, buy- ing the house with below-market financing appears to be desirable.

Final PDF to printer

bru19684_ch06_150-184.indd 172 11/01/17 02:54 PM

172 Part 2 Mortgage Loans

Solution: Function: n = 15 × 12 = 180 PV (i, n, FV, PMT ) i = 11%/12 = 0.91666%

PMT = $709.99 FV = 0

Solve for PV = $62,466.30

Assuming a Lower Loan Balance For simplicity, it was assumed in the above example that the balance of the assumable (below-market) loan was the same as the amount available for a new loan at the mar- ket rate. As discussed previously, an assumable loan may have a lower balance than a new market rate loan because the seller has paid down the loan and the property may have increased in value. Suppose the balance on the assumable loan in our example is only $50,000 and monthly payments are $507.13. The buyer, however, needs financing of $70,000, the amount that can normally be borrowed at market rates. The borrower may also obtain a second mortgage of $20,000 for 15 years at a 14 percent rate, with payments of $266.35 per month. Is it still desirable to assume the loan, take a second mortgage, and pay $5,000 more for the property? We can make the following calculations:

Down Payment Payment

Market rate loan $30,000 $795.62 Loan assumption + second mortgage   35,000   773.48*

$  5,000 $  22.14

*$507.13 on the $50,000 loan assumption plus $266.35 on the second mortgage.

The return is now –2.90 percent. The buyer is clearly better off by not paying $5,000 more for the property to assume the loan. How much more would the buyer be willing to pay? This is the subject of the next section.

Cash Equivalency

In the previous section, we considered how a buyer could analyze whether a premium should be paid for a property with a below-market-rate loan. We now extend that discus- sion to consider how much the buyer could pay to be indifferent to purchasing the property with a below-market-rate loan or one that must be financed at the market rate.

We will use the example from the last section, where a $70,000 loan could be assumed at a 9 percent rate with a remaining term of 15 years and payments of $709.99 per month. Recall that a comparable property with no special financing available would sell for $100,000 and could be financed at a market rate of 11 percent. How much more than $100,000 could the buyer pay if he or she chose to assume the 9 percent loan and still be as well off as if the property were purchased for $100,000 and financed with an 11 percent loan? We first find the present value of the payments that can be assumed using the market rate. This is the market value or cash equivalent value of the assumable loan. It repre- sents the price at which the old loan could be sold to a new lender/investor.

By assuming the existing loan balance, the buyer would obtain financing equal to $70,000.00 instead of $62,466.30 for the same $709.99 payment. Thus, the buyer receives

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 173

bru19684_ch06_150-184.indd 173 11/01/17 02:54 PM

a net benefit of $70,000.00 – $62,466.30 = $7,533.70. Therefore, the buyer could pay $7,533.70 more for the property, or $107,534 (rounded).

In the previous section, we calculated that the return to the buyer would be 19.41  percent if an additional $5,000 more, or $105,000, were paid for the property. It is possible to verify that by paying $107,534, the buyer’s return would be exactly 11 percent, the same as the market interest rate on the loan.

Based on the above analysis, the property with an assumable loan could probably sell for as high as $107,534. The buyer would be paying a cash equivalent value of $100,000 for the property plus an additional financing premium of $7,534 to obtain the benefit of the below-market-rate loan. The value of the property remains $100,000. This is referred to as the cash equivalent value for the property. This differs from the price paid for the house, which includes the $7,534 financing premium. The recognition of this premium is important because if we knew that the property had actually sold for $107,534 but did not consider that it had an assumable below-market-rate loan, we would have an inflated opinion of value. Alternatively, the buyer would never want to agree to pay $107,534 for the property unless the 9 percent below-market financing could be obtained.

Note that the amount of cash (equity) invested in the property is $107,534, less the mort- gage balance of $70,000, or $37,534. When $37,534 is added to the cash equivalent value of the loan of $62,466, we obtain the cash equivalent value for the property of $100,000.

Cash Equivalency: Smaller Loan Balance

In the previous section, we determined the indifference price for a property that had an assum- able below-market-rate loan. The loan balance was the same as the buyer could obtain with a market rate loan. However, when loan assumptions occur, it is likely that the loan balance is significantly less than would normally be desired. We now modify the example in the last section by considering that the balance of the assumable 9 percent loan is only $50,000 and the buyer would have to borrow an additional $20,000 through a second mortgage to obtain the $70,000 needed. We assume that the second mortgage could be obtained at a 14 percent rate for a 15-year term. We continue to assume that a $70,000 new first mortgage (70% of the property value) could be obtained at an 11 percent rate with a 15-year term.18 Now, how much could the buyer pay for the property and be indifferent to the two methods of financing?

We begin by finding the present value of the sum of the payments on the assumable loan ($507.13) plus payments on the second mortgage ($266.35), using the 11 percent market rate. The difference between the present value ($68,052.27) and the $70,000 available at the market rate is $1,947.73. Thus, the buyer would now pay only an additional $1,947.73 for the property to get the below-market-rate loan. Therefore, the property would probably sell for no more than $101,950 (rounded). This is considerably less than the $107,500 obtained where the assumable loan had a balance of $70,000 instead of $50,000. There are two reasons that the premium is less: First, because the balance of the assumable loan is less, the saving (from lower payments) is less. Second, because this balance is less than the amount of the loan that could be obtained at the market rate, the benefit from lower pay- ments on the assumable loan is reduced by the necessity of obtaining a second mortgage at a higher interest rate than the rate on a new first mortgage. It is important to realize that when carrying out this analysis, the need for a second mortgage must be considered; other- wise, the benefit of the loan assumption is overstated.

18 Even if an investor did not need a second mortgage, we can only evaluate the benefit of the loan assumption by comparing it with what is currently available in the market. Since market rates are usually based on a loan-to-value ratio of 70 percent or more, a second mortgage must be considered in the analysis.

Final PDF to printer

bru19684_ch06_150-184.indd 174 11/01/17 02:54 PM

174 Part 2 Mortgage Loans

Cash Equivalency: Concluding Comments

In the previous two sections, we showed how to analyze the impact of below-market financing on the sale price of a property. It is important to recognize the relationship between the price at which a property sells and any special (e.g., below-market) financing that might be available. Although we have considered several examples of cash equiva- lency calculations, we have only introduced a few of the possible situations that could arise in practice. At least three additional situations could arise that would affect the analysis: 1. If the below-market financing is not transferable to a subsequent buyer, this means

that a previous buyer may not benefit from the below-market-rate loan for its remain- ing term. This obviously affects any financing premiums that would be paid for properties.

2. Even if below-market loans were always assumable by subsequent buyers, the value of this type of financing over the remaining term of the loan to a subsequent buyer depends on the market rate of interest at the time of subsequent sales. These rates may be higher or lower than rates prevailing at the time that the present owner purchased the property. If market rates at the time the property is sold are no longer greater than the contract rate on the assumable loan, then the subsequent buyer would not pay a pre- mium. Hence, the likelihood of subsequent sales and interest rates at such points in time adds an element of uncertainty to the benefit of assuming any loan and should tend to reduce the amount buyers are willing to pay for such loans.

3. Even if the buyer plans to own the property for a time period exceeding the loan term, interest rates could drop after the loan is assumed. Because borrowers can usually refi- nance when interest rates drop, a below-market-rate loan has less value if interest rates are expected to fall. In effect, the value of the below-market financing is reduced by the “option” to refinance if interest rates fall. All of the situations discussed above tend to reduce the premium a buyer would pay for

a below-market-interest-rate loan. Thus, our analysis is likely to indicate the upper limit on the premium associated with below-market-rate loans. The best way to verify the value of such premiums is by observing how much more buyers pay for below-market financing in contrast to properties without special financing.

Wraparound Loans

Wraparound loans are used to obtain additional financing on a property while keeping an existing loan in place. The wraparound lender makes a loan for a face amount equal to the existing loan balance plus the amount of additional financing. The wraparound

Solution: Function: n = 15 × 12 = 180 PV (n, i, PMT, FV) i = 11%/12 = 0.91666%

PMT = $773.48 FV = 0

Solve for PV = $68,052.27

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 175

bru19684_ch06_150-184.indd 175 11/01/17 02:54 PM

lender agrees to make the payments on the existing loan as long as the borrower makes payments on the wraparound loan. Instead of making payments on the original loan in addition to payments on a second mortgage, the borrower makes a payment only on the wraparound loan.

Suppose a property owner named Smith has an existing loan with a balance of $90,000 and monthly payments of $860.09. The interest rate on the loan is 8 percent and the remain- ing loan term is 15 years. From the time Smith originally obtained this loan, the prop- erty has risen in value to $150,000. Smith’s current loan balance is 60 percent of the current value of the property. He would like to borrow an additional $30,000, which would increase his debt to $120,000, or 80 percent of the property value.

Assume that the current effective interest rate on a first mortgage with an 80 percent loan-to-value ratio is 11.5 percent with a term of 15 years, and the current effective interest rate on a second mortgage for an additional 20 percent of value ($30,000) would be 15.5 percent for a term of 15 years.

A lender other than the holder of Smith’s existing loan is willing to make a wraparound loan for $120,000 at a 10 percent rate for a 15-year term. Payments on this loan would be $1,289.53 per month. If Smith makes this loan, the wraparound lender will take over the payments on Smith’s current loan; that is, Smith will pay $1,289.53 to the wraparound lender, and the wraparound lender will make the $860.09 payment on the original loan. Thus, Smith’s payment would increase by $429.44 ($1,289.53 – $860.09) per month. Because the wraparound lender is taking over the payments on the old loan, Smith will actually receive only $30,000 in cash (the $120,000 amount for the wraparound loan less the $90,000 balance of Smith’s current loan).

Is the wraparound loan a desirable alternative for Smith to obtain an additional $30,000? The rate on the $120,000 wraparound loan (10%) is less than the market rate (11.5%) on a new first mortgage for the entire $120,000. Thus, the wraparound loan would be more desirable than refinancing with a new first mortgage.19 Why would the wraparound lender make a loan that has a lower rate than a new first mortgage? The answer is that the wrap- around lender is primarily concerned with earning a competitive rate of return on the incremental funds loaned (i.e., the additional $30,000). It is the effective cost of the incre- mental funds loaned that the borrower also should be concerned about.

What is the cost of the incremental $30,000? This is analogous to determining the incremental borrowing cost of a loan that we discussed at the beginning of the chapter. That is, we want to know the incremental cost of the 80 percent wraparound loan versus the 60 percent existing loan. To get the additional $30,000 on the wraparound loan, the borrower must pay a 10 percent interest rate on the entire $120,000, not solely the additional $30,000. Because the rate on the existing $90,000 is only 8 percent, the incremental cost of the additional $30,000 is greater than 10 percent. The question is whether the incremental cost is more or less than the 15.5 percent rate for a second mortgage of $30,000.

The incremental borrowing cost of the wraparound loan can be determined by finding the interest rate that equates the present value of the additional payment with the addi- tional funds received. Using a financial calculator, we find that the interest rate is 15.46 percent or about 15.5 percent. This is the same rate as that for a second mortgage, which is what we would expect. The wraparound lender can charge a lower rate on the wraparound loan and still earn a competitive rate on the incremental funds loaned because the existing loan is at a below-market rate. The wraparound rate of 10 percent is, in effect,

19 It is assumed that there are no points on the wraparound loan so that the effective cost of the wraparound loan is 10 percent. The cost of a wraparound loan can be compared with the cost of a new first mortgage because both rates reflect the cost of a loan for $120,000.

Final PDF to printer

bru19684_ch06_150-184.indd 176 11/01/17 02:54 PM

176 Part 2 Mortgage Loans

a weighted average of the rate on the existing loan (8 percent) and the rate on a second mortgage (15.5%).20 If the existing loan were at the market rate for a 60 percent loan, then the wraparound rate would have to be equal to the rate on an 80 percent loan, so that the wraparound lender would earn a rate of return on the incremental funds equal to a second mortgage rate.

20 The weighted average is (90,000 ÷ 120,000 × 8%) + (30,000 ÷ 120,000 × 15.5%) = 9.875 percent, or about 10 percent, which is the rate on the wraparound loan. Note that the weighted average is less than the 11.5 percent rate on a new $120,000 first mortgage, which indicates that the existing loan is at a below-market rate.

Solution: Function: n = 15 × 12 = 180 i (n, PV, PMT, FV )

PV = –$30,000 PMT = $429.44

FV = 0 Solve for i = 15.46%

Is there any reason why the wraparound lender should be willing to make the loan at a rate that is more attractive than a second mortgage? The wraparound loan is, in effect, a second mortgage because the original loan is still intact. Furthermore, the loan-to-value ratio is increased by the same amount with the wraparound loan as it would be with a sec- ond mortgage. However, the wraparound loan has one advantage: The wraparound lender makes the payments on the first mortgage loan. Hence, control is retained over default in its payment, whereas if a second mortgage was made, the second mortgage lender would not necessarily be aware of a default on the first mortgage loan and might not be included in foreclosure action resulting from it. In a typical wraparound mortgage agreement, the wraparound lender is obligated to make payments on the original mortgage only to the extent that payments are received from the borrower, and the borrower agrees to comply with all of the covenants in the original mortgage except payment. Any default by the bor- rower will be realized by the wraparound lender, who may not want to see the property go into foreclosure. The wraparound lender may make advances on the first mortgage and add them to the balance on the wraparound loan, foreclose on its mortgage, or negotiate for the title to the property in lieu of foreclosure, while still making payments on the first lien. Thus, the wraparound lender may be willing to earn an incremental return that is slightly lower than a second mortgage rate.

It should be noted that the original mortgage may contain a prohibition against fur- ther encumbrances or a due-on-sale clause that may preclude use of a wraparound loan to access equity in, or finance the sale of, property. In the absence of these restrictions, the original lender may also be willing to work out a deal with Smith that would be attractive to both of them. For example, this lender might offer Smith a new first mort- gage at the same 10 percent rate as the wraparound loan (rather than the 11.5% market rate on a first mortgage) if Smith agrees to borrow the additional $30,000 from the bank. Again, because the 10 percent rate applies to the entire $90,000 (not only the additional $30,000), the original lender can earn an incremental return of 15.5 percent on the incremental funds advanced. Thus, the existing lender can earn a competitive rate of return on the new funds and keep the existing borrower as a customer. The lender still earns only 8 percent on the existing loan, but this would also be true if the

Final PDF to printer

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 177

bru19684_ch06_150-184.indd 177 11/01/17 02:54 PM

borrower gets a second mortgage or a wraparound loan from a different lender. Thus, the original lender may be willing, in effect, to offer the same deal as a wraparound lender by charging a rate on a new first mortgage that is equal to the wraparound rate of 10 percent.21

Buydown Loans

The final type of loan situation we consider is the buydown loan. With a buydown loan, the seller of the property (frequently a builder) pays an amount to a lender to buy down, or lower, the interest rate on the loan for the borrower for a specific period of time. This may be done in periods of high interest rates to help borrowers qualify for financing. For example, suppose that interest rates are currently 15 percent and a purchaser of a build- er’s property has only enough income to qualify for a loan at a 13 percent fixed rate. Let us assume that the loan will be for $75,000 with monthly amortization based on a 30-year term. Payments based on the market rate of 15 percent would be $948.33 per month. Payments at a 13 percent rate would be only $829.65 per month. Based on the buyer’s income, the buyer would qualify to make payments of $829.65 but not $948.33. Suppose that the  builder wanted to buy down the interest rate from 15 to 13 percent, thereby enabling the bank to make the loan, so that payments are only $829.65 per month for the first five years of the loan term but will increase to $948.33 for the remaining loan term. To accomplish this, the builder would have to make up the difference in payments ($118.68 per month for the five-year period). If this difference were paid by the builder to the lender at the time the loan closed, the amount paid would have to be the present value of the difference in payments, discounted at the market rate of 15 percent. The builder would therefore pay $4,988.67 to the lender to buy down the loan. When coupled with the payments received from the buyer, the lender would earn a market rate of 15 percent and be willing to qualify the buyer.

21 This is often referred to as a “blended rate” because the 10 percent rate is a weighted average of the rate on the existing loan and the rate on the incremental funds loaned.

Solution: Function: n = 5 × 12 = 60 PV (n, i, PMT, FV ) i = 15% ÷ 12 = 1.25%

PMT = $118.68 FV = 0

Solve for PV = $4,988.67

The buydown has the advantage of allowing borrowers to qualify for the loan when their current income might not otherwise meet the lender’s payment-to-income criteria. Based on our discussion of cash equivalent value, however, you should realize that the builder will probably have added the buydown amount to the price of the property. Thus, the borrower might be better off bargaining for a lower price on the property and obtain- ing his or her own loan at the market rate. Probably, the same home or a similar one could be obtained for $4,988.67 less without a buydown. The borrower is, in effect, paying $4,988.67 in “points” to lower the interest rate to 13 percent from 15 percent.

Final PDF to printer

bru19684_ch06_150-184.indd 178 11/01/17 02:54 PM

178 Part 2 Mortgage Loans

It should also be noted that many buydowns are executed with graduated payments for three or five years; that is, to continue with our current example, they may be initiated with monthly payments of $829.65 and step up each year by a specified amount until $948.33 is reached in the fifth year.

Some buydown programs are also used in conjunction with adjustable rate mortgages, where the initial rate of interest will be bought down. Because initial rates on ARMs are typically lower than those on fixed rate mortgages, this results in even lower initial pay- ments, thereby allowing more buyers to qualify. However, this type of buydown practice has been discouraged because payments may increase considerably, particularly if there is an increase in the market rate of interest. In these cases, payments would rise because of higher market rates and because future payments have not been bought down.

Conclusion This chapter has illustrated a number of problems concerning financing situations that borrowers and lenders might face. In today’s era of creative financing, many other examples could be discussed. However, we have chosen examples that illustrate the main concepts and approaches to solving important problems. These can be applied to other situations that you might want to analyze. Thus, this chapter should be viewed as introducing various tools that can be used to handle problems relat- ing to both residential and commercial properties.

To keep our analysis as straightforward as possible and focus on the key new concepts we wanted to introduce, we have used fixed rate mortgages in all our examples in this chapter. However, the analyses also apply to other types of mortgages, such as ARMs, and floating rate and other loans.

Key Terms biweekly payments, 162 buydown loan, 177 cash equivalent value, 172 effective cost of

refinancing, 161 financing premium, 173

home equity line of credit, 170

home equity loan, 170 incremental cost of

borrowing, 150 loan refinancing, 158

marginal cost of borrowing, 150

market value of a loan, 165 origination fees, 153 wraparound loan, 174

Useful Web sites

www.businessfinance.com/wraparound-mortgage.htm—Examples of wraparound loans. www.fha-home-loans.com/buydown_fha_loan.htm—Discussion of how FHA buydown loans are structured. www.bankrate.com—Good source of rates and articles on different kinds of mortgages. Includes some useful mortgage calculators to choose between loan alternatives. www.mgic.com—Mortgage Guarantee Insurance Corporation, a national provider of private mortgage insurance. www.freddiemac.com/pmms/pmms30.htm—This is a good site for finding fixed rates and points for 30-year mortgages. www.freddiemac.com/pmms/pmmsarm.htm—This is a good site for finding monthly average commitment rates and points on one-year adjustable rate mortgages. www.ipd.com—This website provides objective measurement and analysis of various properties. The company that runs this website does not invest in the market and does not offer any direct investment advice, so it tends to be unbiased.

Questions 1. What are the primary considerations that should be made when refinancing? 2. What factors must be considered when deciding whether to refinance a loan after interest rates

have declined? 3. Why might the market value of a loan differ from its outstanding balance?

Final PDF to printer

bru19684_ch06_150-184.indd 179 11/01/17 02:54 PM

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 179

4. Why might a borrower be willing to pay a higher price for a home with an assumable loan? 5. What is a buydown loan? What parties are usually involved in this kind of loan? 6. Why might a wraparound lender provide a wraparound loan at a lower rate than a new first

mortgage? 7. Assuming the borrower is in no danger of default, under what conditions might a lender be will-

ing to accept a lesser amount from a borrower than the outstanding balance of a loan and still consider the loan paid in full?

8. Under what conditions might a property with an assumable loan sell for more than comparable properties with no assumable loans available?

9. What is meant by the incremental cost of borrowing additional funds? 10. Is the incremental cost of borrowing additional funds affected significantly by early repayment

of the loan?

Problems 1. A borrower can obtain an 80 percent loan with an 8 percent interest rate and monthly payments. The loan is to be fully amortized over 25 years. Alternatively, he could obtain a 90 percent loan at an 8.5 percent rate with the same loan term. The borrower plans to own the property for the entire loan term.

a. What is the incremental cost of borrowing the additional funds? (Hint: The dollar amount of the loan does not affect the answer.)

b. How would your answer change if two points were charged on the 90 percent loan? c. Would your answer to part (b) change if the borrower planned to own the property for only

five years? 2. An investor has $60,000 to invest in a $280,000 property. He can obtain either a $220,000 loan

at 9.5 percent for 20 years or a $180,000 loan at 9 percent for 20 years and a second mort- gage for $40,000 at 13 percent for 20 years. All loans require monthly payments and are fully amortizing.

a. Which alternative should the borrower choose, assuming he will own the property for the full loan term?

b. Would your answer change if the borrower plans to own the property only five years? c. Would your answers to (a) and (b) change if the second mortgage had a 10-year term?

3. An investor obtained a fully amortizing mortgage five years ago for $95,000 at 11 percent for 30 years. Mortgage rates have dropped, so that a fully amortizing 25-year loan can be obtained at 10 percent. There is no prepayment penalty on the mortgage balance of the original loan, but three points will be charged on the new loan and other closing costs will be $2,000. All pay- ments are monthly.

a. Should the borrower refinance if he plans to own the property for the remaining loan term? Assume that the investor borrows only an amount equal to the outstanding balance of the loan.

b. Would your answer to part (a) change if he planned to own the property for only five more years?

4. Secondary Mortgage Purchasing Company (SMPC) wants to buy your mortgage from the local savings and loan. The original balance of your mortgage was $140,000 and was obtained five years ago with monthly payments at 10 percent interest. The loan was to be fully amortized over 30 years.

a. What should SMPC pay if it wants an 11 percent return? b. How would your answer to part (a) change if SMPC expected the loan to be repaid after five

years? 5. You have a choice between the following two identical properties: Property A is priced at

$150,000 with 80 percent financing at a 10.5 percent interest rate for 20 years. Property B

Final PDF to printer

bru19684_ch06_150-184.indd 180 11/01/17 02:54 PM

180 Part 2 Mortgage Loans

is priced at $160,000 with an assumable mortgage of $100,000 at 9 percent interest with 20 years remaining. Monthly payments are $899.73. A second mortgage for $20,000 can be obtained at 13 percent interest for 20 years. All loans require monthly payments and are fully amortizing.

a. With no preference other than financing, which property would you choose? b. How would your answer change if the seller of Property B provided a second mortgage for

$20,000 at the same 9 percent rate as the assumable loan? c. How would your answer change if the seller of Property B provided a second mortgage for

$30,000 at the same 9 percent rate as the assumable loan so that no additional down payment would be required by the buyer if the loan were assumed?

6. An investor has owned a property for 15 years, the value of which is now to $200,000. The balance on the original mortgage is $100,000 and the monthly payments are $1,100 with 15 years remaining. He would like to obtain $50,000 in additional financing. A new first mort- gage for $150,000 can be obtained at a 12.5 percent rate and a second mortgage for $50,000 at a 14  percent rate with a 15-year term. Alternatively, a wraparound loan for $150,000 can be obtained at a 12 percent rate and a 15-year term. All loans are fully amortizing. Which alterna- tive should the investor choose?

7. A builder is offering $100,000 loans for his properties at 9 percent for 25 years. Monthly payments are based on current market rates of 9.5 percent and are to be fully amortized over 25 years. The property would normally sell for $110,000 without any special financing.

a. At what price should the builder sell the properties to earn, in effect, the market rate of inter- est on the loan? Assume that the buyer would have the loan for the entire term of 25 years.

b. How would your answer to part (a) change if the property is resold after 10 years and the loan repaid?

8. A property is available for sale that could normally be financed with a fully amortizing $80,000 loan at a 10 percent rate with monthly payments over a 25-year term. Payments would be $726.96 per month. The builder is offering buyers a mortgage that reduces the payments by 50 percent for the first year and 25 percent for the second year. After the second year, regular monthly payments of $726.96 would be made for the remainder of the loan term.

a. How much would you expect the builder to have to give the bank to buy down the payments as indicated?

b. Would you recommend the property be purchased if it was selling for $5,000 more than similar properties that do not have the buydown available?

9. An appraiser is looking for comparable sales and finds a property that recently sold for $200,000. She finds that the buyer was able to assume the seller’s fully amortizing mortgage which had monthly payments based on a 7 percent interest rate. The balance of the loan at the time of sale was $140,000 with a remaining term of 15 years (monthly payments). The appraiser determines that if a $140,000 loan was obtained on the same property, monthly pay- ments at the market rate for a 15-year fully amortizing loan would have been 8 percent with no points.

a. Assume that the buyer expected to benefit from the interest savings on the assumable loan for the entire loan term. What is the cash equivalent value of the property?

b. How would your answer to part (a) change if you assumed that the buyer only expected to benefit from interest savings for five years because he would probably sell or refinance after five years?

10. A borrower is making a choice between a mortgage with monthly payments or biweekly pay- ments. The loan will be $200,000 at 6 percent interest for 20 years.

a. How would you analyze these alternatives? b. What if the biweekly loan was available for 5.75 percent? How would your answer change?

Final PDF to printer

bru19684_ch06_150-184.indd 181 11/01/17 02:54 PM

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 181

The preceding chapters have dealt with numerous situations where financing alternatives were evaluated. In all cases, the analysis was made without considering that mortgage interest is tax deductible. An obvious question is whether consider- ation of federal income taxes affects the conclusions in our analyses. To gain insight into this question, we first consider the after-tax effective cost of borrowing with a standard fixed rate mortgage loan.

Example Suppose that a borrower makes a $100,000 loan with annual payments at a 10 percent rate and a 10-year term. The loan is fully amortizing; however, payments are made on an annual basis to simplify the initial illustration. The annual loan pay- ment is calculated as follows:

Solution: Function: PV = $100,000 PMT (PV, i, n, FV )

i = 10% n = 10

FV = 0 Solve for PMT = $16,275

Appendix

After-Tax Effective Interest Rate

A loan schedule is calculated in Exhibit 6A–1 for the 10-year loan term. The pretax cost of this loan is simply 10 percent because there are no points or prepayment penalties. We now want to see the effect of interest being tax deductible. The tax benefit of the interest tax deduction is calculated by multiply- ing the loan interest each year by the borrower’s tax rate. For example, the first year interest is $10,000. At a 28 percent tax rate, this means that the borrower can reduce taxes by $2,800 by deducting the interest.

The after-tax cost of the loan can now be found by sub- tracting the tax savings from the loan payment. The after-tax cost is calculated in Exhibit 6A–2.

To calculate the after-tax effective cost of borrowing, we need to find the annual compound interest rate that equates the after-tax payments to the initial amount of the loan ($100,000). Calculating this rate indicates an after-tax cost of borrowing of exactly 7.2 percent. This is verified in Exhibit 6A–3.

Adding the present value column in Exhibit 6A–3 results in a net present value of zero, which verifies that the after-tax cost is 7.2 percent.

Now that we have performed the calculations the “long way,” you may wonder if the pretax and after-tax costs are in

End of Year Payment Interest Principal Balance

1 $16,275 $10,000 $6,275 $93,725 2 16,275 9,373 6,902 86,823 3 16,275 8,682 7,592 79,231 4 16,275 7,923 8,351 70,880 5 16,275 7,088 9,187 61,693 6 16,275 6,169 10,105 51,588 7 16,275 5,159 11,116 40,472 8 16,275 4,047 12,227 28,245 9 16,275 2,825 13,450 14,795

10 16,275 1,480 14,795 0

EXHIBIT 6A–1 Loan Schedule

Year Payment After-Tax Value of Deduction*

After-Tax Payment

1 $16,275 $2,800 $13,475 2  16,275   2,624  13,650 3  16,275   2,431  13,843 4  16,275   2,218  14,056 5  16,275   1,985  14,290 6  16,275   1,727  14,547 7  16,275   1,444  14,830 8  16,275   1,133   15,141 9  16,275     791  15,484

10   16,275     414  15,860

*Interest times tax rate.

EXHIBIT 6A–2 After-Tax Cost of Loan Payment

Year ATCF PVIF* Present Value

  0 −$100,000 $1.00000 −$100,000   1 13,475   0.93284 12,570   2 13,650   0.87018 11,878   3 13,843   0.81174 11,237   4 14,056   0.75722 10,644   5 14,290   0.70636 10,094   6 14,547   0.65892  9,585   7 14,830   0.61466  9,115   8 15,141   0.57338  8,682   9 15,484   0.53487  8,282 10 15,860   0.49894  7,913 Total present value 0

*For a discussion of present value interest factors, see Exhibit 3–6.

EXHIBIT 6A–3 Net Present Value of After-Tax Payments

Final PDF to printer

bru19684_ch06_150-184.indd 182 11/01/17 02:54 PM

182 Part 2 Mortgage Loans

some way related to the borrower’s tax rate. There is a very simple relationship in this situation:

After-tax effective cost

=

( Pretax effective cost )

×  ( 1 − Tax rate )

= 10%  ( 1 − .28 )

=

7.2%

We see that the after-tax borrowing cost is inversely pro- portional to the complement of the borrower’s tax rate; that is, if the tax rate is 28 percent, the complement of the tax rate is 72 percent and the after-tax cost is 72 percent of the pretax cost. (In effect, the entire interest cost is tax deductible.) This relationship will hold even if the loan is repaid early. The relationship also applies to loans with points if the points are deductible when they are paid. If the points cannot be deducted in the same year they are paid, the relationship will not hold exactly. Even where it does not hold exactly, it is usually a good approximation of the effective cost.1 It should also be clear that the higher the borrower’s tax rate, the greater the benefit of the inter- est tax deduction.

Monthly Payments The above example assumed that the payments on the loan were made annually, for example, at the end of the year, which coincided with the time the borrower received the tax deduction. If the loan payments were monthly, would the answer differ significantly? If we assumed that the buyer realized tax benefits from the interest deductions monthly, then the answer would not change at all. It could be argued that taxes are paid only once each year (on April 15 of the following year!) and thus the tax deduction is not received at the exact time as the loan payment. However, knowing that the tax benefit from the interest deduction will affect tax forms at the end of the year may also mean that borrowers pay less estimated taxes during the year.2 Furthermore, bor- rowers may have less taxes withheld from their monthly pay because they know that the interest will reduce their taxable income at the end of the year. Because of these possibilities, it may be more realistic to assume, when calculating the after-tax cost of financing, that interest deductions occur at different points in time than the mortgage payment. However, even if the tax deduction was not assumed to occur until the end of the year, it would not affect the calcu- lated effective interest rate significantly. Thus, for practical

1 For example, if points are charged on loans for income property, the relationship may not hold exactly. This is because the timing of the tax deduction for the points may not correspond with the actual payment of the points. Whereas the points are paid at the time the loan is closed, they must be amortized over the loan term for tax purposes. Points paid when purchasing an owner-occupied residence are generally deductible, although points paid when refinancing a residence must be amortized over the loan term.

purposes, we can conclude that the after-tax effective monthly interest cost is equal to the pretax effective monthly cost multiplied by the complement of the investor’s tax rate (1 – Tax rate).

Effect of After-Tax Interest Cost on Loan Decisions We have seen that the after-tax effective interest rate is pro- portional to the borrower’s tax rate. This will be true as long as the interest is tax deductible in the year it is paid.3 When this is true, tax considerations will not affect any of the conclusions regarding selection from alternative mortgages because taxes affect each loan in a similar manner. Thus, we can still compare pretax effective interest costs when choos- ing a loan and be confident that tax considerations will not affect financing decisions. Similarly, we can compute the incremental borrowing cost, the effective cost of refinancing, and other decision criteria discussed in the preceding chapter on a pretax basis. We do not mean to imply that interest deductions for tax purposes are an unimportant consideration when deciding to borrow money. Clearly, a borrower should consider the tax deductibility of the interest payments as part of the cost of making borrowing decisions. The higher a bor- rower’s tax rate, the lower the after-tax cost of borrowing. This affects one’s willingness to borrow on investment real estate, as you will see later in the book when we evaluate financial leverage.

Negative Amortization Loans We have seen that the after-tax effective cost of a loan is equal to the pretax effective cost multiplied by the comple- ment of the investor’s tax rate. This is true as long as all inter- est “charged” on the loan is tax deductible in the year that the interest is paid. By interest charged we mean the portion of each monthly payment which is not principal.

In the case of loans with negative amortization, interest charged will exceed the payment during some or all of the loan term. One example we have discussed is the graduated payment mortgage (GPM). We will now see how the after- tax effective cost is calculated for a loan with negative amor- tization. Consider a loan for $100,000 at a 10 percent interest rate with annual payments of $8,000 per year for the first five years, followed by payments of $12,000 per year until the entire balance is repaid.

Because interest charged is $10,000 (.10 × $100,000) the first year and the payment is only $8,000, negative amor- tization will be $2,000. This increases the balance of the

2 The IRS requires taxpayers to estimate their tax liability and in many cases quarterly payments must be made to the IRS.

3 Some alternative mortgages such as the graduated payment mortgage have interest charged (due to negative amortization) which is not deductible in the year it is paid. This is discussed later in this appendix.

Final PDF to printer

bru19684_ch06_150-184.indd 183 11/01/17 02:54 PM

Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications 183

loan to $102,000 after one year. The interest the second year is, therefore, $10,200 (.10 × $102,000). Proceeding in this manner, we can construct the loan schedule in Exhibit 6A–4.

From the exhibit, we see that negative amortization for the first five years increases the balance. In year 6, when the pay- ments increase to more than the interest charged, the loan bal- ance begins to decline. However, it takes until the end of year 15 before the balance decreases below the initial $100,000.

The question now is how much interest can the borrower deduct for tax purposes each year? Most borrowers, at least with owner-occupied homes, compute taxes on a “cash basis”; that is, their income and expenses for tax purposes are based on actual cash income and expenditures.4 For these borrowers, current tax regulations require that interest deductions may not exceed the amount of payment. Thus, in our example, only $8,000 could be deducted each year during the first five years. Starting with year 6, we see that the pay- ment exceeds the interest. What happens to the interest that could not be deducted during the first five years (due to the negative amortization)? The answer is that the borrower can continue to deduct the entire loan payment until the loan bal- ance is reduced to its initial balance, in this case, $100,000. Thus, the borrower can deduct the $12,000 payment until year 14. In year 15, the borrower can deduct the $10,161 interest, plus the remaining negative amortization that will reduce the balance to $100,000, or $1,630. After year 15, interest is deducted at the applicable rate in the same manner used on any constant payment mortgage. Exhibit 6A–5 illus- trates the relationship among the mortgage payment, interest charges, and loan balance in this example.

After-Tax Effective Cost We now have the information we need to calculate the tax deductions and after-tax effective cost of the loan. We can create the schedule in Exhibit 6A–6.

We could compute the effective cost for the entire loan term or for repayment of the loan at any time prior to the end of the loan term. For purposes of illustration, we will 4 The alternative is an “accrual basis,” where an accrual-based accounting system is used to determine income and expenses.

Year Beginning Balance Payment Interest Amortization

  1 $100,000 $ 8,000 $10,000 $(2,000)   2  102,000   8,000  10,200  (2,200)   3  104,200   8,000  10,420  (2,420)   4  106,620   8,000  10,662  (2,662)   5  109,282   8,000  10,928  (2,928)   6   112,210  12,000   11,221    779   7   111,431  12,000   11,143    857   8  110,574  12,000   11,057    943   9  109,631  12,000  10,963  1,037 10  108,594  12,000  10,859   1,141 11  107,453  12,000  10,745  1,255 12   106,198  12,000  10,620  1,380 13   104,818  12,000  10,482   1,518 14  103,300  12,000  10,330   1,670 15  101,630  12,000   10,161  1,837 16   99,793  12,000      9,979  2,021

. . . . .

. . . . .

. . . . .

EXHIBIT 6A–4 Loan Schedule

EXHIBIT 6A–5 Tax Deductions—Negative Amortization Loan

$120

110

100

90

80

70 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Interest is greater than the payment until year 5, resulting in negative amortization

Balance falls below original loan amount after year 15

Only interest deductible

Entire payment deductible until year 15

Lo an

b ala

nc e (

th ou

sa nd

s)

Year

Final PDF to printer

bru19684_ch06_150-184.indd 184 11/01/17 02:54 PM

184 Part 2 Mortgage Loans

compute the after-tax effective cost for repayment of the loan at the end of year 15, when the balance is $99,793. We have the following cash flows:

Year Payment Interest

Deductions Tax*

Savings After-Tax

  1 $ 8,000 $ 8,000 $2,240 $5,760   2   8,000   8,000  2,240  5,760   3   8,000   8,000  2,240  5,760   4   8,000   8,000  2,240  5,760   5   8,000   8,000  2,240  5,760   6 12,000  12,000  3,360  8,640   7 12,000  12,000  3,360  8,640   8 12,000  12,000  3,360  8,640   9 12,000  12,000  3,360  8,640 10 12,000  12,000  3,360  8,640 11 12,000  12,000  3,360  8,640 12 12,000  12,000  3,360  8,640 13 12,000  12,000  3,360  8,640 14 12,000  12,000  3,360  8,640 15 12,000  11,791  3,302  8,699

*28 percent tax rate.

EXHIBIT 6A–6 After-Tax Payments cost multiplied by the complement of the borrower’s tax rate. That is

After-tax cost =  ( Pretax cost ) ( 1 − Tax rate )

If the entire amount of interest charged is not deductible, as was illustrated for negative amortization loans, the effec- tive after-tax cost will be higher than it would be for the fully amortized loan. This results from the delay in receiving the tax deduction. However, even in this situation, multiplying the pretax cost times the complement of the borrower’s tax rate provides a close approximation of the after-tax borrowing cost.

If all loans evaluated for tax purposes are treated about the same, taxes do not have to be considered in the analysis since they affect all loans in the same manner and thus “wash out” in the final analysis. Thus, the types of analyses discussed in previous chapters can still be made without explicitly con- sidering taxes. However, tax deductibility of interest is still important when deciding whether to borrow in the first place since it reduces the cost of using debt to finance the purchase of real estate. This is particularly important when determin- ing whether to borrow money for investment property since the after-tax cost of the funds borrowed must be compared with the after-tax return on the property (before considering borrowing money) to see whether it is favorable to use debt to finance the purchase.

Problems

1. A $100,000 loan can be obtained at a 10 percent rate with monthly payments over a 15-year term.

a. What is the after-tax effective interest rate on the loan, assuming the borrower is in a 30 percent tax bracket and the loan is held only three years? Assume that the benefit of interest deductions for tax purposes occurs at the same time payments are made.

b. Calculate the after-tax effective cost for the above loan, assuming that 5 points are charged and that the points are tax deductible at the time they are paid.

c. How does the after-tax cost in part (b) compare with the pretax effective cost of the loan?

2. A mortgage for $100,000 is made with initial payments of $500 per month for the first year. The interest rate is 9 percent. After the first year, payments will increase to an amount that makes the loan fully amortizable over the remaining 24 years with constant monthly payments.

a. Calculate the interest deductions for the loan for the first year.

b. How much, if any, interest must be deferred until the second year?

c. How much interest will be deducted in the second year?

Year After-Tax Cash Flow

0 –$100,000 1–5          5,760 6–14          8,640 15    108,492

The IRR for the above cash flows is 7.32 percent. Recall that the pretax effective cost was 10 percent; thus, we see that the after-tax effective cost is slightly higher than it would be for a fully amortizing loan, which would have an after- tax effective cost of exactly 7.2 percent. The higher after- tax effective cost for the negative amortization loan occurs because of the deferral of interest deductions. During the period of time that the loan balance is increased, less interest is deducted than is charged. The portion of interest that is not tax deductible during those years becomes deductible from the time the loan balance begins to fall until it reaches the original balance.

Conclusion The tax deductibility of interest payments reduces the after- tax cost of debt. As long as the entire amount of interest charged in a given year is tax deductible that year, there is a very simple relationship between the pretax cost of a loan and the after-tax cost. The after-tax cost is equal to the pretax

Final PDF to printer

185

bru19684_ch07_185-221.indd 185 11/01/17 04:25 PM

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations In previous chapters, we covered the nature of real estate assets, property rights, a broad range of fixed and adjustable rate mortgage loans, and the loan underwriting process. In this chapter, we focus on single-family residential housing as an investment. In doing so, we provide an analysis of homeownership as an alternative to renting, the characteristics of supply and demand for housing, pricing, federal income tax treatment for homeowners, and investing in “distressed” properties. All of the topics in this chapter are essential for prospective investors in housing.

Overview

Homeownership has long been considered to be an important goal for many individuals in the United States. In addition to providing shelter, homeownership, in the view of many, is an important investment vehicle for personal wealth accumulation. Some have come to think of housing as both a consumption good (shelter) and an investment. As our economy has developed, many institutions have evolved to support the growth in the housing indus- try. These include financial institutions, developers and builders, mortgage lenders, real estate brokers, the property insurance industry, and many other service providers. Indeed, it has been estimated that housing and related services account for as much as 15 percent of total U.S. output. In addition, federal income tax policy has long favored homeowner- ship by providing for the deductibility of mortgage interest and, under certain conditions, excluding capital gains from taxation when properties are sold. These tax incentives stem from the belief by members of Congress that homeownership encourages stronger social networks, better educational achievement rates, and lower crime rates. Consequently, they have continued to provide special tax incentives to encourage homeownership. What fol- lows is a more detailed examination of factors that influence housing as an investment.

House Prices One element related to housing as an investment is the rate of price appreciation (or depre- ciation) and what drives it. To begin our discussion, it is useful to review a list of important influences on price appreciation, as shown in Exhibit 7–1. Data for all of these concepts are

Final PDF to printer

186 Part 3 Residential Housing

bru19684_ch07_185-221.indd 186 11/01/17 04:25 PM

available at the metropolitan statistical area (MSA) level for each metro area (see website references for the U.S. Census Bureau, U.S. Bureau of Labor Statistics and U.S. Department of Commerce/Bureau of Economic Analysis at the end of this chapter). The right-hand col- umn in Exhibit 7–1 shows the direction of influence, holding all else constant, that each variable should have on housing demand. These influences should be interpreted based on increases in each variable. For example, increases in population, households, income, and employment, when considered individually, should affect the demand for housing positively. However, increases in interest rates would have a negative effect. Increases in federal income tax rates would have a negative effect. And if the cost of rental housing increases relative to house prices, demand should increase. Obviously, if the change for any of the variables in the above list were in the opposite direction, the impact on housing would be the reverse of what we have discussed (e.g., a decline in interest rates would have a positive effect on housing).

Finally, when attempting to forecast a trend in the above variables, we see two ques- tions of fundamental importance: (1) What drives each variable? (2) Why do changes in the variables vary by city? In recent years, population growth has been greatly affected by immigration. It has been estimated that immigration accounted for as much as one-third of recent increases in population.  It is also important to note that the growth rate in house- holds tend to parallel population increases. As already indicated, households tend to form as younger individuals leave home, get married, and so on. 

Social trends have also tended to increase the number of households. These include delays in the average age at which marriages are occurring, the increasing number of divorces, and the number of people never marrying. These factors result in greater demand for separate, or individual, housing units. Increases in the average life expectancy have also resulted in households occupying housing units for longer periods of time. This, in turn, has reduced “housing turnover,” or the inventory of existing housing units that would oth- erwise be available to younger household groups.

Other important industry data indicate that: (1) first-time home purchasers tend to be 28–32 years of age, (2) households tend to sell their first home and purchase a different home (upgrade) by age 40, and (3) potential purchases of vacation or second homes usu- ally occur by age 48–52. Retirement homes are usually considered when households reach 60 years of age or older.

Income and Employment While growth in population and households is a necessary condition for housing demand, employment is also an important driver of housing affordability. Recent data indicate that U.S. employment growth has averaged about 1 percent annually during the past 10 years. Sunbelt cities have enjoyed the greatest growth in employment. The share of the popula- tion employed also has increased as more women have joined the labor force. Many of these women represent single-parent households, which reinforces the demand for more housing units. Although we will discuss the economic base of cities later in the chapter, we should point out that there are differences in the nature of employment opportunities

Increases In Direction of Impact on Demand

(1) Population growth + (2) Household formations + (3) Employment + (4) Household income + (5) Interest rates – (6) Federal income tax benefits + (7) Cost of renting housing +

EXHIBIT 7–1 Economic Influences on Housing Demand

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 187

bru19684_ch07_185-221.indd 187 11/01/17 04:25 PM

and the types of businesses that locate in various regions of the United States. The relative desirability of regions that attract businesses (1) affects the ability of households to earn income that they use to acquire housing and (2) also affects house prices. An important item to remember is that the quality and nature of employment and the salaries earned by the labor force also vary by metro area. So, while employment growth is important, the quality of jobs and the wages and salaries earned in these occupations are also important. There is a very strong association between house price appreciation and income/employ- ment growth. Therefore, when viewing housing as an investment, we must remember that, for cities under consideration, basic research concerning these trends is very important.

Interest Rates Many factors determine interest rates. The more important factors include the supply and demand for loanable funds as the economy expands and contracts and Federal Reserve pol- icy in the course of its management of the monetary system. The Federal Reserve generally has a significant effect on interest rates, which in turn affects housing demand. Because real estate has a “high debt capacity” and many loans are made as a large percentage of property value, monthly payments may rise or fall substantially, depending on changes in interest rates. The effects of interest rate changes also tend to spill over into many areas of the housing industry. These areas include construction, land development, financing, bro- kerage, inspections, appraisals, and other housing-related service businesses. Because of these far-reaching influences, housing is a very important sector of the economy.

As indicated in Exhibit 7–1, holding all else constant, increases in interest rates tend to have a negative influence on home ownership. This relationship is somewhat intuitive because as interest rates increase, this is analogous to raising the cost on borrowed funds, thereby raising the cost of financing home ownership. Conversely, as interest rates fall, the effects on home ownership tend to be positive.

While the effects of interest rates on demand are relatively clear, the magnitude of the impact has become more complex to understand in recent years because of a greater vari- ety of mortgage loan options. As discussed in Chapters 4 and 5, these options are no longer limited to fixed interest rate mortgages (FRMs). Adjustable rate mortgage (ARM) loans and many other types of loans now provide for different rates, loan amortization periods, and other features. In addition, some of the other terms of lending, such as financing fees, prepayment options, and the rigor with which lenders apply underwriting standards, tend to reinforce the direction of mortgage interest rates. For example, during periods of appre- ciating house prices and/or low interest rates, lenders may tend to be more flexible on such things as credit scores when underwriting. The impact of changes in lender underwriting standards is difficult to predict.  However, more restrictive underwriting usually occurs when interest rates are rising and these standards usually become more lenient when inter- est rates are declining. So changes in underwriting standards usually  tend to reinforce effects that the direction of interest rates have on homeownership.

Renting versus Owning Another important consideration when analyzing the demand for home  ownership invest- ment is the cost of renting. If individuals find that renting is more cost-effective than own- ing, home ownership may not always be a better investment. What follows is a comparative analysis of the relative costs of owning versus renting the same residence. The goal of this exercise is to compile all cash flows associated with each form of occupancy, and then cal- culate the rate of return that will be earned on the funds used to make an equity investment (down payment) if the property is purchased. Alternatively, it is this rate of return that an investor would have to earn on the “down payment” saved if renting is chosen, to make renting the financial equivalent of owning.

Final PDF to printer

188 Part 3 Residential Housing

bru19684_ch07_185-221.indd 188 11/01/17 04:25 PM

The framework for making a comparison between renting and owning is presented in the example summarized in Exhibit 7–2. In this example, we have a property that could be rented for $12,000 per year ($1,000 per month) or purchased for $150,000 with $30,000 down and financed with a fully amortizing mortgage loan of $120,000 at 7 percent inter- est for 30 years. Other costs associated with owning include maintenance, insurance, and property taxes. In our example, these expenses would not have to be paid if renting is cho- sen. All other expenses would have to be paid regardless of whether the property is owned or rented, such as utilities, and so on. Because they offset, they do not have to be included in our analysis. Other assumptions include (1) a federal income tax rate of 28 percent, (2) escalation in expenses, rents, and property value at 2 percent per year, and (3) a five- year period of analysis, at the end of which, the property would be sold (if owned). Selling expenses of 7 percent would have to be paid at that time.

Cash flows associated with our analysis are summarized annually for convenience and pre- sented in Exhibit 7–3. Note that for the ownership alternative, cash flows must be developed both before and after taxes because, as indicated, owners of residential property are provided with special federal income tax treatment (see summary of tax provisions in Exhibit 7–4). This treatment is not available to renters; therefore, cash outflows for renters are the same on a before- and after-tax basis (see part C). Looking to Exhibit 7–3, note that in panel A, we have summarized before-tax cash outflows associated with owning. These total $12,830 during year 1. Included in these cash outflows are constant monthly mortgage payments of $798.33 · (12), or $9,580, each year. The tax treatment shown in part B includes allowable deductions for property taxes and mortgage interest. These deductions reduce the owner’s federal income tax1 payments and therefore reduce net outflows associated with home owner- ship. These deductions reduce taxes at a rate of 28 percent, or by a total of $2,971 in year 1.

1 This assumes that the homeowner itemizes for tax purposes.

1. Property Information Loan Information

Purchase price $150,000 Loan-to-value ratio 80.00% Initial rent $12,000 Loan amount $120,000 Rental growth rate 2.00% Interest rate 7.00% Property growth rate 2.00% Loan term 30 years Insurance $500.00 Payments 12 per year Maintenance $500.00 Annual debt service (payment) $9,580 Expense growth 2.00% Annual loan constant 7.98% Marginal tax rate 28.00% Equity investment/down payment $30,000 Property tax as % of value 1.50% Selling expenses 7.00%

2. Annual Loan Schedule

End of year 0 1 2 3 4 5

Mo. Payments · 12 $ 9,580 $ 9,580 $ 9,580 $ 9,580 $ 9,580 Balance 118,781 117,474 116,072 114,569 112,958 Interest (year) 8,361 8,273 8,179 8,077 7,969 Amortization (year) 1,219 1,307 1,402 1,503 1,612

3. Property Data

Property value $150,000 $ 153,000 $ 156,060 $ 159,181 $166,365 $165,612 Rents 12,000 12,240 12,485 12,734 12,989

EXHIBIT 7–2 Rent versus Own Analysis of a Personal Residence www.mhhe.com/bf16e

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 189

bru19684_ch07_185-221.indd 189 11/01/17 04:25 PM

Interest deductions decline to $7,969 in year 5 because interest on the loan declines over time. The net annual after-tax cash outflows if owning is chosen are summarized in part D and are $12,830 (from part A) less $2,971 in tax savings (from part B), resulting in a net outflow of $9,859. If the property is owned, this also means that rent of $12,000 does not have to be paid. To complete the annual outflow in our analysis, we must consider rent savings if owning is chosen. This amounts to $12,000 the first year and when included in the analysis produces a net after-tax savings from home ownership of $2,141, as shown in part D. Note that savings in

Year 1 Year 2 Year 3 Year 4 Year 5

A. Before-tax cash flows—owner: (1) Property taxes $ 2,250 $ 2,295 $ 2,341 $ 2,388 $ 2,435 (2) Insurance 500 510 520 530 540 (3) Maintenance 500 510 520 530 540 (4) Mortgage payments (P&I) 9,580 9,580 9,580 9,580 9,580

(5) Cash outflows before taxes $ 12,830 $ 12,895 $ 12,961 $ 13,028 $ 13,095

B. Tax deductions—owner: (1) Property taxes $ 2,250 $ 2,295 $ 2,341 $ 2,388 $ 2,435 (2) Interest 8,361 8,273 8,179 8,077 7,969

(3) Total deductions 10,611 10,568 10,520 10,465 10,404

(4) Tax savings @ 28% $ 2,971 $ 2,959 $ 2,945 $ 2,930 $ 2,913

C. Renter status: (1) Rents $ 12,000 $ 12,240 $ 12,485 $ 12,734 $ 12,989

D. Net cash flows—owning: (1) Before-tax outlays (A.5) $ (12,830) $ (12,895) $ (12,961) $ (13,028) $ (13,095) (2) Tax savings (B.4) 2,971 2,959 2,945 2,930 2,913 (3) After-tax cash flows (9,859) (9,936) (10,016) (10,190) (10,182) (4) Rent saved (C.1) $ 12,000 $ 12,240 $ 12,485 $ 12,734 $ 12,989

(5) After-tax cash flows—owning $ 2,141 $ 2,304 $ 2,469 $ 2,635 $ 2,807

E. Before-tax cash flow—for sales occurring in years 1–5: (1) Property value $ 153,000 $ 156,060 $ 159,181 $ 162,365 $ 165,612 (2) Less: Selling expenses 10,710 10,920 11,143 11,366 11,593 (3) Less: Mortgage payoff 118,781 117,474 116,072 114,569 112,958

(4) Before-tax cash flow sale $ 23,509 $ 27,666 $ 31,966 $ 36,430 $ 41,061

F. After-tax cash flow—for sales occurring in years 1–5: (1) Property value $ 153,000 $ 156,060 $ 159,181 $ 162,365 $ 165,612 (2) Less: Selling expenses 10,710 10,920 11,143 11,366 11,593 (3) Less: Basis 150,000 150,000 150,000 150,000 150,000

(4) Gain on sale (7,710) (4,860) (1,962) 999 4,019 (5) Less: Exclusion — — — 999 4,019 (6) Tax 0 0 0 0 0 (7) After-tax cash flow (E.4 − F.6) $ 23,509 $ 27,666 $ 31,966 $ 36,430 $ 41,061

G. After-tax IRR on equity ($30,000) if sold: (1) ATIRR (D.5 + F.7) −14.50% 3.57% 9.63% 12.34% 13.71%

EXHIBIT 7–3 Cash Flow Analysis—Rent versus Own Analysis of a Personal Residence

Final PDF to printer

190 Part 3 Residential Housing

bru19684_ch07_185-221.indd 190 11/01/17 04:25 PM

I. Tax Treatment of Personal and Qualified Residences* A. Interest Deductions and Qualified Residences. Interest is deductible on “qualified residences.” A taxpayer’s

qualified residences are a personal residence and one other residence. The second residence does not have to be used by the taxpayer during the taxable year to be a qualified residence as long as it is not rented during the year. If it is rented for part of a year, a specified amount of personal use is required (see II.A, below). Interest on three or more homes is not deductible, unless the home is a business or investment property not used personally by the taxpayer. Under certain conditions, mobile homes, boats, trailers, time-shares, and stock in a cooperative housing corporation may be a qualified residence.

B. Maximum Interest Deductions. Interest on two types of home mortgage debt is deductible. (1) Interest is deductible on “acquisition debt,” which is secured debt used to purchase, build, or substantially

improve a qualified residence. Interest on acquisition debt is deductible as long as the debt does not exceed the cost of the residence and its improvements. The maximum amount of indebtedness upon which interest is calculated may not exceed $1,000,000 for couples filing jointly.

(2) Interest is also deductible on “home equity debt.” For couples filing jointly, the amount of indebtedness upon which interest is based can be up to the lesser of $100,000 or the amount of equity in the residence. Home equity debt must be secured by a qualified residence.

C. Points on Mortgage Loans. The term points is used to describe certain charges paid, or treated as paid, by a borrower to obtain a home mortgage. Points may also be called loan origination fees, loan charges, loan discounts, or discount points. Points can be deducted in the year paid if all of the following tests are met:

(1) The loan is secured by a qualified residence. (2) The funds the borrower provided at or before closing, plus any points paid by the seller, were at least as

much as the points charged. (3) If the loan was used to buy or build a home (qualified residence). (4) The points were computed as a percentage of the principal amount of the mortgage. (5) The amount is clearly shown on the settlement statement as points charged for the mortgage. The points

may be shown as paid from either the borrower’s funds or the seller’s funds. If the above tests are not met, points must be deducted over the life of the loan.

D. Real Estate Taxes. Property taxes must be a direct tax on interests in real property. The tax is deductible in the year paid only by the owner of the property upon which the tax was imposed and paid. Generally, prepaid real estate tax can be deducted in the year of the prepayment.

E. Capital Gain Exclusions. For sales of a personal residence after 5/6/97, a homeowner may exclude from income $250,000 of gain, and a married couple may exclude up to $500,000 of gain realized on the sale.

(1) Individual must have owned and used the home as a principal residence for at least two of the five years prior to the sale (the two years do not have to be consecutive).

(2) Exclusion applies to only one sale every two years. II. Tax Treatment of Second Residences A. Interest Deductions. All rules relating to personal residence interest deductions apply. B. Points. Points paid on loans secured by a second home are amortized and deducted over the life of the loan. C. Sale of Second Residence: Capital Gains Exclusion. Generally only one home (either the primary or secondary)

that is used for a majority of the time during the year will be considered the principal residence and will qualify for the exclusion. Second homes do not qualify for the exclusion.

III. Tax Treatment of Second or Vacation Homes A. If the property is not rented and is owned for personal use only, then deductions are determined as though it is

a non-primary, qualified residence (see: I.A above). B. If the property is owned for personal use and rented for 14 days or less per year, no rents or expenses must be reported. C. If the property is owned for both personal use and rented, all rental income must be reported and all expenses

can be deducted. Personal use cannot exceed 14 days or 10 percent of the number of days for which it was rented (whichever is greater).

D. If the property is owned for both personal use and rented, and the number of days of personal use exceeds 14 days or 10 percent of the number of days for which it was rented, then all rental income must be reported and deductions are limited to the amount of rental income. Any expenses in excess of rental income may be carried forward to offset income earned in future years.

EXHIBIT 7–4 Summary of Tax Provisions Important to Residential Housing

* Generally based on Internal Revenue Code P 163(h)(4) and P 1.163-10T. The reader should not rely on this general discussion when making investments and/or tax elections. This discussion may not be complete, and the Internal Revenue Code is modified frequently.

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 191

bru19684_ch07_185-221.indd 191 11/01/17 04:25 PM

year 2 are $2,304 and so on. This analysis must be carried out for each year to assess (1) the net effects of increasing nondeductible expenses such as maintenance and insurance, (2) increasing rents, (3) increasing deductible expenses such as property taxes, and (4) declin- ing deductible expenses such as the interest portion of payments on the mortgage loan.

Finally, we must consider the proceeds from sale of the property. We calculate this for each year in sections E and F of Exhibit 7–3. The before-tax cash flow in section E is sim- ply the sale price, less selling expenses and the mortgage loan balance. After-tax cash flows must include any taxable gains on sale. The latter is based on the selling price, less selling expenses, less the tax basis for the residence which in this case is the original pur- chase price.2 Should a sale occur, the tax consequences are shown to be zero in each of the first three years because the property appreciation rate is not sufficient to offset the selling expenses. Therefore, if the property is sold, the borrower would not recover the initial acquisition price and no taxable gain or deductible loss would result. It should be noted that, beginning in year 4, a $999 gain from sale results, as does a $4,019 gain in year 5. However, because of the capital gains exclusions that apply to residential real estate (see Exhibit 7–4), these capital gains are not taxable. The annual after-tax cash flows up to the year of sale and the cash flows produced from sale are combined, and internal rates of return are calculated and presented in section G of Exhibit 7–3. 

Note that if the property was sold at the end of year 1, the after-tax IRR on the $30,000 investment would be negative. This means that if the property is expected to be sold after only one year, renting may be the wiser choice. However, returns from ownership improve in years 2 through 5, as the annual after-tax cash flows and the property value increase.3 The IRRs during those years indicate that in order to justify renting, an investor would have to earn from 3.5 percent to 13.7 percent on an after-tax basis on other investments equal in risk with the $30,000 equity saved to make renting equivalent to owning.

Other Considerations After we summarize the cash flows associated with owning and renting, a number of additional questions arise. For instance, our example assumes a sale at the end of year 5. Inasmuch as people must have shelter, what should be done with the proceeds from sale after year 5? Will the investor choose to own or rent from the end of year 5 into the future? What if the owner chooses not to sell after year 5, but continues to own for the indefinite future—how should this possibility be analyzed? One guide that may help to answer these questions would be to first consider the likelihood that a sale may occur in a relatively short period of time. Generally, if frequent sales are likely to occur because of employment changes/relocation, renting should tend to become more desirable unless house appreciation rates and rents are increasing at significant rates in the area where the residence is located. In the latter case, when a sale occurs, a borrower would be more likely to recover selling expenses and save increasing rents that would otherwise have to be paid. On the other hand, if house prices are expected to remain flat or decline, a short period of occupancy would tend to make renting more favorable. Alternatively, other com- binations that could make renting more favorable than owning would include (1) expected rents would have to decline, or (2) non-tax-deductible housing expenses (maintenance, insurance, etc.) would have to be expected to increase dramatically, or (3) the initial inter- est rate available on mortgage loans would have to be much higher than the 7 percent shown in our example.

2 If any improvements or remodeling expenses have been incurred, these should be added to the original purchase price to establish the tax basis for the residence in the year of sale. “Fixing up” expenses immediately prior to sale may also be included. 3 To calculate the after-tax IRR in year 2, one must find the interest rate (discount rate) that makes the present value of $2,141 in year 1 and $2,304 plus $27,666 at the end of year 2 equal to the equity outlay of $30,000.

Final PDF to printer

192 Part 3 Residential Housing

bru19684_ch07_185-221.indd 192 11/01/17 04:25 PM

As to periods beyond five years, it is apparent from Exhibit 7–3 that net benefits from homeownership continue to increase over time. While this pattern cannot be expected to continue with certainty, an examination of the importance of appreciation in house prices and equity investment may be helpful.

If one examines the cash flow analysis again in Exhibit 7–3, it becomes clear that advan- tages to homeownership are substantial because of house appreciation rates (E.1 and F.1) and the capital gains exclusion.

The Rent versus Own Decision—Other Issues What has been presented above is a purely financial analysis of owning or renting the same place of residence. In the example, it was apparent that ownership was generally the favored choice, particularly if the property was to be owned and occupied for three years or more. One interesting question that may occur to the reader is: “Is there a level of rent at which benefits from homeowning are eliminated?” That is, at what level of rent would you be indifferent between renting and owning? This would be a level of rent that results in an after-tax IRR from owning that is just sufficient to compensate for capital invested as a down payment. We will assume that this is 5 percent. This is about the same as the after- tax cost of the loan [ 7% × (1 − .28)  = 5% rounded ] .

We recalculate the net cash flows in Exhibit 7–3 by changing rent saved (part C) to $9,155 for the first year, which changes results in part D(4) and produces the following after-tax IRRs on the $30,000 equity investment:

Revised annual cash flows and after-tax IRR recalculation:

Year 1 2 3 4 5

After-tax IRR −23.98% −6.19% .19% 3.27% 5.00%

From this analysis, it is apparent that if the same residence could be rented for $9,155 per year, then based on financial considerations only, the investor would be indifferent as to whether the property is owned or rented for five years. It could also be said that almost no advantage exists between the purely financial elements of owning and renting. The rent of $9,155 could be found by trial and error or using “Goal Seek” in Excel.

Historical Trends Based on historical trends in the United States, approximately 67 percent of all residen- tial housing is owned and 33 percent is rented. This suggests that homeownership is both strongly preferred and may be a good investment. However, there are other issues to con- sider. Renting could be favored in spite of financial returns on equity in residential owner- ship for a number of reasons. These include 1. Need for flexibility because of frequent relocation of employment, family, or other

reasons. 2. Lack of funds for a down payment. 3. Credit quality of the resident. 4. No desire to bear the risk of ownership and volatility in house prices. 5. A desire to shift maintenance, security, and management to others. 6. A desire to avoid volatility, or risk of loss because of “bubbles,” in house prices. This

may occur when house prices rise relative to rents to such an extent that the prospect of further appreciation in prices becomes problematic. In some housing markets affected by sharp increases in employment tied to higher cyclical industries, should contraction in employment occur in those industries, volatility in house prices may be affected.

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 193

bru19684_ch07_185-221.indd 193 11/01/17 04:25 PM

To the extent that any or all of the above considerations are important to residents, they may be willing to forgo returns available from homeowning and pay an implicit premium or opportunity cost to maintain renter status. For this and other reasons, there are many investors and developers who develop, own, and manage rental housing units. We will deal with that type of real estate investment in a later chapter.

Analyzing Expected House Prices There are many other facets of the housing market that are important when considering a purchase. When investing in housing, investors find it useful to measure the expected rate of appreciation in house prices (EAHP). This is calculated as

H P 1 − H P 0 _________ H P 0

 = EAHP%

where H P 0 is the house price in year zero and H P 1 is the expected price at the end of year one. To illustrate, if H P 0  = $100,000 and H P 1  = $103,000, then the expected appreciation in house prices for one year is 3 percent, shown as

$103,000 − $100,000 __________________ $100,000

 = 3%

To extend this analysis and provide more perspective for investors, a useful exercise is to consider the expected appreciation rate on home equity (EAHE). This concept can be calculated as follows:

H P 1 − H P 0 ___________ H P 0 (1 − L / V)

 = EAHE%

defining L/V as the loan-to-value ratio. Assuming a 3 percent house appreciation rate and an 80 percent loan-to-value ratio, the annual equity appreciation rate expected for a one- year period would be

$103,000 − $100,000 __________________

$100,000 (.2)

=

EAHE

$3,000 _______ $20,000

=

15.0%

Alternatively, the expected average annual appreciation in home equity (EAHE) can be approximated from the average house price appreciation rate (EAHP) of 3 percent by mul- tiplying it by the ratio of house price to equity (HP/E), which is 100% ÷ 20%, or 5.0. Using this formulation, we have

EAHP (HP / E)  = EAHE 3% ⋅ 5 = 15.0%

These calculations show that a 3 percent annual average rate of appreciation in house price results in a 15 percent appreciation rate on equity when 80 percent financing is used. This example can be thought of as a method of providing investors with an estimate of unrealized equity gains, which the owner has the option of realizing by: (1) selling the residence (although proceeds may be subject to federal income taxes— see Exhibit 7–4) or (2) refinancing, in which case there may be no federal income taxes to pay because refinancing is not a “taxable event.” This example also clearly

Final PDF to printer

194 Part 3 Residential Housing

bru19684_ch07_185-221.indd 194 11/01/17 04:25 PM

illustrates why investing in housing financed with mortgage loans has provided an extremely powerful financial incentive for households, particularly those interested in long-term wealth accumulation. Research has also been done by economists on the so-called “wealth effect.” This is the effect that expected appreciation in assets, including home equity, may have on consumer spending on other goods and services in the economy. This comes about as consumers feel more financially secure about their future economic well-being, because their stocks, bonds, and houses are rising in value. Consequently they tend to spend more on other goods and services. When asset prices are declining however, consumer spending also may decline as a result of a “reverse wealth effect.”

Unrealized Annual Rates of Appreciation on Equity The above calculations provide a good approximation in situations where rate of house appreciation is expected to be a constant or when a rough estimate is adequate for the reader. In cases where the rate of house price appreciation is expected to be different each year, or should a more exact calculation be needed, the above calculation may be modified as shown in the following example for a $100,000 property financed with an 80 percent loan.

End of Year House Price

Appreciation Rate Equity Calculation

Annual EAHE

0 $100,000 — $20,000 — — 1 103,000 3% 23,000 3,000 ÷ 20,000 15.0% 2 105,060 2% 25,060 2,060 ÷ 23,000 9.0% 3 109,262 4% 29,262 4.202 ÷ 25,060 16.8%

Solution:

n

=

3

PV

=

− 20,000

FV = 29,262 PMT

=

0

Solve for i

=

13.55%

Function: i (n, PV, FV, PMT )

As shown in the above example, average expected appreciation in home equity for the three-year time period is equivalent to an annual compounded rate of interest equal to 13.55 percent. See Concept Box 7.1, which contains very important data sources that are used frequently when forecasting house prices.

Regional Economic Influences on Property Values An important concept in real estate analysis is the fact that the house prices are highly dependent on the regional or geographic area in which they are located. The demand for properties in local markets is highly influenced by the nature of the industries, busi- nesses, and so on, that are attracted to a region. Business activity and its growth determine employment and income in a region, which influence the demand for all property types. In short, when a real estate analysis is undertaken, the regional economic drivers must be identified and a judgment must be made about whether these drivers will provide a source of growth or decline in a region. To determine the latter, trends must be established for the future global outlook for growth in those industries (e.g., computer technology, com- munication technology, medical-pharmaceutical, and tourism/recreation).

Final PDF to printer

bru19684_ch07_185-221.indd 195 11/01/17 04:25 PM

HOUSING STATISTICS

1. National Association of Realtors (NAR): www.realtor.org

A. Median House Prices Essentially, prices on all existing housing units sold during each month (single-family, condominium, co-ops) are ranked from high to low. The midpoint, or median sale price, of all sales throughout the United States is selected and reported. A quar- terly series also is reported by most metropolitan areas (!"# = metropolitan statisti- cal area, as defined by $!% − 2004) . Issues: When calculating appreciation rates based on median prices selected for specific time periods, some observers have questioned the comparability of housing units over different time periods. In addition to price changes, house size, lot size, and location of housing units also are believed to change over time. This makes the interpretation of price changes problematic, thereby limiting the usefulness of the appreciation data.

B. Pending Home Sales This is an indicator of sales volume that is compiled monthly based on the number of signed contracts to purchase homes. Given that two to three months are required to obtain loan commitments and close the title, this “pre-final sale” series is used as a leading indicator for analysis of the housing industry. Data are available only for the United States and four major census regions.

C. Housing Affordability Index (HAI) The HAI is a monthly series consisting of (1) median family income and (2) median qualifying income (income needed to make mortgage and housing expense payments on a median price house with a 20 percent down payment). The ratio of median family income to median qualifying income is then calculated and used as an indicator of the extent to which a housing purchase is affordable for median income families.

2. Federal Housing Finance Agency: www.fhfa.gov

A. Purchase-Only House Price Index (HPI) The Federal Housing Finance Agency publishes the Purchase-Only HPI, which is a quarterly average series based on prices obtained from repeat, “purchase-only” trans- actions for the same properties over time for all MSAs in the United States. An aver- age for the United States also is calculated by weighting these prices by a population weighted index as compiled by the U.S. Census Bureau. By focusing on repeat sales of the same houses over time, this index attempts to maintain comparability of housing characteristics based on size, age, and so on.

B. All Transactions House Price Index (HPI) In addition to data used to compile the quarterly Purchase-Only HPI, appraisal data from refinancing are included in this “All Transactions” HPI. Issues: Both data sources are obtained from FHLMC-FNMA loan files. These files are based on conforming loans, or loans that conform to underwriting stan- dards for these agencies. Because maximum loan limits are set by these agen- cies, mortgages made for amounts above those maximum loan limits are not included in either database. Therefore, house prices used to compile both indexes are useful only when analyzing transactions in the “conforming” segment of the housing market.

House Price and Related Data Sources Concept Box 7.1

195

Final PDF to printer

196

bru19684_ch07_185-221.indd 196 11/01/17 04:25 PM

House Price and Related Concept Box 7.1 Data Sources (Continued)

3. S&P Case-Shiller® Index: www.homeprice.standardandpoors.com

The S&P Case-Shiller® Index is a monthly"repeat sale"  house price index based on data obtained from repeat sales of the same housing units in 20 MSAs. A U.S. national home price index is also calculated. When computing price changes, a statistical technique is employed to use only paired sales of the same housing units sold over time. Houses are removed from the sample if any improvements, remodeling, or the like have been undertaken between sale dates. This methodology is used in an attempt to capture price changes on housing units with the same characteristics over time. Issues: Data are a three-month moving average, published monthly and are available for up to 20 MSAs only.

Why do certain kinds of economic activity tend to “cluster” more in some regions and urban areas than others? We do not intend to provide an extensive discussion of the phenomena here as there have been volumes written on this subject by many regional economists. However, we do believe that an understanding of the underpinnings of this economic behavior is critical when thinking about the relative attractiveness of real estate investments. As we will stress in this chapter and in others, making an investment in a specific real estate asset cannot be separated completely from making an investment in an economic region because the real estate is permanently located in that region. Therefore, the need to know the forces that drive economic growth in an area is essential to the suc- cess of an investment.

Analogy with the Law of Comparative Advantage This concept, stated very simply, says that some geographic regions have a compara- tive advantage over other regions in that certain goods/services can be produced more efficiently and profitably in that region than in other regions. This advantage may exist because of (1) natural advantages (e.g., seaport, minerals, low-cost energy, and beaches), (2) employee characteristics such as a highly trained, educated workforce (e.g., location of universities, workforce training in technical industries), and/or (3) proximity to many major consumer markets (e.g., transportation hub). Regional examples would include high-tech research and development (California, Seattle, Boston), oil and gas exploration (Houston), communication and computer assembly (Austin, San Diego), medical technol- ogy/clinics (Minnesota, Boston), and production of entertainment (Los Angeles). These industries tend to locate in certain geographic areas because land, labor, and capital can be combined cost-effectively or revenues can be enhanced by locating in those regions. This simple concept is very useful in real estate investing because when researching markets for real estate investment opportunities, those markets having industries with the highest likelihood of future growth will have a positive effect on house prices.

Identifying Regional Economic “Drivers” or Base Industries One obvious way to identify the drivers of economic growth in an area is to identify base, or driver, industries, which are those businesses producing the greatest profits. Unfortunately, data pertaining to profits is difficult to collect on a regional basis because (1) much of it is private information and (2) for publicly owned firms, multiple operat- ing divisions may make profits by region very difficult to break down. As a result, many

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 197

bru19684_ch07_185-221.indd 197 11/01/17 04:25 PM

analysts rely on employment data that are collected by the U.S. Department of Labor and by various agencies in all 50 states. The underlying logic for using employment data for real estate investment research is that expanding businesses will have expanding needs for labor. Identifying the number of those industries with a comparative advantage in that region will help to estimate the number of employees in these industries and, in turn, the number of housing units needed. While employment data are generally thought to be the best tool available for analysis, this method is not ideal because labor may not always be added in direct proportion to increases in revenues or the output of goods and services pro- duced by a company. Furthermore, the method may tend to underestimate the importance of less labor-intensive businesses in a region that may be very profitable and pay high wages to fewer employees.

Economic Base Analysis—Location Quotients One widely accepted approach in economic analysis for identifying driver industries in a region—the economic base—is to calculate what are referred to as location quotients. This is done very simply by using the following relationship:

( R E j _____ R E TOT ) __________

( US E j _______ US E TOT ) >1.0?

Terms in this relationship are as follows:

RE

=

Regional employment

USE = U.S. employment j =

Industry classification

TOT

=

Total

For example, if we let j represent the computer assembly industrial classification, then this ratio will tell us if the proportion of regional employment (RE) in the computer assembly business ( j) as a percentage of total employment in that region (RETOT ) is greater or less than the proportion of those employed in industry j throughout the United States as a percentage of the total employment throughout the country. If this ratio is greater than 1.0, then industry j would be identified as a base or driver industry for a region because it employs a greater-than-proportionate amount of workers in that industry than is the case for the United States as a whole. Obviously, if the ratio is less than 1.0, then that industry would not be a base industry. Industry classifications with ratios less than 1.0 are usually referred to as supporting industries. Examples of the latter could be accounting firms, advertising firms, and so on. These supporting businesses are also important for real estate investment, particularly for retail establishments, personnel services, and similar firms, all of which must also lease operating space in properties.

Data classifications for various industries (designated above as j) have been developed and published by the U.S. Office of Management and Budget and are used by the U.S. Department of Labor. This department collects and categorizes data on all employees in the United States. Depending on the level of detail desired, all employment data are broken into several industry classifications. These classifications are referred to as North American Industry Classification System, or NAICS. The data are collected for over 300 metropolitan areas.

Final PDF to printer

198 Part 3 Residential Housing

bru19684_ch07_185-221.indd 198 11/01/17 04:25 PM

Employment Multipliers This aspect of economic base analysis is conducted to determine how total employment in a region is affected by changes in base employment. After a complete analysis is con- ducted for every employment classification ( j) in a region and all base employment has been identified with location quotients and totaled, employment in the remaining catego- ries is totaled. Then, the ratio of total to basic employment is calculated. If, for exam- ple, total employment in a metropolitan area equals 1,000,000 and base employment or employment in classifications with a location quotient >1.0 totals 400,000, supporting employment would be 600,000. In this case, the total-employment to basic-employment multiplier would be 1,000,000 ÷ 400,000, or 2.5. Therefore, if a forecast called for an increase of 40,000 jobs in all basic employment categories, it may be the case that total employment would increase by 40,000 × 2.5, or 100,000, of which 60,000 would be sup- porting employment. Obviously, a real estate investor would like to know how many of the 100,000 expected new jobs would likely result in the construction of new houses, apartments, and office and warehouse space to provide for these workers. An exami- nation of population data would shed light on the expected age distribution and sizes of households. It should be stressed that there can be instances where employment in base industries in a metropolitan area is expected to decline. In these instances, total employment rates would be expected to decline by an amount greater than declines in base industry employment.

This method of analysis is not without its shortcomings. Furthermore, this analysis usu- ally provides a snapshot of employment at a point in time. In order to better understand employment relationships, economic base analysis should be done at various points in time so as to identify shifts and trends in an area’s employment base.

Housing Supply: An Overview

When trying to complete the analysis of housing as an investment, we must also consider the supply side of the market. In general, the supply of housing is determined by the rela- tive cost of land, labor, and capital (materials). Two barometers of housing activity that are monitored by investors are housing starts and sales of existing homes. Two observations should be made concerning these data. One is that the supply of new single-family housing and sales volumes for existing units are price elastic and highly volatile. The other is that both of the latter relationships are highly influenced by interest rates. Although we include interest rates in our discussion of housing supply, it is also very important on the demand side of the market, as it affects the financing cost that a household must pay from incomes earned primarily from employment.

Other influences on supply costs on a more local level include the existence of restric- tions such as zoning, building codes, environmental factors, and the physical differences in land terrain and how these vary between locations. These latter influences have a sig- nificant impact on costs that builders incur when producing housing. Many of these influ- ences are thought to result in a restriction on supply (new construction), which results in higher house prices. Some MSAs (such as San Francisco, Boston, and others) restrict development density by requiring adherence to very rigid building codes, requiring open space, assessing impact fees, and so on, all of which affect housing availability. Over the long run, this may cause house price appreciation and construction costs to be greater than in other metro areas. Any investor in the housing market must assess these supply-side fac- tors when making housing choices. See Concept Box 7.2, which describes very important data sources that may be used to assess the supply of new housing units as well as sales and inventory.

Final PDF to printer

199

bru19684_ch07_185-221.indd 199 11/01/17 04:25 PM

Submarkets: Neighborhoods/Municipalities While the above discussion is important when trying to differentiate among MSAs, a number of other issues are important when trying to select housing among submarkets /municipalities within MSAs. A list of important considerations that should be analyzed when making such a selection is contained in Exhibit 7–5. Many of these attributes include services and goods that must also be acquired when the housing investment is made. Many of these attributes are referred to as public goods that are acquired along with housing. These factors have been studied over the years and deemed to be important in driving house price appreciation in different submarkets.

Capitalization Effects: Price Premiums Many of the attributes in Exhibit 7–5 have been deemed important in explaining differ- ences in house prices among neighborhoods and jurisdictions. However, it is difficult to generalize the extent (dollar amount) to which each factor affects price. There is another concept in the urban economics literature, called the capitalization effect, that relates to the quality of the public services that individuals receive relative to the taxes (usually property tax and fees) that are paid for these services when they choose to purchase hous- ing in a particular neighborhood or municipality. To the extent that residents perceive that services received have a value greater than the taxes and fees paid for them, net benefits may exist. These net benefits are reflected or capitalized in house prices (land prices) because households are willing to pay for these net benefits which can only be obtained by purchasing housing in the location where the benefits are present. For example, if

1. National Association of Home Builders (NAHB): www.nahb.org

A. A subscription-based data source that provides data for: ∙ Housing starts (single family and multifamily) ∙ New home sales ∙ New home sales price (average, median)

2. U.S. Department of Commerce/U.S. Census Bureau: www.census.gov

A. Housing statistics published monthly, including:

∙ Housing construction permits ∙ Construction starts ∙ Housing units under construction ∙ Housing units completed

B. Quarterly survey of housing vacancies

∙ 75 Metro areas Comment: Many analysts make estimates of current housing supply conditions in local hous- ing markets from data on (1) construction permits approved, (2) the number of permits actu- ally started, (3) units under construction, and (4) completions.

After the timing in all stages of production and new home sales has been taken into account, the inventory of houses available for sale can be estimated. From these data, judg- ments can be made as to whether or not an excess supply condition may exist, how long any excess supply may persist, and implications for future house prices.

Single-Family Housing Supply: Data Sources Concept Box 7.2

Final PDF to printer

200 Part 3 Residential Housing

bru19684_ch07_185-221.indd 200 11/01/17 04:25 PM

two otherwise identical houses are located in two different neighborhoods or municipali- ties and one sells for a higher price, the question is, “Which combination of the above influences caused the buyer to pay a higher price?” Was it the net benefits from educa- tional quality or some other public good? When housing is viewed this way, it becomes clear that many public good consumption choices are being made simultaneously with the housing decision.

Finally, there has also been discussion regarding the optimal size of cities or of jurisdictions. This concept has to do with the relationship between the size (population and geographic area) of separate political jurisdictions (townships, cities, etc.) and how cost-effectively they provide services such as education, police protection, and the like. Some argue that there may be cost savings in providing public services as cities (politi- cally defined) get larger and annex surrounding areas. However, there may be a limit on size (in terms of both area and/or population) such that when this size is exceeded, (1) costs begin to rise relative to the quality of services delivered or (2) the quality of ser- vices begins to deteriorate. Thus, communities in which there exists a balance between size, efficiency, and scale of operations may be producing public services very cost- effectively. This efficiency may be reflected in lower property taxes for the flow of ser- vices being produced, which may, in turn, be capitalized in the prices of properties in such jurisdictions.

Description Measurements/Indicators 1. Quality of school districts SAT scores, percentage of HS graduates that go to college, library facilities 2. Crime rates/police/fire Data relative to various crime categories per 1000 residents, response times 3. Parks/recreation Relative to size of population, quality of programs 4. Housing market indicators Number of listings, time on market prior to sale, percentage of asking price

achieved by submarket 5. Quality of utilities Cost and source of water, electric, gas, sewer. Any assessments related to each 6. Size of submarket Population, percentage of nearby land area available for future development,

and zoning related to such areas 7. Health care facilities Number of physicians and beds per thousand residents 8. Building codes/zoning Restrictions, regulation of construction quality, minimum lot sizes 9. Insurance rates Premiums may vary based on response times by location

10. Noise levels Proximity to, and decibel levels of (airports, freeways, etc.) 11. Environmental Open spaces, pollution, water, air, and so on 12. Transportation/access Distance and travel time to major employment centers, airports

EXHIBIT 7–5 Public Goods and Other Attributes Affecting House Prices in Different Submarkets and Neighborhoods within Metropolitan Areas

The Federal Home Loan Mortgage Corporation (Freddie Mac) and the Federal Housing Finance Agency pub- lish house price indexes. These are available at www .freddiemac.com/finance/cmhpi and www.fhfa.gov /default.aspx?page=14, respectively. These indexes provide a measure of typical price inflation for houses within the United States. Values are calculated nationally, for each state, and for major MSAs.

Using one of these price indexes, select one of the MSAs and analyze the growth rate in home prices for the MSA versus the rest of the state and for the nation over the past five years. Are homes in the MSA grow- ing at a slower or faster rate than the rest of the state and nation? If you were doing a rent-versus-own analysis as discussed in this chapter, what growth rate would you assume for home prices in the selected MSA?

Web App

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 201

bru19684_ch07_185-221.indd 201 11/01/17 04:25 PM

Pricing Property in Specific Submarkets/Locations At some point in the acquisition process, after the prospective homebuyers have evalu- ated the regional drivers affecting house price appreciation, they must estimate whether a specific property in a specific location that is being considered for purchase is com- petitively priced. Prospective buyers want to be sure that they are not “overpaying” for a property. Also, lenders want assurance concerning the price of the property because it will be serving as security for repayment for the mortgage debt and, over time, it must remain sufficiently high to repay the outstanding loan balance in the event of default. While prospective buyer-investors may estimate a value for a property, lenders will usu- ally require that an estimate of value be made by an independent fee appraiser, which is someone who specializes in performing appraisals for a fee. An appraiser must be unre- lated to the parties to the transaction and must have no vested or financial interest in the property being appraised.

The objective of the appraisal is to establish a market value, usually meaning the most probable price that would be paid for a property under competitive market condi- tions. The reader should understand that this notion of value may be different from the price that an individual buyer may be willing to pay for the property. For example, one person’s individual preference for attributes of a property being acquired may be such that she may be willing to pay a significantly higher price for a property than the majority of potential buyers in the market. Because the lender is more concerned about what the market price would be in the event of default, the appraiser must make an independent estimate of the most probable price that a property would bring if it were sold under competitive market conditions, where individuals other than the prospective buyer would be bidding. In a sense, the appraiser’s estimate of value will help the lender determine whether the price being offered by the borrower-applicant is an “outlier,” or a price that is significantly different from what would be paid by most buyers in the market for similar properties. (Although there are some differences in appraisal requirements used in con- ventional, FHA, and VA mortgage underwriting, the general approaches to estimating value are similar.)

To produce an estimate of value, the appraiser generally begins with an assessment of national, regional, and local economic conditions, stressing income, population, employ- ment, and interest rate trends, which, as discussed above, form the determinants of demand for the property in question. Supply is examined by assessing the relative cost of land and the factors of production (wages, capital). Current market equilibrium conditions in the housing market are then considered by examining the current availability (inventory) of housing units, absorption rates, rental vacancies, and trends in rents to gauge the likeli- hood of any short-run price movement that may affect the estimate of value. Finally, the appraiser must identify the area-relevant location, or submarket, in which the property being valued is viewed as being competitive or substitutable with other properties. This submarket also may be thought of as a neighborhood because of the proximity of retail, educational, religious, and other facilities which may appeal to households with similar income, tastes, and preferences. This is important because, as will be seen, price and other data will be obtained on properties that have sold recently in this area. Submarket selec- tion is very important as the appraiser seeks to eliminate any differences that could be attributable to school districts, police and fire services, libraries, and so on in the analysis. These data will serve as a basis for estimating the price for which the property in question is likely to sell.

When estimating the value for the specific property (usually referred to as the “subject property”), the appraiser usually relies on three approaches: the market, cost, and income capitalization approaches. In residential appraisals, only two approaches, cost and market, are usually thought to be reliable. The market, or sales comparison, approach involves

Final PDF to printer

202 Part 3 Residential Housing

bru19684_ch07_185-221.indd 202 11/01/17 04:25 PM

selecting properties in the same submarket or in close proximity to the subject property. Comparables are chosen from those properties that have sold most recently and where adjustments for dissimilarities (such as size of dwelling, lot, amenities) can be kept at a minimum. This approach is based on the principle that at the time of the appraisal, buyers should be willing to pay the same price for otherwise identical properties. By adjusting the sale price of comparable properties for dissimilarities, the appraiser is trying to make prop- erties that have recently sold very comparable to the subject property. The adjusted price of the comparables can then be used to price the subject.

The cost approach involves estimating the cost to reproduce the structure (less depre- ciation), and then adding the value of the land (site) to it in arriving at a value. The rationale for this approach is that no knowledgeable buyer would pay more for a property than the cost at which it can be reproduced. Finally, the income approach is a process, whereby comparable residences that are currently renting for income are used to estimate the value of the subject. This process usually involves establishing a ratio between the selling price and income of such recently sold comparables. The rent is then adjusted for dissimilarities with the subject. A comparable rent for the subject is then established and the ratio of price to rent for comparables is used to convert the adjusted rent into a value for the subject. This latter approach is not frequently used when pricing owner-occupied residential properties because it is generally the least reliable method. This is because there are usually few com- parable residences that are rented.

Based on these approaches, the appraiser makes a final estimate of value and reports it to the prospective homebuyer and the lender. The lender will review the report and, if in agree- ment with the approach used by the appraiser, will use the lower of appraised value or the market price in establishing the maximum loan amount. For a more detailed examination of each of these approaches, we now consider a problem example. In the example, we use the uniform appraisal form (see Exhibit 7–6, panels A and B) required by the Federal National Mortgage Association and Federal Home Loan Mortgage Corporation. Today most residen- tial mortgages utilize this form because it is a part of the required documentation any lender would need if it wished to sell a loan to either of these entities after origination.4

The Sales Comparison Approach As previously indicated, when using this method, the appraiser estimates the value of a property by comparing the selling prices of properties similar to, and near, the property being appraised. Because no two properties are exactly alike, the appraiser adjusts the values of similar properties (called comparable properties) for dissimilarities. These differences are isolated, and adjustments are made by the appraiser, who, using her judg- ment and knowledge of current market conditions, establishes what the market value is for each major attribute of a comparable that is different from the subject property. Because the value of the subject property is unknown, the price of the comparables will be adjusted until all differences have been taken into account. If this process is carried out correctly, the adjusted value of the comparable properties may then be used to approximate the price of the subject property. When selecting the comparables, the appraiser must be careful to establish that the sales of the comparable properties were arm’s-length transactions between the buyer and seller. For instance, if a seller was under duress, as in a foreclosure sit uation, or if a sale was between relatives, such a sale would not be desirable for use as a

4 For more detailed information see Underwriting Guidelines, Home Mortgages, Federal Home Loan Mortgage Corporation. The sale of mortgages to institutions in the secondary mortgage market will be covered in a later chapter. While all residential appraisals are made using the three approaches to value discussed above, additional specifications concerning condition and construction quality of the dwelling being appraised are sometimes included in FHA and VA appraisals. While such specifications are too numerous to be considered here, the following sources provide additional information: for an overview of FHA appraisal policies, see HUD Handbook 4150.1; for VA policies, see VA Bulletins and Benefits Circulars.

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 203

bru19684_ch07_185-221.indd 203 11/01/17 04:25 PM

EXHIBIT 7–6 (Panel A) Property Description

comparable because the buyer may not have paid a fair market price for the property. Once the appraiser has determined that all comparable sales were arm’s-length transactions, the appraiser’s process of adjusting the comparable sales can begin.

To illustrate how the appraiser will adjust the comparable sales for any differences between the subject property and the comparable properties, Exhibit 7–6 contains a prop- erty description in panel A and an example of the three approaches to value used in the

Final PDF to printer

204 Part 3 Residential Housing

bru19684_ch07_185-221.indd 204 11/01/17 04:25 PM

appraisal process in panel B. Note that panel A contains the identification of the property and a general description of the property. Section II of panel B provides an example of the sales comparison approach to value. Some of the items that the appraiser will have to adjust the comparable properties for are: (1) time since the comparable has been sold, (2) location, (3) view, (4) design appeal, (5) quality of construction, (6) age of the property, (7) condition,

EXHIBIT 7–6 (Panel B) Property Description

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 205

bru19684_ch07_185-221.indd 205 11/01/17 04:25 PM

(8) size of rooms, (9) quality of interior finish, (10) functional utility, (11) type and condi- tion of major systems such as central heat and air, and (12) sale or financing concessions.

When thinking about how comparable a property is to the subject property being val- ued, a general rule can be followed.  This rule is: the more adjustments that have to be made to a potential comparable in order to make it more like the subject property, the less comparable it is likely to be.  In other words, if many adjustments in value must be made to a property, it is less likely to be truly comparable to the subject and the likelihood of error in pricing increases.   When selecting properties as comparables, the number of adjust- ments that must be made should be minimized.

When making these adjustments, the appraiser adds to, or subtracts from, the value of the comparable properties to reflect the differences in market value between the comparable and the subject property that are caused by different attributes. If the subject property is superior to the comparable property with regard to a particular attribute, then the appraiser will add to the value of the comparable property. If the subject property has attributes that are inferior to the comparable property, then the appraiser will subtract from the value of the comparable property. Recall that the value of the subject is unknown; hence, adjustments must be made to the comparable properties. After all adjustments have been made to the comparables, the adjusted values of the comparables should be approximately equal to the value of the subject.

The amount that the appraiser adds to, or subtracts from, the price of a comparable prop- erty is an estimate of the market value of attributes that are different when comparing the sub- ject with comparable property. For example, in dealing with differences in the site, in panel B (middle) we see that comparables 1 and 2 are both “inferior” to the subject in the sense that the subject is a corner location and the comparables are not. Comparable 3 is also on a corner lot so no adjustment is made because this attribute is considered to be the same as the subject. The appraiser judges that such a difference is worth $1,950 in additional market value for the subject, and hence increases the prices of the comparables by $1,950. On the other hand, we note that comparable 2 has a two-car garage, whereas the subject has only a one-car garage. In this case, the price of the comparable 2 is adjusted down by the difference in the value of a two-car versus a one-car garage ($4,000). Again, the idea is to adjust the comparables until all positive and negative characteristics are priced and added to or subtracted from the compara- bles, leaving a residual value (after adjustments) that should be approximately equal in price to the bundle of characteristics contained in the subject property. The residual values of all comparables, after adjustments, should approach the value of the subject, which is unknown.

How does the appraiser estimate the value of these characteristics? Estimating is done on the basis of experience, judgment, and knowledge of how individual buyers and sellers tend to price these attributes in various neighborhoods, given the site and other property charac- teristics. In other words, the appraiser must be able to identify and defend the estimated increase or decrease in the total price of a property, given the addition or removal of one or more characteristics (garage, bedroom, bath, etc.). This may seem to be a difficult task; how- ever, in many housing markets hundreds of properties are sold each week and the appraiser generally has access to these data. A process of comparison and continuous updating of information makes the estimation possible. It should be stressed that under the sales com- parison approach to value, adjustments are not based on the cost of constructing improve- ments. All adjustments in value between the property being appraised and comparables must be made on the basis of how the appraiser believes the market value will be affected by the presence or absence of such attributes. This is because the market may not value attributes the same way that an individual may. For example, the cost of adding a swimming pool to a property in an area of small, older, lower-priced homes may not be recovered in the market price when the property is sold, even though the current owner may believe that the value of this addition is at least equal to its cost. In this case, the addition to market value may not be equal to the cost of constructing the pool because the appraiser may judge that buyers

Final PDF to printer

206 Part 3 Residential Housing

bru19684_ch07_185-221.indd 206 11/01/17 04:25 PM

composing the market for the property are not willing to pay as much for such an improve- ment as the current owner. Hence, the swimming pool may be referred to as an overimprovement to the property, and its full cost may not be reflected in the sale price.5

To obtain the final estimate of value under the sales comparison approach, the appraiser gives a qualitative weight to the residual price for each comparable. The weight assigned to each price depends on how many adjustments were made to each comparable. If many adjustments were made to a comparable, it would be given less weight, and vice versa. (Note that Comp.1 had five adjustments, Comp. 2 had six adjustments and Comp.3 had ten adjustments.  However, Comp. 2 had the lowest dollar value adjustment.) The appraiser then assesses the final estimates for each comparable in relation to the qualitative weights (see the comments at the bottom of Panel B, Exhibit 7–6) given to each, and arrives at a final estimate of value. Note that it is not an average of the values for the three comparables. Summarizing from the above:

5 Overimprovements occur when individuals make improvements that they may prefer and/or believe will add value to the property. However, buyers in the market may not agree and will not pay for the full cost of the improvement. Similarly, a homeowner can also make an underimprovement, for example, if too small a house is built on a large site. In this case, individuals may not be willing to pay as much for the property as they would have if the relationship between the site and the improvement had been in conformity with other properties in the market area. Many textbooks are available on appraising if you want to pursue the topic (see the Appraisal Institute for sources).

Summary Comp. 1 Comp. 2 Comp. 3

Sales price $65,000 $73,500 $67,500 Net adjustments +10,200   +3,350   +8,900 Adjusted values of comps:    75,200   76,850    76,400

Based on the various adjustments to comparables and the appraiser’s weighting of these estimates, a value of $76,850 ($77,000 rounded), is assigned to the property being appraised under the sales comparison approach.

An additional concern of appraisers when using the sales comparison approach to value is the possibility that a comparable sale price may contain financing benefits paid for by the seller of a property. The effects of seller financing may be present when the seller of a comparable is attempting to help the buyer qualify for a loan and has paid points or dis- count fees for the buyer, or has taken back a second mortgage at a below-market rate of interest, which usually reduces the borrower-buyer’s monthly payments and cost of financ- ing the property.6 Sellers often recover such financing costs by charging a higher price for the property. If this property is used later by an appraiser as a comparable to estimate the value of another property, the use of its price may be inappropriate. This is a difficult situ- ation for appraisers because unless they know the conditions of a property’s sale, it will not always be clear whether the seller of a property has paid some of the buyer’s financing costs. During times when interest rates are rising and buyers find it difficult to qualify, seller-paid financing is common. During these times, appraisers usually verify that a com- parable transaction does not include seller financing by speaking directly with one of the parties to the transaction or the settlement agent before using the comparable in the appraisal process. If seller financing has been used in the transaction, the appraiser must reflect this in his estimate of value by estimating the cost of the seller financing and

6 “Seller financing” occurs periodically in residential transactions. This problem is more prevalent in periods of high interest rates, when buyers have a difficult time qualifying for a loan. In these situations, sellers may finance all or part of the purchase at below-market rates of interest or contribute in some way to the buyer’s cost of financing. Appraisers must be aware of such a possibility and make adjustments in their estimate of value.

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 207

bru19684_ch07_185-221.indd 207 11/01/17 04:25 PM

subtracting this amount from the comparable value.7 In the example shown in Exhibit 7–6, panel B, we see that no seller financing was present in any of the comparable sales.

The sales comparison approach gives the most reliable indication of value when there are a number of current sales of highly comparable properties and information about the circumstances surrounding the transaction is easy to obtain. When these conditions are in effect, appraisers prefer the sales comparison approach.

The Cost Approach When using the cost approach, the appraiser establishes a value for the land on which the improvement is located, and then determines the cost of reproducing the improvement and adds the two. After adding the cost of the improvement and land value, the appraiser deducts an amount for any depreciation (if appropriate) that improvements have suffered since they were constructed. If the improvement has just been completed, the latter adjust- ment is usually unnecessary. This procedure is illustrated at the top of Exhibit 7–6, panel B.

In arriving at the estimate of land value, a procedure similar to that followed in the sales comparison approach is used. Comparable sites that have been recently sold are selected, and adjustments are made for differences in location, size, shape, and topography. In estimating the improvement cost, the appraiser will usually consult cost manuals for material, labor, and profit (overhead) as well as verify with local construction companies the costs associated with constructing improvements with specific physical and qualitative dimensions. Based on these sources, estimates of construction costs per square foot are made for living space, base- ments, garages, and second floors. Individual estimates are then made for fixtures (kitchen, bath, etc.), landscaping, and additional improvements (pool, porches, etc.).

In the event the improvement is not newly constructed, there are three types of deprecia- tion that the appraiser may choose to deduct from the cost estimate just described. The first is depreciation in the property’s value resulting from normal wear and is referred to as physical depreciation. Examples of physical depreciation include curable items, such as worn carpet- ing or walls needing paint. Incurable items, which include items such as foundation settling, may detract from a property’s appearance but do not necessarily affect the usefulness of the structure. The second is depreciation resulting from internal property characteristics that make the property less livable or marketable than it was when first constructed. This is referred to as functional obsolescence. Examples of incurable functional obsolescence may include excessive amounts of hallway space. Curable obsolescence may include replace- ment of lighting fixtures. The third type of depreciation the appraiser will consider is called external obsolescence. It is caused by characteristics external to the property, such as chang- ing land uses in a neighborhood that cause a structure to become obsolete before the actual building wears out. Examples of external factors that cause economic depreciation to occur include pollution, shifting land uses, or changing legal restrictions on land use.

The older a property becomes, the more difficult it is for the appraiser to estimate the amount of depreciation that should be used in the appraisal process. In the example shown in Exhibit 7–6, panel B, we see that the appraiser has estimated that for the subject prop- erty (which is 10 years old), physical depreciation amounts to $13,500, economic depreci- ation is $7,500, and no functional obsolescence was apparent. Based on the cost approach to value, we see that the appraiser assigns a value of $77,431 to the subject property.

The cost approach to value usually provides the most reliable estimate of value when comparable properties are newly constructed and require very few adjustments for depre- ciation. Appraisers also consider the cost approach when determining value if only a few transactions involving comparable properties exist and the sales comparison approach to value is difficult to use.

7 This will be analyzed in detail in the next chapter.

Final PDF to printer

208 Part 3 Residential Housing

bru19684_ch07_185-221.indd 208 11/01/17 04:25 PM

The Income Approach The income approach, a third appraisal method, establishes the market value of property by determining how much an investor is willing to pay for the income stream that a property produces. Using this method, the appraiser attempts to establish the relationship between a property’s sale price and the monthly income stream it would produce if rented. The appraiser typically uses rents and prices from recent sales of rental properties that are simi- lar to the subject property and determines the ratio of sale price to monthly rental income. This ratio is referred to as the gross rent multiplier. The value of the subject property would then be estimated by judging what the subject property should rent for (again by looking at comparable rental units and adjusting for dissimilarities), and then multiplying this estimate by the ratio established from comparable sales.

In our example we see in the lower portion of panel B in Exhibit 7–6 that the appraiser has estimated that, if rented, the subject would bring $650 per month. Given that com- parable properties have recently sold for 116 times their monthly rents, it is reasonable that the same relationship would also hold for the subject. Hence, a value of $75,400, or $650 × 116, is arrived at by using the income approach.

Typically the income approach is difficult to use because sales of very comparable single-family rental properties are rare in an area. Consequently, appraisers tend to rely on the sales comparison and cost approaches when establishing value. However, it should be stressed that for some properties, such as condominiums, where many units are frequently rented, the income approach may provide a reliable estimate of value.

Final Estimate of Value The appraiser must reconcile the different estimates of value provided by the sales compari- son, income, and cost approaches when making a final estimate of value. This is accomplished by using a qualitative weighting method, in much the same way as in the sales comparison approach. The appraiser assigns subjective weights to each of the three values based on the reliability of the data and the number of adjustments that had to be made in each technique. More weight would be given to the method requiring fewer adjustments where data are verifi- able, current, and complete. In our example, we see that the final estimate of value is $77,000, which, as the appraiser points out, is closest to the sales comparison and cost approaches.

Property Appraisal and Actual Sale Price In our example, the sale price of a property agreed on between a buyer and seller does not exactly correspond to the appraised value. For example, a buyer and a seller agreed on a price of $76,700 for the property (see panel A) and the appraised value was $77,000. When considering the value of a property when making loans, lenders will generally use $76,700, or the lower of sale price or appraised value, as the value on which the loan will be based, unless there is convincing evidence to change it.

Property Values over Time A cardinal rule followed by lenders is that loan security, which is dependent on the value of a mortgaged property, should never fall below the outstanding loan balance at any time during the life of the mortgage. In other words, the lender wants to be assured that the market value of the property will always be higher than the loan balance in the event of default by the borrower.

An additional consideration for the lender when considering the relationship of the mortgage balance and property value over time will be the potential effect of any increases in the mortgage balance relative to property value. This may present problems in the case of mortgage programs in which the loan balance may, or will, increase after the time of loan origination. (Recall the discussion in Chapters 4 and 5 dealing with the possible effects of negative amortization.)

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 209

bru19684_ch07_185-221.indd 209 11/01/17 04:25 PM

Investing in “Distressed Properties”

The term distressed is used to describe various events or circumstances that usually result in the sale of properties that otherwise might not occur. Distressed properties may present opportunities for investors to acquire properties at below current market prices. However, these discounts usually exist for a reason; otherwise, owners would simply sell their properties at current market prices as the properties become distressed. As we will discuss, there are many reasons why properties become distressed and why owners may be willing to sell them for a discount. In such instances, investors usually acquire proper- ties and provide an infusion of cash and hope to eliminate problems that may range from structural damage to legal issues affecting the title to properties. By remedying these prob- lems, investors expect that the property value will increase enough to provide them with a satisfactory investment return.

Some of the personal financial and/or legal situations affecting the owner that may explain why properties become distressed are listed below. One or more of these factors may be occurring simultaneously:

Borrower inability to make mortgage payments. Market value of the property below the mortgage balance. Delinquent property taxes/property tax liens. Internal Revenue Service tax liens. Civil judgments/bankruptcy/divorce. Mechanics and/or construction loan liens. Personal debts. Estate settlements. One very common reason why a distressed property becomes available is the borrow-

er’s inability to make mortgage payments. In this case, the borrower-owner of the property may not yet be formally in default, as the lender may be providing the borrower with a grace period on the loan, hoping that foreclosure proceedings can be averted.8 However, if the borrower cannot “cure” the problem, it is possible that the lender may acquire title to the property directly from the owner (usually referred to as “deed in lieu of foreclosure”). By using this process, both parties may save time and foreclosure costs and avert an auc- tion. However, if the lender and the borrower cannot agree on a deed transfer, the lender may have to foreclose. In these cases, the property may have to be sold at auction.

Another reason for default occurs in cases where property values fall below the out- standing loan balance. When this happens, properties are said to be “underwater” or “upside down.” Situations like this can come about because owners may have overpaid for a property or overimproved a property relative to other comparable properties. Should property owners have difficulty making monthly loan payments on such an “underpriced” property, they may default.

Deterioration in local economic conditions, such as unemployment because of layoffs, plant closings, and the like, may lead to an increase in the number of distressed properties available for sale. Increases in unemployment may reduce household incomes and nega- tively affect the demand for housing. Such a market downturn may cause an extraordinary number of properties to become distressed and available for purchase.

There are also a number of events, usually unanticipated by homeowners, that may result in a distressed property situation. These events may not necessarily be related to the 8 If the borrower’s situation is believed to be temporary, a lender may also be willing to consider restructuring the terms of the loan. Such a loan restructuring is referred to as a workout.

Final PDF to printer

210 Part 3 Residential Housing

bru19684_ch07_185-221.indd 210 11/01/17 04:25 PM

condition of the property and could include liens because of unpaid income taxes or prop- erty taxes, judgments because of civil actions stemming from lawsuits or business failures, bankruptcy, divorce, default on personal loans and/or business loans, or the need to settle an estate. Property owners may be seeking a financial solution to these unrelated financial or legal problems and may be considering the sale of properties to raise funds.

In addition to the causes listed above, it should be stressed that real estate is not like financial assets such as stocks and bonds, many of which have very active and liquid markets where they can be traded. Real estate requires a considerably longer period of time to buy and sell. Trading residential properties with the attendant requirements to finance and close may require at least 60 to 90 days under normal circumstances. In cases involving distressed properties, it may take even longer. Furthermore, in cases where the current owner may have overpaid for a property, because of aggressive lending prac- tices or poor estimates of price appreciation, buyers of distressed properties may have to carry properties until “repricing” occurs in a market environment that is changing. In these cases, investors are providing financing and taking “repricing” risk until the market stabilizes.

Financial Framework for Analyzing Distressed Properties When analyzing an investment in distressed properties, investors usually consider a financial framework as shown in Exhibit 7–7. Note that items listed in Exhibit 7–7 are classified into three phases: (A) acquisition, (B) holding period, and (C) disposition. For the investment to be profitable (D), net cash inflow from the sale phase (C) must exceed costs expended in phases (A) and (B). When the exhibit is reviewed, a number of factors must be analyzed. Perhaps, the most important considerations have to do with thinking about the following general questions: (1) Why does the so-called distressed property situation exist? (2) Why cannot the current property owners remedy the things causing the problem and sell or rent the property themselves? (3) What services and investment will an investor have to make to restore the property value and justify its acquisition?

Acquisition Phase Sources of Information for Identifying Distressed Properties Banks and lenders maintain REO (real estate owned) lists that are usually made avail- able upon request. These lists contain information on properties that lenders have acquired by deed in lieu of foreclosure or through foreclosure and auction. Because lenders are not in the business of investing and managing real estate, they are generally interested in

A. Acquisition Phase Acquisition costs: Purchase price Market and legal research costs Inspection costs Elimination of liens Other                  Total acquisition cost

B. Holding Period Phase Interim costs: Renovation costs Insurance, property taxes, and so on Interest on investor financing Other                 Total costs during holding period

C. Provision Phase Expected sale price Less: Selling expenses Net cash from sale

D. Profitability C − (A + B)

EXHIBIT 7–7 Summary of Financial Considerations When Investing in “Distressed Properties”

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 211

bru19684_ch07_185-221.indd 211 11/01/17 04:25 PM

selling such properties as soon as possible. REO lists also are maintained by the FHA, VA, and HUD. Properties are usually acquired by these agencies when a foreclosure occurs in conjunction with one of the FHA insurance, VA guarantee, and/or HUD affordable hous- ing programs. These properties are usually advertised for sale or they may be auctioned to the public.

Many individual property owners advertise their desire to sell properties because of financial difficulty. One reason why this is done is so that they may try and avoid default and preserve their credit standing. The latter may be important to these individuals at some future time, if they re-enter the market to buy a property. At that time, they may have to apply for mortgage financing and will have to supply lenders with a credit history. Other sources of information include public announcements, by county property tax authorities, regarding properties that are being sold for delinquent taxes. Other auctions are announced by the Internal Revenue Service, which obtains court orders to auction properties that have been seized to satisfy tax liens.

Legal Research A search of a property’s title history is perhaps one of the most important activities that will require an expenditure by the investor. It often must occur prior to the acquisition of a property. This is very important because if the investor plans to eventually sell a distressed property, the next owner may require a general warranty deed to obtain title insurance and financing. Therefore, any legal issues must be known by investors prior to acquisition in order to estimate the cost of extinguishing liens and other factors affecting title. It should be pointed out that in some situations, when purchasing distressed properties, investors do not always receive a general warranty deed. For example, if an investor is purchasing a foreclosed property from a lender, the lender may be willing to provide the investor with only a “bar- gain and sale deed.” This means that the lender will provide the investor with a title “as is.” It is then up to the investor to decide if the title record is satisfactory. If the title record is not satisfactory, the investor may have to expend time and money to clear the title. In some other cases, lenders may be willing to give a “special warranty deed.” This means that the lender will warrant the title against liens and encumbrances that occurred only during the period when the lender held title. No warranty is made by the lender regarding any liens or title imperfections prior to that time. In summary, unless the lender provides the investor with a general warranty deed, the investor may have to expend funds and negotiate with all lienhold- ers and obtain releases, thereby clearing the title in order to sell the property at a later date.

The Auction Process The auction process is important to understand (1) because of possible delays between the time that foreclosure and sale occur and (2) because other bidders are likely to be present at auction. Because of possible delays, investors must make a judgment as to if, or when, the property will actually be sold before expending funds on extensive legal or market research. It is important to note that each state has its own auction process that investors should understand. Generally, the auction process in the United States can be described under three categories. For example, in states following the lien theory of mortgages, foreclosures generally require a civil action (lawsuit) against the borrower- owner who is in default. A court hearing is held and a judicial declaration must be made terminating the property owner’s equitable rights. This is followed by an order directing the sheriff to conduct an auction. In some cases, as a part of the civil action, delays may be requested by the borrower for many reasons. This may prolong the time from foreclo- sure to actual sale.

In states favoring the so-called title theory of mortgages, title is usually vested in the lender when the mortgage loan is made and reconveyed to the borrower when the loan

Final PDF to printer

212 Part 3 Residential Housing

bru19684_ch07_185-221.indd 212 11/01/17 04:25 PM

is repaid. In addition to having title, the lender is empowered to take certain steps in the event that the borrower defaults. These steps generally include providing the borrower notice of default and acceleration on the note, and that the sale of the property will occur to satisfy the debt. However, during this process, the borrower may bring an action to enjoin the lender from proceeding to sell the property. Actions taken by the borrower to prohibit and/or delay sale obviously affect the likelihood of a timely acquisition by inves- tors. In some states, the so-called modified lien theory of mortgages is followed. Under this system, when a loan is made, title is invested in an independent third party (trustee). The trustee receives a deed of trust containing instructions to be followed if the lender pro- vides notice to the trustee that a mortgagor is in default. In this event, the trustee usually notifies the borrower that the deficiency must be cured by a certain date or the trustee will proceed to auction the property. This process is different from the procedures described above in that it does not require a civil action or a court hearing. In order to delay this process, borrowers may take legal action and request that the court instruct the trustee to delay the property sale.

In summary, under all three systems, there may be opportunities for borrowers to bring legal action to delay the foreclosure-and-sale process. These range from claims that the lender and/or trustee did not give the borrower proper notice of default, challenges regarding contractual provisions in the note and/or the mortgage agreement, delays because of other actions pending against the borrower, bankruptcies, and so forth. In short, if the sale of the property at auction is delayed, the investor (1) may expend time and money on title research, (2) may have to wait even longer until the auction actually occurs, and (3) may not be a successful bidder when the auction occurs. These examples represent some of the costs and risks associated with the business of investing in dis- tressed properties.

Lenders at Auctions When properties are sold at auction, lenders holding notes and mortgages will bid for prop- erties. Lenders are usually allowed to bid an amount at least equal to the mortgage balance owed them without providing additional cash. If the amount owed to the lender is close to the current market value of a property, the lender may be the successful bidder and will add the property to its REO list. But if the market value of the property is greater than the loan balance, an investor may outbid the lender. In the latter event, the lender must be repaid in order for the lien to be extinguished.

In cases where the current property value is less than the amount owed, the lender may bid an amount equal to the property value and sue the borrower for the deficiency. In this case, the property becomes a part of the lender’s REO list and the lender will try to sell the property for as much as possible. In summary, as a part of the acquisition phase, inves- tors must do a considerable amount of legal and market research. They must also decide whether or not there will be delays before an auction actually occurs and whether or not they will be successful bidders. Finally, they also must determine the amount of time, effort, and cost that will need to be expended to “clear the title” to the property they are acquiring. Otherwise, they may expend a considerable amount of time and money and not make a successful acquisition of the property.

Other Issues—Equitable Rights Prior to bidding for properties at auction, investors must also identify the extent to which previous owners may have any equitable rights after an auction is completed. For example, in some states, statutory provisions are made for “equitable rights of redemption.” This generally means that even after auction occurs and a new investor acquires title to a prop- erty, it may be possible for the previous owner to reacquire title. Generally, this may be

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 213

bru19684_ch07_185-221.indd 213 11/01/17 04:25 PM

done if a previous owner pays all deficiencies plus any interest and penalties to the previ- ous lender and the investor who obtained a property at auction.

In some other cases, courts of equity may award borrowers in default such redemp- tion rights. Usually, such awards will be made based on the court’s analysis of the extent to which a borrower has accumulated equity in a property prior to default (e.g., borrower defaults in the 29th year and 11th month of a 30-year mortgage). Obviously, investors interested in distressed properties in these situations must consider the likeli- hood that borrowers will be able to cure past deficiencies and reacquire title to such properties.

Buying at Auctions Conducted by Public Entities When buying properties at auctions conducted by public agencies, investors should deter- mine the nature of the title that they may receive if they make a successful bid. In some states, for example, if investors obtain title at an auction resulting from delinquent property taxes, the investor may receive from the county what is referred to as a “tax deed.” These deeds may provide that if the previous property owner in arrears can cure the past-due taxes within a prescribed time period and pay the holder of the tax deed an additional amount of interest and/or penalties, they may reacquire title to the property. Even if the previous owner fails to cure the deficiency, the county tax authority may not provide the new inves- tor with a general warranty deed. It may be the responsibility of the holder of the tax deed to institute appropriate legal action in the state where the property is located to assure pos- session of legal and marketable title.

To reiterate, the quality of title is usually critical to the success of investing in a dis- tressed property. Typically, in order to successfully sell the property at a later time, the investor generally must eventually have a marketable title. That is, the investor must be able to convey a deed of sufficient quality so the next purchaser of the property is able to obtain mortgage financing from conventional financing sources. Since lenders usually insist that the borrower acquire title insurance and that the title record be free of liens, investors must decide if this requirement can be met during the acquisition phase, or prior to bidding at auction.

Market Research/Costs Expenditures on market research must also be made by investors prior to making an acqui- sition. The goal of the research is to determine the value of comparable properties that are likely to compete with the distressed property when it is ready for sale. This must also be done to establish the extent to which the distressed property must be improved or renovated in order to compete against other properties for sale and to set a sale price upon disposition. In cases where the value of a property has fallen below its original purchase price, investors must estimate whether prices are likely to fall further, or if and when prices are likely to recover. This research is also important because it will help to establish the offer that an investor must make at auction or when purchasing properties from indi- viduals or lenders.

Inspection Costs In addition to legal and market research, property inspections should be made at the begin- ning of the acquisition phase when developing a bid for a property. Items that are usually inspected include ∙ Land/building. ∙ Foundation. ∙ Drainage.

Final PDF to printer

214 Part 3 Residential Housing

bru19684_ch07_185-221.indd 214 11/01/17 04:25 PM

∙ Building quality and building code compliance. ∙ Environmental issues: lead paint, asbestos, and the like.

If problems are discovered, investors must estimate any outlays that must be made to rem- edy problems. These costs must be factored in during the acquisition phase and will affect the investment analysis made by the investor.

Holding Period Phase Depending on what is required to achieve their investment objective, investors generally make outlays for various items during the period of ownership, including

∙ Renovation costs. ∙ Interest or other financial carrying costs. ∙ Property taxes and insurance.

In many cases, investors will choose to finance their investment. Typical financing sources include

∙ Assumption of outstanding mortgage debt. ∙ Personal loan or credit lines. ∙ Personal equity/other equity sources. ∙ First or second mortgages on other real estate owned. ∙ Home equity credit line on other real estate owned.

In some cases, the existing lender who has acquired a distressed property at auction or through a deed in lieu of foreclosure may be willing to finance the sale of a property to an investor. This may occur if the lender wants to dispose of a property and/or if the lender believes that it may avert a loss by allowing an investor to renovate and market a property.

As noted above, investors also may borrow by using their personal credit or by using other real estate that they may own as security for a loan. Such loans may be obtained by refinancing properties that they may own or by obtaining loans secured by second liens. In some cases, if investors plan on continuously bidding for a number of properties, lend- ers may be willing to provide credit lines to investors to acquire properties and to finance necessary improvements. See Exhibit 7–8 for an example of an investment analysis of a foreclosed property.

ABC Bank has title to a 3,000-square-foot, three-bedroom, two-bath home situated on one- quarter acre of land. The bank acquired the property at auction for the loan balance owed by a previous owner and has added this property to its REO list. It has indicated that the asking price for the property is $200,000 and that it can convey a general warranty deed to the purchaser. GMI Sharpe Investors is considering the purchase of this property. An estimate of costs associated with the acquisition and expenses of owning the property for a period of one year is as follows:

Phase A. Acquisition fees: Legal counsel/research $  2,000 Inspection fee/report 500 Payoff of existing property tax lien      8,000 Total $10,500

EXHIBIT 7–8 Example: Investment Analysis of a Foreclosed Property

Final PDF to printer

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 215

bru19684_ch07_185-221.indd 215 11/01/17 04:25 PM

Phase B. Renovation costs: Carpet $  6,000 Dry wall repair/paint 1,000 Countertops/cabinets 3,000 Utilities during renovation 200 Roof repair 8,000 Plumbing/electric 3,000 Property taxes (1 year) and insurance 4,000 Interest ($200,000 personal loan @ 7%)   14,000 Total $39,200

Phase C. Sale phase: Broker commission (is) $  6,000 Total $  6,000

Question Assuming that GMI Sharpe acquires the property for $200,000, how much must the property sell for in order for Sharpe to achieve a 20 percent return (annual rate, compounded monthly) on its investment during this one-year period?

Cash Flow Analysis

Phase B: Phase A: Acquisition

Average Monthly Outflows

Phase C: EOY Sale

Purchase Price $ 200,000 $3,267 Sale Price: TBD Plus Acquisition fees 10,500 Less: Loan    200,000 Less: Selling expenses =  $6,000 Equity $   10,500 $3,267 Repayment of loan       = $200,000 Present value analysis:

PV

=

− 10,500

PMT

=

− 3,267

n = 12 months i =

20% ÷ 12

Solve for FV

=

?  (net cash needed in year of sale)

Solution/Interpretation

A sale price at the end of year 1 must be great enough to repay the $200,000 loan plus $6,000 in selling fees and have enough cash flow remaining to make the investment worthwhile. Solving for FV produces $55,808, which is the net cash flow after the loan repayment and selling fees ($206,000) that must be realized at the EOY1 in order to achieve a 20 percent return

This means that GMI Sharpe must be able to sell the property for at least $261,808 ($206,000 + $55,808) in order to repay the loan; pay all costs of acquisition, holding, renovation, and sale; and earn a 20 percent IRR (annual rate compounded monthly). The investor must conduct careful market research to determine whether any comparable properties have sold in this price range or when, if ever, properties are likely to sell in this price range

Pre-foreclosure Investments

In some situations, unanticipated events that affect the property owner but that are not directly related to the property or market conditions may result in properties becoming distressed. As indicated earlier, there are many events that may require a homeowner to obtain funds to repay business creditors.* In turn, this may cause a homeowner to sell a property to raise funds to satisfy debts. In some cases, it may be possible for an investor to contract to purchase a property, whereby the seller delivers title on a future date and the

EXHIBIT 7–8 (Concluded)

Final PDF to printer

216 Part 3 Residential Housing

bru19684_ch07_185-221.indd 216 11/01/17 04:25 PM

investor immediately conveys title to a new buyer. In the meantime, the seller retains title and keeps existing loans alive. In the interim, the investor implements a necessary strategy to sell the property and acts as a middleman, taking title only briefly immediately before the property is sold. For example, the owner of a distressed property and an investor may agree on a specific selling price (or “strike price”) and enter into an option contract to provide the investor title on or before a future date. This option may be exercised at the investor’s option anytime between the date of the contract and the expiration date. The seller agrees not to abandon the property and also agrees not to enter into any other contracts that would encumber title to the property. The investor hopes to find a buyer before the expiration date of the option and simultaneously take title and sell the property and give title to a new buyer immediately. The funds received by the investor from the new buyer at closing are used to purchase the property from the seller who agrees to repay the outstanding debt. Title is then transferred from the previous owner to the new owner with the investor obtaining title only briefly at the closing when transferring title to the new owner.

*In some states, the debtor’s homestead may be protected from bankruptcy judgments caused by business failures or personal debts. However, such homesteads are not usually protected if the borrower defaults on a mortgage loan secured by the homestead.

EXHIBIT 7–8 (Concluded)

A. OPTION CONTRACT WITH SIMULTANEOUS TITLE CLOSING Typical terms and conditions:

1. Investor contracts with seller for seller to deliver a deed at the option of investor at any time up to one year from the contract date.

2. Investor does research on real estate values and must be convinced that the distressed property can be resold at a favorable price. Investor determines the extent of liens. Investor may have to provide funds to clear title such as paying past-due property taxes prior to sale.

3. Investor may or may not agree to make monthly mortgage payments for seller during the option period. Investor usually obtains interim financing with a personal line of credit or home equity loan.

4. Seller agrees not to abandon the property, execute any contracts further encumbering the property, or make any physical modifications to the property in any way during the contract period.

5. When a new purchaser is identified by investor, investor exercises the option to buy the property. Seller then sells the property and delivers title to investor at the contract (strike price). Seller pays off mortgage debt with funds received from investor. Investor simulta- neously sells property and transfers title to third party.

Summary—The investor does not take title until a new buyer is found. This usually saves the investor closing costs and financing fees. The risk is that no buyer will be found during the option contract period. Unless the option contract is extended, the investor loses all cash flows expended on research, monthly payments, and so on. The seller benefits in that fore- closure is avoided, thereby preserving credit. Assuming that the market price that the investor receives from the new owner exceeds the option price, the investor would keep any differ- ence between the final sale price and option price as a return on investment. In the event that

Other Approaches to Investing in Distressed Properties Concept Box 7.3

Final PDF to printer

bru19684_ch07_185-221.indd 217 11/01/17 04:25 PM

Other Approaches to Investing Concept Box 7.3 in Distressed Properties (Continued)

the market value does not exceed the option price, the investor may elect not to exercise the option. However, as long as the market value exceeds the strike price on the expiration date, the investor may elect to exercise the option in order to minimize losses. Another reason for this option approach, as opposed to an outright purchase of the property by the investor, is to avoid transactions costs that may have to be paid twice during a short ownership period. Recall that the investor plans to have the property sold within six months. Therefore, taking title and incurring various closing costs during a short ownership period may significantly reduce the investor’s returns and make the required sale price higher and could make the transaction not feasible. The risk to the investor is the potential loss of all cash outlays during the acquisition and holding period should the property value upon sale not increase enough to recover these costs and achieve the desired return. A related question is this: Why does the homeowner need the investor? In many cases, homeowners may not have sufficient cash to make monthly payments, pay property taxes in arrears, clear up title problems, and so on. Furthermore, this homeowner remains in the property for six months and does not have to make payments on the mortgage, property taxes, or insurance. Finally, this homeowner may not want to default on the mortgage loan, thereby avoiding future bad credit issues. Additionally, other issues relating to employment, marital status, possible business failure, and so on, may have higher priority and preclude the homeowner from investing the time and effort needed to dispose of the real estate. There is another risk that must be considered by the investor in the event that the market value of the property exceeds the option price. In this case, it is imperative that the investor execute a very well-written option contract in order to avert any motivation by the seller to default on the option contract with the investor and attempt to sell the property independently.

B. CONTRACT FOR FUTURE DEED

In some cases an investor may purchase a property; however, in order to sell the property, the investor and a buyer may have to enter into a contract for a future deed. This situation devel- ops when a buyer would like to purchase the property, but cannot do so because of insufficient credit and has difficulty in obtaining financing. The investor may be willing to provide financ- ing, but does not want to convey title as yet in order to avoid legal and other costs should the buyer default on the loan. Both parties agree on a specific selling price (“strike price”) and enter into an option contract, whereby the investor agrees to deliver title to the new owner at a future date. This option may be exercised at the buyer’s option anytime between the date of the contract and the expiration date. The buyer agrees not to abandon the property and also agrees not to enter into any other contracts involving the property. The buyer also must make monthly rent payments, some, or none, of which may be credited toward the selling price

Typical term/conditions:

1. Investor purchases property and takes title. 2. Investor enters into a contract with a potential buyer to purchase the property at a speci-

fied price by a specific date. Investor agrees to deliver and close title if terms and condi- tions of contract are met.

3. Investor obtains financing and may pay property taxes and hazard insurance to avoid liens and to protect title to property during the contract period.

4. Potential buyer makes monthly payments (rent) to investor. Buyer attempts to accumulate additional equity and or repair any credit problems.

5. As a buyer eventually qualifies for financing and executes the purchase option, investor delivers title and receives strike price from buyer.*

*The effect of federal income taxes is not included in this analysis.

217

Final PDF to printer

218 Part 3 Residential Housing

bru19684_ch07_185-221.indd 218 11/01/17 04:25 PM

Disposition Phase—Exit Strategies The obvious strategy that can be used to complete an investment in distressed properties would be to sell the property upon completion of the holding period phase. However, if a sale cannot be achieved because of a change in market conditions or for other reasons, an investor could consider converting a distressed property into a rental property to earn income or, perhaps, using the property as a personal residence.

Conclusion Readers should now have a general understanding of the determinants of house prices and appraisal procedures used for residential mortgage lending. We have provided techniques for determining the appreciation rates in house prices and on equity, as well as federal income tax treatment for home- owners and comparisons with the cost of renting. We have also reviewed the three approaches used by appraisers to estimate the market value of residential properties. Various issues involving housing bubbles and investing in distressed properties have been discussed. Lenders and investors should be familiar with these concepts and with the assumptions made by each and their effects on value.

base industries, 196 capitalization effect, 199 capital gains exclusion, 192 comparable properties, 202 cost approach, 202 distressed properties, 209 driver industries, 196 economic base, 197 expected appreciation rate on

home equity (EAHE), 193

expected rate of appreciation in house prices (EAHP), 193

gross rent multiplier, 208 income approach, 202 loan-to-value ratio, 193 location quotient, 197 market value, 201 optimal size of cities, 200 overimprovement, 206

public goods, 199 REO (real estate owned)

list, 210 sales comparison, 201 seller financing, 206 submarket, 201 unrealized equity gain, 193 wealth effect, 194

Key Terms

Useful Websites

www.nahb.org—National Association of Home Builders. www.realtor.com—National Association of Realtors. www.freddiemac.com/finance/cmhpi—Freddie Mac’s Conventional Mortgage Home Price Index (FMHPI). www.bestplaces.net—Statistics, including crime rates, on places to live. https://data.ers.usda.gov—U.S. Department of Agriculture. This link includes median household income and unemployment data on every county in the United States. www.statetaxcentral.com/—Provides tax information for every state. www.fairmark.com—This website is a good resource for finding tax-related policies. It can help in doing real estate analysis from a tax-saving perspective. www.fhfa.gov—Federal Housing Finance Agency. www.census.gov—U.S. Census Bureau. Publishes housing statistics monthly. www.bls.gov—U.S. Bureau of Labor Statistics. Publishes employment data for the entire United States and by metropolitan areas. www.bea.gov—Bureau of Economic Analysis in U.S. Department of Commerce. Provides data on income, RGDP, and other economic aggregates. www.homeprice.standardandpoors.com—S&P/Case-Shiller® Home Price Index.

Final PDF to printer

bru19684_ch07_185-221.indd 219 11/01/17 04:25 PM

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 219

Questions 1. Why is the income approach to value often difficult to use on a single-family residential appraisal?

2. What are the differences between the cost and sales comparison approaches to appraising property?

3. What are the capital gains rules as applied to residential property owners? 4. List four important drivers of housing demand and price appreciation. 5. What are public goods? How may they be reflected in house prices? 6. When considering an investment in “distressed” properties, what are the two most important

areas of research that should be undertaken?

Problems 1. You are considering an option to purchase or rent a single residential property. You can rent it for $2,000 per month and the owner would be responsible for maintenance, property insurance, and property taxes. Alternatively, you can purchase this property for $200,000 and finance it with an 80 percent mortgage loan at 6 percent interest that will fully amortize over a 30-year period. The loan can be prepaid at any time with no penalty.

You have done research in the market area and found that (1) properties have historically appreciated at an annual rate of 3 percent per year, and rents on similar properties have also increased at 3 percent annually; (2) maintenance and insurance are currently $1,500.00 each per year and they have been increasing at a rate of 3 percent per year; (3) you are in a 26  percent marginal tax rate and plan to occupy the property as your principal residence for at least four years; (4) the capital gains exclusion would apply when you sell the property; (5) selling costs would be 7 percent in the year of sale; and (6) property taxes have generally been about 2  percent of property value each year.

Based on this information you must decide a. In order to earn a 10 percent IRR after taxes on your equity, should you buy the property or

rent it for a four-year period of ownership? b. What if your expected period of ownership was to change to five years?Would owning or

renting be better if you wanted to earn a10 percent percent IRR after taxes? c. Approximately, what level of rents would make you indifferent between owning and renting

for a four-year period? Assume that a 4.5 percent after-tax IRR would be the minimum you would need to earn on capital invested in the home.

2. You are considering the purchase of a property today for $300,000. You plan to finance it with an 80 percent loan. The appreciation rate on the property value is expected to be 4 percent annu- ally for the next three years.

a. Approximate the expected annual average rate of appreciation on home equity for the next three years.

b. What if you now think that a $300,000 purchase price may be somewhat high and that if you pay this price, the expected appreciation rates in your house price will be as follows: year 1=0%, year 2=2%, and year 3=3%. How will your answer to part (a) change?

3. You are trying to estimate the value of a property that you are interested in buying. The subject property is located at 322 Rock Creek Road in a new suburb of a large metropolitan area. The property is like many others in the area, with three bedrooms, two baths, a living room, a den, a large kitchen, and a two-car garage. The residence has about 1,800 square feet of air-conditioned space and is of traditional design. The property is located on an interior lot with no potential flooding problems. The quality of construction appears to be about average for the market area. The property being purchased was built within the past two years. Three properties have been chosen as comparables and they also were constructed within the past two years.

Final PDF to printer

bru19684_ch07_185-221.indd 220 11/01/17 04:25 PM

220 Part 3 Residential Housing

Comparable properties in the area have the following characteristics:

Comparable I Comparable II Comparable III

Address 123 Clay St. 301 Cherry Lane 119 Avenue X Sale price $85,000 $79,000 $75,000 Time of sale 6 months ago 7 months ago 13 months ago Design Modern Traditional Traditional Parking 2-car garage 2-car carport 1-car garage Location Corner lot Interior lot Interior lot Drainage Good Below average Good Bedrooms Four Three Two Baths Two Two Two Construction Average Average Below average

Inspection $      500 Title search 1,000 Renovation 13,000 Landscaping 800 Loan interest 12,800 Insurance 1,800 Property taxes 6,000 Selling expenses 8,000

You have come to some conclusions concerning what you believe the different attributes of the comparable properties are likely to be worth in the market area. Appreciation in house values in the area has been very low over the past eight months, and you think that any properties that have sold within that period would probably not require any adjustments for the time of sale. However, one of the comparable properties sold over a year ago, and you think it will require a $1,500 upward adjustment. You also believe that properties in the area that are located near the creek sell for about $1,200 less than other properties in the area because of a slower rate of runoff after heavy rains. Properties on corner lots generally sell for a premium of about $1,000. Houses with the fashionable modern design usually bring about $1,000 more than those that have traditional design characteristics. Because three-bedroom homes are considered desirable by buyers in the area, an additional fourth bedroom will generally only add about $1,200 in value to a property. However, properties that contain only two bedrooms are rather difficult to sell, and often bring $2,000 less than their three-bedroom counterparts when they are sold. Most homes in the area have a two-car garage, but when properties have a one-car garage, they usu- ally sell for about $800 less. A two-car open carport generally reduces the value of the property by a similar amount, or $800. The inferior construction quality exhibited by comparable III should reduce its value by about $1,500.

a. You plan to complete the sales comparison approach to value and assign an estimate of value to the subject property. Give specific reasons for your choice of value.

b. A second approach using the cost method of valuation will also be used to estimate value. Comparing vacant lot sales in the market area indicates that the value of the lot the subject property is constructed on is $13,000. Air-conditioned space in the dwelling would cost about $36.00 per square foot to reproduce, and the garage would cost approximately $3,700 to reproduce. Complete the cost approach to value, assuming that, because the property being valued is relatively new, no depreciation of the structure is required.

4. An investor is considering the acquisition of a “distressed property” which is on Northlake Bank’s REO list. The property is available for $200,000 and the investor estimates that he can borrow $160,000 at 8 percent interest and that the property will require the following total expenditures during the next year:

Final PDF to printer

bru19684_ch07_185-221.indd 221 11/01/17 04:25 PM

Chapter 7 Single-Family Housing: Pricing, Investment, and Tax Considerations 221

a. The investor is wondering what such a property must sell for after one year in order to earn a 20 percent return (IRR) on equity. What other issues must he consider?

b. The lender now is concerned that if the property does not sell, he may have to carry the prop- erty for one additional year. He believes that he could rent it and realize net cash flow before debt service of $1,200 per month. However, he would have to make an additional $12,800 in interest payments on his loan during that time, and then sell. What would the price have to be at the end of year 2 in order to earn a 20 percent IRR on equity?

5. You have an opportunity to acquire a property from First Capital Bank. The bank recently obtained the property from a borrower who defaulted on his loan. First Capital is offering the property for $200,000. If you buy the property, you believe that you will have to spend (1) $10,500 on various acquisition-related expenses and (2) an average of $2,000 per month during the next 12 months for repair costs, and so on, in order to prepare it for sale. Because First Capital Bank would like to sell the property as soon as possible, it is willing to provide $180,000 in financing at 8 percent interest for 12 months payable monthly (interest only). Your market research indicates that after you repair the property, it may sell for about $225,000 at the end of one year. Furthermore, you will probably have to pay about $3,000 in fees and selling expenses in order to sell the property at that time.

If you wanted to earn a 20 percent return compounded monthly, do you believe that this would be a good investment? If not, what counteroffer would you have to make First Capital in order to achieve the 20 percent return?

6. Spreadsheet Problem. Use the Ch7_Rent_vs_Own worksheet in the Excel workbook provided on the website. Determine the after-tax IRR for owning versus renting in each of the five years with the following changes in the original assumptions in the spreadsheet:

a. The homeowner has a 15 percent marginal tax rate instead of 28 percent. b. Rents and property values will not increase over the five years. c. The loan amount is $105,000 instead of $120,000. d. The initial rent for year 1 is $15,000 instead of $12,000.

www.mhhe.com/bf16e

Final PDF to printer

222

bru19684_ch08_222-253.indd 222 11/01/17 04:06 PM

Chapter 8 Underwriting and Financing Residential Properties This chapter deals with the process of seeking long-term mortgage financing for owner- occupied residential properties. Here, we focus on two aspects of this process: loan under- writing and closing. When discussing the underwriting process, we consider borrower and property characteristics and how loan terms are established. We also consider the size of the loan relative to property value, loan payments relative to borrower income, and default risk undertaken by lenders. We discuss the use of mortgage insurance or guarantees that may be necessary to grant a given loan request in cases where the total risk of lending to a specific borrower is too great for a given lender to undertake. Insurance may be provided by private insurers, or, depending on the property and borrower characteristics, insurance or guarantees may be available from various government agencies.

We look at the loan-closing process in terms of the necessary accounting between the borrower, lender, seller, and other parties to a transaction in which transfer of title and a loan closing occur simultaneously, and we consider federal regulations that require certain practices from the lender regarding uniform disclosure of interest charges, closing state- ments, and collection of credit and other information about the borrower.

Underwriting Default Risk

The process of evaluating a borrower’s loan request in terms of potential profitability and risk is referred to as underwriting. This function is usually performed by a loan officer at a financial institution or mortgage banking company. The loan officer performs this analysis based on information contained in (1) the loan application submitted by the bor- rower and (2) an appraisal of the property. This analysis is made in the context of a lend- ing policy, or guidelines, that a particular institution specifies. In some cases, lenders will require that borrowers obtain default insurance. The borrower purchases this insurance policy to protect the lender from potential losses, should the borrower default on the loan. In such cases, the lender is not willing to bear the total risk of borrower default, or the loan may be sold to a third-party investor (recall the process of assignment of the note and mortgage discussed in Chapter 2). In the latter case, the lender must consider underwriting standards required by such investors; otherwise, the lender may lose the option of selling

Final PDF to printer

Chapter 8 Underwriting and Financing Residential Properties 223

bru19684_ch08_222-253.indd 223 11/01/17 04:06 PM

mortgages later. In deciding whether a loan application should be accepted or rejected, the loan officer follows some fundamental concepts in loan risk analysis.

Before beginning a detailed discussion of specific underwriting standards and poli- cies, we first consider some basic relationships and terms used in mortgage underwriting. Two fundamental relationships that must be assessed by any lender when considering the risk of making a mortgage loan are the expected payment-to-income ratio and the loan-to-value ratio. The payment-to-income ratio is simply the monthly payment on the loan amount being applied for plus other housing expenses divided by the borrower’s income. The loan-to-value ratio is the loan amount requested divided by the estimated property value.

The first ratio is important because the borrower will generally be personally liable on the note and must be able to make payments either as scheduled (in the case of a fixed rate mortgage) or as market conditions change interest rates (in the case of adjustable rate mortgages). Clearly, the greater the ratio of mortgage payment to income for a given borrower, the greater is the default risk. Hence, a higher risk premium must be earned by the lender. Similarly, because the property being acquired by the borrower also serves as security for the note, as the loan-to-value ratio increases, the likelihood of loss increases. This is because the property may not bring a sufficient price at a foreclosure sale to cover the outstanding loan balance, any past due payments, and foreclosure costs. Therefore, the major problems facing a lender when reviewing a loan request made by a borrower are: (1) assessing the many variables that affect default risk, (2) determining whether a fixed interest rate or adjustable rate mortgage can be made, and (3) if the total risk on a particular loan request is too great, deciding whether the loan should be refused or made with default insurance or guarantees from third parties.

Classification of Mortgage Loans

In previous chapters, we discussed and classified mortgage loans mainly in terms of inter- est rate risk, that is, whether a loan was a fixed rate mortgage (FRM) or an adjustable rate mortgage (ARM). While those chapters also included a basic discussion of default risk, specific methods and procedures for assessing borrower default risk are primary topics in this chapter.

Recall from the previous chapter that default risk was defined as a potential loss that could occur if the borrower failed to make payment on a loan. This failure could be caused by a borrower having insufficient income, or because the market value of the property fell below the outstanding mortgage balance, or both. There are several ways that default risk can be shared. Default risk may be fully assumed by the lender, shared by the lender and a third-party insurer, or fully assumed by a third-party insurer or guarantor. To facilitate discussion, we use the following classifications: 1. Conventional mortgages. 2. Insured conventional mortgages. 3. FHA-insured mortgages. 4. VA-guaranteed mortgage loans.

Conventional Mortgage Loans Conventional mortgage loans are negotiated between a borrower and lender. From these negotiations, the loan-to-value ratio, interest rate (or ARM terms), and the payment-to-income ratio are established. The loan-to-value ratio establishes the

Final PDF to printer

bru19684_ch08_222-253.indd 224 11/01/17 04:06 PM

224 Part 3 Residential Housing

borrower’s down payment, or equity. Should the borrower default on the loan, both the lender and borrower may incur losses. Losses usually include any past due interest, costs of selling the property, and the extent to which the sale price is less than the mortgage balance. In the event of loss, the borrower absorbs such losses first to the extent of any equity. If losses exceed the amount of borrower equity, the lender will then incur a loss, which then becomes a claim against the borrower and (depending on state law) may be used to attach other assets owned by the borrower (recall the discussion of deficiency judgments in Chapter 2).

Typically, if the borrower desires a conventional loan, the maximum loan amount will be 80 percent of the value of the real estate being purchased. Location of the property— for example, in a platted subdivision with city utilities—is also a key factor. Because the lender must look to the sale of the property for repayment of the mortgage loan, should the borrower default, regulations governing the operation of most savings institutions gen- erally require that for conventional loans, equity of at least 20 percent of value must be provided by the borrower. Therefore, such losses must exceed 20 percent of the origi- nal property value before the lender would suffer a loss. Much of the lending activity in the conventional loan market is affected by the Federal National Mortgage Association (FNMA) and the Federal Home Loan Mortgage Corporation (FHLMC). See Concept Box 8.1 for a brief discussion.

Insured Conventional Mortgage Loans In many instances, borrowers do not have the necessary wealth to make a down payment of 20 percent of value when purchasing a property. However, if the income-earning ability of the borrower and the location of the property being acquired are satisfactory, lenders may be willing to grant a loan request in excess of 80 percent of value with a condition that the borrower purchase mortgage insurance against default risk. Many firms provide this insurance for a premium, which is paid by the borrower and is based on the amount of risk assumed by the mortgage insurer. A useful way of thinking about mortgage insur- ance is to view the borrower as negotiating for a larger loan from the lender, and then paying an insurer to assume the increase in default risk above that taken by the lender on a conventional loan. In other words, only the amount of the loan in excess of 80 percent of the property value at the time of loan origination is usually covered under the mortgage insurance policy. Therefore, if a mortgage is made for 95 percent of value and private mortgage insurance is purchased, the borrower would make an equity down payment of 5 percent of the property value and the mortgage lender would make a 95 percent loan. However, the lender would have 80 percent of the loan amount at risk and the mortgage insurer would insure any losses to the lender in an amount equal to 15 percent of the prop- erty value. Borrowers evaluating a 95 percent loan must weigh the incremental cost of the additional 15 percent by considering the combination of a possibly higher rate of interest plus the cost of mortgage default insurance. (Recall the discussion of incremental borrow- ing costs in Chapter 6.) This incremental cost may be compared to the cost of acquiring second-lien financing or the opportunity cost associated with borrowers making a greater down payment.

Mortgage insurers are private companies that operate by collecting premiums from borrowers based on the incremental risk being assumed as loan amounts rise above 80  percent. These premiums are pooled and the insurers maintain reserves that are used to pay claims to lenders, should mortgage defaults occur. These companies can usually take this additional risk at a premium that would be lower than individual lenders would have to charge because they insure many different borrowers making mortgage loans nationally, whereas individual lenders make loans to fewer individuals in fewer geographic regions. Consequently, mortgage insurers are able to diversify the additional default risk more

Final PDF to printer

225

bru19684_ch08_222-253.indd 225 11/01/17 04:06 PM

The influence of FNMA and FHLMC (Fannie Mae and Freddie Mac) goes far beyond the standardization of documents (appraisal forms, etc.) noted in Chapter 7. As will be described in detail in later chapters dealing with mortgage-backed securities, these two government- sponsored enterprises (GSEs) dominate the secondary residential mortgage market in the United States.

These organizations (1) purchase mortgages from lenders, (2) create large mortgage pools (often in the billions of dollars), and then (3) using these pools as collateral, issue mortgage-backed securities, which are sold to investors such as pension funds, insurance companies, and overseas investors. In order to accomplish this securitization process cost- effectively and efficiently, FNMA and FHLMC have instituted many requirements that lend- ers must adhere to and that have resulted in considerable standardization in the mortgage lending process.

GSEs classify loans that they are willing to purchase as (1) conforming or (2) noncon- forming mortgages. The conforming category specifies the loan amount that Congress has authorized as the maximum mortgage loan that these GSEs may purchase from lenders and for which the U.S. Treasury will provide credit backing. These loans also must meet the underwriting standards of FNMA/FHLMC. FNMA and FHLMC dominate the conforming loan market because of their GSE status, which includes possible market support at the option of the U.S. Treasury. Because of the implied market support by the Treasury, FNMA and FHLMC can borrow at lower rates of interest than other entities and can buy conforming loans at lower yields than their competitors.†

Nonconforming loans are: (1) loans made in amounts greater than the loan maximums set for conforming loans or (2) loans that do not meet the underwriting standards used for con- forming loans. Because jumbo loans are made in larger amounts and are not backed with government guarantees, FNMA and FHLMC must compete for them with non-GSE lenders. Because of this competition, jumbo loans are usually made by many lenders at higher inter- est rates than those of conforming loans.

Two additional nonconforming loan categories are subprime and ALT-A loans. As will be discussed further in the underwriting section of this chapter, subprime loans usually indi- cate situations where some aspect of a borrower’s credit listing is deficient. The term ALT-A stands for “alternative to A paper,” where “A paper” is a low risk, conforming loan. When ALT-A loans are underwritten, some aspect of the loan application cannot be verified, such as self-employment income. However, the borrower may have sufficient assets (cash, stocks, etc.) to be approved for a loan. ALT-A loans also are sometimes referred to as “low doc” (low documentation) loans.

†For a description of the U.S. Treasury Preferred Stock Purchase Agreement, see: https://www.fhfa.gov /Conservatorship/Pages/History-of-Fannie-Mae--Freddie-Conservatorships.aspx.

The Secondary Mortgage Market and Increasing Standardization in the Mortgage Lending Industry Concept Box 8.1

effectively than a single lender can. A single lender could be more adversely affected, should an economic decline occur in a particular region.

When an insured conventional mortgage is made, the maximum loan that a borrower is likely to obtain will be 95 percent of value, although some lenders will go even higher. Because a greater potential for loss exists and much of the risk of loss is being assumed by the mortgage insurer, underwriting requirements that the lender uses to evaluate the borrower are likely to be heavily influenced by the insurer. Lenders must rigidly adhere to these standards when this type of loan is considered. Premiums will be based on the extent to which the loan-to-value ratio exceeds 80 percent for any given borrower.

Final PDF to printer

bru19684_ch08_222-253.indd 226 11/01/17 04:06 PM

226 Part 3 Residential Housing

FHA-Insured Mortgage Loans A mortgage loan can also be insured by the Federal Housing Administration (FHA). Unlike conventional insurance, which protects the lender against some portion of the potential loan loss, FHA mortgage insurance insures the lender completely against any default losses. It should be stressed that FHA does not make loans but provides insurance. Because FHA accepts the entire risk of borrower default, it maintains strict qualification procedures before the borrower and property will be accepted under its insurance program.

The FHA was created in 1934 with the passage of the Federal Housing Act.1 The origi- nal intent of the FHA was to stabilize the housing industry after the Depression of the early 1930s. It has also had a long-standing policy objective to make housing affordable to lower- and middle-income families. This has been accomplished by allowing such families to purchase homes with lower down payments than would be required under conventional lending standards. The FHA operates as an insurance program, collecting premiums from borrowers, usually as a part of their monthly payments. These premiums are pooled to cre- ate reserves for payment of lender claims. Because FHA mortgage loans are made with higher loan-to-value ratios than conventional uninsured loans and because the FHA assumes the entire risk of default, mortgage insurance premiums charged by FHA are usu- ally higher than private mortgage insurance premiums. This is because private mortgage insurance is usually limited to a fixed percentage of the loan amount (e.g., 15%). FHA insures lenders against all losses caused by borrower default, and this could be greater or less than a fixed percentage of the loan amount originated.

Why is there a need for both FHA and private mortgage insurance? Regulations place loan maximums on FHA-insured mortgage loans which may not be sufficient for many borrowers who purchase higher-priced properties.2 Hence, qualified borrowers will nor- mally choose a conventional, privately insured loan when a larger loan is necessary to purchase higher-priced property with a low down payment. In general, borrowers with higher incomes, who desire to purchase higher-valued properties with low down payments, opt for private mortgage insurance because the loan amount can be greater than the maxi- mum available under FHA at a lower insurance cost. FHA borrowers are likely to have lower incomes and purchase properties in lower price ranges, within the maximum loan limits set by FHA. Because of the borrowers’ lower incomes, lenders may insist that the entire mortgage loan be insured; consequently, these borrowers will pay higher insurance premiums to FHA.

FHA extends insurance to buyers under a number of programs. The most common is Section 203b, which insures loans on one- to four-family detached residences. This pro- gram requires fixed interest rate financing with a term of between 15 and 30 years. Other FHA loan programs include Section 251, an ARM program; Section 234c, a con- dominium insurance program; and Section 245, a graduated payment mortgage insur- ance program.3

VA-Guaranteed Mortgage Loans Qualified veterans who desire to purchase a residential property and who meet certain length-of-service tests may obtain a mortgage loan guarantee from the Department of Veterans Affairs (VA). The VA provides guarantees that compensate lenders for

1 The National Housing Act of 1934, as amended. 2 For a discussion of FHA maximum insurable loan amounts, see HUD Handbook 4000.2 and subsequent revisions. FHA maximum insurable loan amounts depend on the geographic region in which the loan is made. These amounts also change from time to time. 3 For a detailed listing of FHA mortgage insurance programs, see HUD Handbook 4000.2.

Final PDF to printer

Chapter 8 Underwriting and Financing Residential Properties 227

bru19684_ch08_222-253.indd 227 11/01/17 04:06 PM

losses on loans made to veterans (borrowers). The amount of the guarantee varies with the home loan amount and the veteran’s remaining entitlement. The amount of the guarantee varies over time and usually cannot exceed 25 percent of FNMA-FHLMC conforming loan limits. As is the case with the FHA program, VA does not make mortgage loans. It does, however, make direct loans to the public in connection with the sale of reposses- sions. Unlike the FHA program, the VA provides a loan guarantee, not default insurance. The certificate of guarantee is provided at no charge to the lender. Unlike FHA and pri- vate mortgage default insurance, the borrower does not pay any monthly or other insur- ance premiums for the VA guarantee. All losses incurred by VA under this program are paid by the U.S. government through its budget allocation to the Department of Veterans Affairs. Because of this guarantee, VA underwriting is very structured, particularly regard- ing appraisals and property inspections.

The amount of the loan that may be guaranteed is generally limited to the amount shown on the Certificate of Reasonable Value (CRV). Veterans also may use their VA home loan entitlement more than once. The amount of entitlement available to a borrower at any given time depends on the current guarantee maximum, amounts of pre- viously used entitlement, plus any amounts restored from previously used entitlement. For example, if the current maximum entitlement is $36,000 and a borrower purchases a property for $80,000, the VA will issue a certificate of guarantee for 40 percent, or $32,000, leaving $4,000 of entitlement for future use by the borrower. If after a time the borrower meets the legal requirements for restoration, the $32,000 of previously used entitlement would be added back to the remaining entitlement, making the full entitle- ment $36,000 once more.

If the borrower sells the property on assumption to another qualified veteran bor- rower with entitlement who agrees to substitute his entitlement for the entitlement used by the original borrower on the loan, the original borrower’s entitlement would be restored.

Many other influences affect the amount of entitlement for which a borrower may qual- ify, for example, when both husband and wife are qualified veterans.4

The Underwriting Process

Regardless of the type of mortgage (conventional, conventional insured, FHA, or VA), much of the underwriting process is common to all types of mortgage loans. The under- writer begins by collecting data to determine whether credit should be extended. The goal of this process is to determine whether the loan-to-value ratio, the payment-to- income ratio, assets of the borrower, and borrower credit history are acceptable to the lender or the lender and insurer. Next, we discuss (1) how borrower income is estimated and the relationship of that income to the proposed mortgage payments and other obli- gations of the borrower and (2) how the value of the property is established through an appraisal.

Borrower Income The underwriting process usually begins with the underwriter obtaining the data needed to determine whether credit should be extended. An item of primary importance will be bor- rower income. To gather the necessary data regarding income, the borrower is requested to

4 For a discussion of VA loan guarantee eligibility requirements, see Title 38, U.S. Code, Section 3701.

Final PDF to printer

bru19684_ch08_222-253.indd 228 11/01/17 04:06 PM

228 Part 3 Residential Housing

allow the lender to (1) verify place of employment, (2) verify wages (via W-2 forms, pay- check stubs, etc.), and (3) inquire as to whether employment is likely to continue into the future. Typically, where a borrower is employed on a full-time basis and obtains regular income from this employment, there is little problem in verifying income. In cases where a borrower’s income is derived from more than a single source, the process of verifying the amount and the likelihood of that income continuing is more difficult.

Other possible income sources include  ∙ Part-time employment ∙ Working spouse ∙ Rentals ∙ Alimony or child support ∙ Commissions ∙ Self-employment ∙ Bonuses ∙ Dividends or interest ∙ Retirement annuity ∙ Social Security ∙ Public assistance

Generally, two tests must be met before any of these sources will be included in estab- lishing borrower income in the underwriting process. First, the underwriter must judge that the income is likely to continue. This usually means that a source of income must have already occurred continuously for a sufficient time for the underwriter to judge whether that income will continue. Second, the income must be verifiable, usually by reviewing the borrower’s federal income tax returns for at least two years. When the income is nontax- able, such as distributions from retirement annuities, canceled checks or verification of deposits may be used to verify the existence of the income.

In addition to deciding what sources of income should be included, difficulties also arise when determining how much income should be used in the underwriting process. For example, the amount of income from a particular source may vary from period to period. When income is variable in nature, such as the earnings from commission sales positions, rentals, or self-employment, a borrower’s income will generally be averaged over a period of at least two years from amounts shown on tax returns. Any expenses incurred in earning that income will be deducted from the amount of income earned.

When two individuals are employed, the question arises of what constitutes income. The general rule applied by the lender takes a long-run viewpoint; that is, it asks whether both individuals will remain employed indefinitely, or at least until the income of one is sufficient to meet the monthly mortgage payments. This question often presents difficulty when the value of the property and the loan amount being requested are high in relation to the income of only one of the earners. Obviously, the lender will have to exercise judg- ment about the future stability of the joint incomes. Generally, if both parties have been employed for several consecutive years, future income stability is more likely. If the intent of one of the parties is to end employment after a given number of years and this individual is presently employed in a professional activity with employment stability, both incomes may be included for the time both expect to remain employed. An estimate may be made as to what the primary worker’s total income will be at the time the other party ceases employment.

Although income forms much of the basis for risk analysis by the lender, recent federal regulations have limited the extent to which lenders may obtain information or make

Final PDF to printer

Chapter 8 Underwriting and Financing Residential Properties 229

bru19684_ch08_222-253.indd 229 11/01/17 04:06 PM

inferences concerning a loan applicant’s background. Regulation B of the Board of Governors of the Federal Reserve System provides guidelines that lenders must comply with when gathering information about potential borrowers.5

Verification of Borrower Assets Another step in the data collection process is the verification of borrower assets. Assets of the borrower must at least be sufficient to close the transaction. This means that borrower assets must be sufficient to pay closing costs and make a down payment. Moreover, lenders usually do not allow borrowed funds to be used as the borrower’s down payment. Thus, how long a borrower’s assets have been on deposit will be used as an important indicator of whether the borrower is planning to use borrowed funds to make a down payment. Gifts, on the other hand, are usually allowed for all funds necessary to close. A gift letter stat- ing that no repayment is required, signed by both the borrower and gift donor, is usually required. The lender will usually document the transfer of funds from the donor’s account to the borrower’s account. Any assets that are not required to close the lending transaction will reflect favorably upon the creditworthiness of the borrower.

Other assets of the applicant also play an important role in rating the loan quality by the lender. The rating is improved if the applicant has demonstrated a consistent ability to save as evidenced by savings accounts or investments in other property, ownership of life insurance (cash value), purchase of securities, and the like, as well as the ability to carry the obligations associated with the acquisition of these assets. For example, an older applicant whose remaining life expectancy is less than the term of the mortgage being sought may be granted a loan with the desired maturity, even though it exceeds the years of life expectancy remaining, if adequate life insurance exists to pay off the mortgage loan in the event death occurs before the loan is repaid. In most cases, the lender will request that the appli cant sign a request allowing other financial institutions, investment companies, and credit agencies to disclose to the lender the nature and amount of the applicant’s assets. These could include stocks, bonds, savings accounts, and any recent activity in the accounts.

Assessment of Credit History Typically, the underwriter will also make a judgment about the acceptability of the bor- rower’s past payment history on other obligations. Credit reports from a central credit

5 (1) The use of sex, marital status, race, religion, age, or national origin in a credit underwriting procedure is prohibited. (2) Creditors may not inquire into birth control practices or into childbearing capabilities or intentions, or assume, from her age, that an applicant or an applicant’s spouse may drop out of the labor force due to childbearing and thus have an interruption of income. (3) A creditor may not discount part-time income but may examine the probable continuity of the applicant’s job. (4) A creditor may ask and consider whether and to what extent an applicant’s income is affected by obligations to make alimony or child support or maintenance payments. (5) A creditor may ask to what extent an applicant is relying on alimony or child support or maintenance payments to repay the debt being requested, but the applicant must first be informed that no such disclosure is necessary if the applicant does not rely on such income to obtain the credit. Where the applicant chooses to rely on alimony, a creditor shall consider such payments as income to the extent the payments are likely to be made consistently. (6) Applicants receiving public assistance payments cannot be denied access to credit. If these payments and security provided for the loan meet normal underwriting standards, credit must be extended. (7) An individual may apply for credit without obligating a spouse to repay the obligation, as long as underwriting standards of the lender are met. (8) A creditor shall not take into account the existence of a telephone listing in the name of an applicant when evaluating applications. A creditor may take into account the existence of a telephone in the applicant’s home. (9) Upon the request of an applicant, the creditor will be required to provide reasons for terminating or denying credit.

Final PDF to printer

bru19684_ch08_222-253.indd 230 11/01/17 04:06 PM

230 Part 3 Residential Housing

bureau, located in most cities, will give a history on a borrower’s payment habits for up to 10 years. Such things as slow payment of past borrower obligations may reflect unfa- vorably upon the loan applicant. Many examples of adverse credit experience will surely cause the loan application to be rejected. However, a brief interruption in an otherwise acceptable credit history caused by explainable events such as divorce or interruption in income will sometimes be overlooked by the underwriter if an explanation is provided— assuming that the borrower has recovered financially from the adverse circumstances that caused this problem. Even bankruptcy may not automatically cause a loan application to be rejected if there were extenuating circumstances and the borrower has had several years of acceptable history since the problem occurred. For developments in analysis and credit scoring, see Concept Box 8.2.

Estimated Housing Expense Determining the housing expense used to establish the payment-to-income ratio that a bor- rower is proposing to undertake is relatively straightforward. The following is a list of items that are likely to be included in the estimate of monthly housing expense: ∙ Principal and interest on the mortgage being applied for. ∙ Mortgage insurance (if any). ∙ Property taxes. ∙ Hazard insurance. ∙ Condominium or cooperative homeowners association dues (if applicable).

The underwriter will have to estimate many of these items because their exact amounts will not be known at the time of underwriting. Very often, the lender may require that the borrower pay monthly, prorated installments toward mortgage insurance, hazard insurance, and property taxes, in addition to the mortgage payment. Judgment concerning the risk associated with making the mortgage loan will depend upon the total cost of home owner- ship relative to borrower income. If this total cost of home ownership is too high, then an applicant’s loan application may be rejected. Specific examples of how these expenses are estimated and related to income will be discussed later in the chapter.

Other Obligations In most cases, borrowers will have other obligations in addition to the mortgage loan being applied for. Obvious examples include auto loans, credit card accounts, other mortgage debts, or alimony and child support payments. The underwriter will request that the bor- rower disclose all debts at the time of application, and then verify these commitments by obtaining a credit report with the approval of the borrower. Courthouse records in the borrower’s county of residence also may be checked to determine whether there are any judgments outstanding against the borrower for unpaid debts. Another item on the credit report of importance to the underwriter will be whether the borrower has ever filed for bankruptcy.

Compensating Factors It is possible that the underwriter will find other favorable factors about the borrower that can offset certain unfavorable factors during the underwriting process. Typically, it is con- sidered favorable for a borrower to have liquid assets that could be used to make monthly mortgage payments should the borrower’s income be interrupted. Another favorable factor is if the borrower is employed in a field in which his or her skills are in high demand and the likelihood is that the borrower’s income will increase over time. These factors may prove sufficient to allow a borrower to devote more income to housing expenses, even

Final PDF to printer

bru19684_ch08_222-253.indd 231 11/01/17 04:06 PM

The evolution of credit scoring models has had a profound impact on all areas of lending, includ- ing mortgage lending. When underwriting mortgage loans, lenders usually require that a credit report be obtained on borrowers. Most credit reports contain credit scores.* This credit score is a three-digit credit rating that represents an estimate of an individual’s financial creditworthi- ness as determined by a statistical model. Lenders use the borrower/applicant’s credit score as one of many inputs in the underwriting process. The credit score attempts to quantify the likelihood that a prospective borrower will fail to repay a loan during a specified period of time. Credit scores have an important influence on (1) loan approval and (2) the interest rate that will be quoted on a loan. The maximum credit score is usually in the range of 850. High credit scores increase the probability that the loan will be approved and that it will be made at a lower interest rate than may be quoted to borrowers with lower credit scores. Scores below 600 to 700 may result in rejection of the loan application, unless the lender has additional compelling information, such as other assets owned by the loan applicant that may serve as security.

While the contents of credit-scoring models are private, it is generally believed that the major variables used in the models to determine the final credit score include the following (approximate weights are shown in parentheses):

A. Punctuality of past payments (35%). B. Capacity used: the ratio of current debt (credit card balances, etc.) to total available credit

card limits (30%). C. Years of credit experience (15%). D. Types of credit used (10%). E. Recent searches for credit and/or the number of credit cards/accounts applied for recently (10%).

A. Punctual payment. A prompt payment history has a very positive effect on credit scores. Any payments reported more than 30 days late have a negative affect on credit scores. Any account placed in “collection status” (usually after it is six months past due) has a very nega- tive effect on scores. (To increase credit scores, borrowers should strive to pay: (1) an amount greater than the minimum payment due each month on credit cards and installment loans or (2) an amount greater than the interest due for the month, which will reduce the loan balance. If possible, borrower should repay the outstanding loan/credit balance in full each month.)

B. Capacity used. Large total outstanding loan balances as a percentage of total credit limits available on all credit cards used by a borrower will generally have a negative effect on the credit score. Capacity used is calculated as the maximum credit balance used anytime during the bill- ing cycle divided by the total credit limit available. When consolidating the credit card debt, bor- rowers should be aware that the capacity used ratio may increase if some credit accounts are closed and outstanding credit balances are transferred to fewer accounts. Unless the total credit limit is increased on the remaining credit accounts when consolidation takes place, this could result in a lower total credit limit relative to total credit outstanding and, therefore, a greater percentage of capacity used.  This would have a negative effect on the credit score.

C. Length of credit history experience. A lengthy experience with managing credit usually has a positive influence on borrower credit scores. Individuals with less credit experience will not score as well. This tends to favor older individuals with a long history of successful credit management.

D. Types of credit used. Loans made with consumer finance companies or other entities that make loans to high-risk individuals at high interest rates have a negative effect on scores.

E. Searches/inquiries. The number of applications, credit cards issued, and inquiries to credit bureaus regarding the status of the borrower’s credit tend to have a negative impact on credit scores. Frequent inquiries regarding borrower credit reporting balances may also adversely affect scores.

* The basis for most credit scores is the so-called FICO score, developed by the Fair Issac Corporation and based on a statistical default risk model. Such models have been used by the three major credit reporting agencies (TransUnion, Equifax, and Experian). However, the suppliers of credit data (retailers, etc.) to these three agencies are not all the same. Consequently, depending on the credit reporting agency chosen, credit scores may differ for the same applicant.

Credit Scoring Models Concept Box 8.2

231

Final PDF to printer

232

bru19684_ch08_222-253.indd 232 11/01/17 04:06 PM

∙ Lock-in period and fee. Most lenders will provide a firm interest quote usually for 30 days prior to closing. This “lock in” period is a commitment by the lender to make a loan at a specific rate of interest for a specified number of days, even though market interest rates may change prior to the actual loan closing. Some lenders may charge a fee to lock this rate in. Lock-in periods may also be extended to 45 or 90 days, usually for a higher fee.

∙ Private mortgage insurance (PMI). This is usually required for loans that are over 80  percent of value. However, borrowers who need loans in excess of 80 percent of value may consider a first lien for 80 percent, and then add a second lien for the addi- tional amount needed. By keeping the first lien at or below 80 percent, borrowers may avoid PMI. However, interest rates on second liens are usually higher, and this higher rate must be compared to PMI premiums.

∙ Option to eliminate PMI or FHA insurance after closing. These requirements may be dropped, usually when loan-to-value ratios fall below 80 percent. This will reduce monthly payments by the amount of the monthly insurance premium. Elimination of this insurance will usually require a new appraisal conducted by an appraiser who must be approved by the lender.

∙ Buying down interest rates. This option may be compared with making larger down payments. As larger down payments are made, interest rates quoted on a loan should be compared to the interest rate available if the borrower buys down the rate from the lender.

∙ Subprime loans. When a deficiency is discovered (e.g., low credit score) during the underwriting phase of the loan application process, lenders may be willing to make a subprime loan. These loans are usually made at higher rates of interest than would otherwise be available and may also include prepayment penalties and significant penalties for late payments. Subprime borrowers may attempt to negotiate a provision in the loan that, if such a deficiency is cured (e.g., the borrower achieves a higher credit score) after closing, the interest rate will be reduced.

Borrower Strategies to Consider during the Loan Underwriting Period Concept Box 8.3

if the borrower’s proposed housing expense ratio is higher than for other borrowers with similar incomes. Of course, making a substantial equity down payment as part of the pur- chase price is considered favorable as well. When any or all of these conditions exist, it is possible that underwriting policies may be relaxed to some degree.

After all of the factual data described above have been determined, the loan underwriter will consider whether or not the loan in question should be granted. The process of making this evaluation varies, depending upon the kind of loan the borrower is seeking. The fol- lowing examples of the underwriting process in conventional, insured conventional, FHA, and VA loan transactions should help to illustrate this point. For a list of other important issues and strategies, see Concept Box 8.3.

The Underwriting Process Illustrated

This chapter section illustrates how each of the four types of mortgage loans described above are generally underwritten by lenders. As indicated earlier, one goal of underwrit- ing is to establish whether the risk of borrower default is acceptable and whether the loan should be granted. We will consider each type of mortgage (conventional, insured conven- tional, FHA, and VA) separately. In this section, we look at how the maximum mortgage amount is established, how it is related to property value, and how that relationship varies

Final PDF to printer

Chapter 8 Underwriting and Financing Residential Properties 233

bru19684_ch08_222-253.indd 233 11/01/17 04:06 PM

with each type of mortgage. We also discuss (1) proposed housing expenses and other obli- gations relative to borrower income, (2) the criteria used to establish acceptable relation- ships between expenses and income, which will serve as the basis for the lending decision, and (3) the role of appraisals in establishing the loan-to-value ratio.

To facilitate the discussion, we use the sample borrower information in Exhibit 8–1 to illus- trate the underwriting process for each category of mortgage loans. Details about the underwrit- ing criteria will be sufficient to allow generalizations beyond the cases used in our discussion.

Underwriting Standards—Conventional and Insured Conventional Mortgages Looking at the data shown in Exhibit 8–1, we see that in addition to the verification of income and outstanding debts, the lender has estimated both property taxes and hazard insurance (fire, storm, etc.), which are also used in estimating housing expenses. These expenses establish the monthly payment-to-income ratio for the borrower-applicants. Looking at Exhibit 8–2, we see some of the general underwriting standards that lenders will apply in making the decision to grant or deny the loan request. In other words, after assem- bling the facts necessary to establish monthly housing expenses and other obligations, the lender will compute the necessary ratios and compare them to the general standards used by the lenders and mortgage insurers. This will help determine whether the default risk is acceptable, given the prevailing rate of interest. Lenders and insurers establish these under- writing standards, or maximum allowable ratios, based on loss experience from previously underwritten loans. Interpret these ratios as a general guide, however, because there may be other assets or compensating factors to be considered as part of the underwriting process.

Also note in Exhibit 8–2 that, in the case of ARMs, more stringent underwriting stan- dards may have to be met in certain cases. This is because an increase in interest rates could result in either an increase in payments or an increase in the loan balance due to a payment cap and negative amortization. Lenders refer to cases where negative amortiza- tion is expected as scheduled amortization and usually take it into account when under- writing the ARM by requiring a lower loan-to-value ratio. If payments are likely to be adjusted because the composite rate (current ARM index plus margin) at the time of origi- nation is higher than the initial interest rate, the underwriter will probably consider the scheduled payment increase when reviewing the payment-to-income ratio.6 Note that

6 When the composite rate is higher than the initial rate at the time of origination, the initial, or start rate, is referred to as the teaser rate, because lenders may be using it as an incentive for borrowers to make ARMs. In some cases, the loan agreement may specify that at closing, any difference between the start rate and the composite rate represents accrued interest and is added to the loan balance. When the first payment adjustment occurs, payments will then increase if the composite rate remains higher than the initial rate. Should the composite rate increase substantially on the payment reset date, the increase in ARM payments may be substantial and is referred to as payment shock in the lending industry.

EXHIBIT 8–1 Sample Underwriting Illustration: Borrower and Property Characteristics

Name of borrower: John and Jane J. Jones Income: $3,542 monthly from salaried employment of both spouses,

$42,500 annually Debts: Installment obligation of $181 per month with 35 months remaining

Credit card obligations, $50 per month with more than 12 months remaining

Sale price: $76,700 Appraised value: $77,000 Estimated property taxes: $797 annually Hazard insurance: $552 annually Desired mortgage: FRM with a 30-year term, constant payment

Final PDF to printer

bru19684_ch08_222-253.indd 234 11/01/17 04:06 PM

234 Part 3 Residential Housing

conventional GPMs are usually underwritten on the basis of scheduled amortization, which is known at the time of origination, and the loan-to-value ratio is usually restricted to 90 percent. Also, in the case of ARMs, initial maximum payment-to-income ratios may be lowered if the mortgage agreement provides for the possibility of monthly payments exceeding prescribed maximums. For example, if an ARM is made with a payment cap greater than 15 percent annually, or if the interest rate cap exceeds 2 percent annually or 5 percent over the life of the mortgage, lower ratios will usually be required. This latter restriction also applies to GPMs.

When computing these ratios for the conventional and insured conventional cases, we take relevant information from Exhibit 8–1 and compute the necessary ratios shown in Exhibit 8–3. Note that in the two cases being considered, the insured conventional loan is larger (95% vs. 80%) and is made at a higher interest rate. Also, the insured loan requires a monthly mortgage insurance premium, and the conventional loan does not. The ratios cal- culated and shown at the bottom of the exhibit indicate that the borrower would probably qualify for either a conventional loan or an insured conventional loan, given that those ratios fall well below the maximum ratios allowed under the general underwriting stan- dards shown in Exhibit 8–2. Whether the borrower will prefer the conventional or insured conventional loan depends on the amount available for a down payment (20% or 5% of appraised value) and whether the borrower wants to pay additional interest and insurance charges. The latter choice also depends on whether the borrower has sufficient funds to make either down payment requirement.7 If the borrower could afford to make either down payment, the borrower must decide whether the difference (15%) can be reinvested at a rate of interest in excess of the added interest and insurance charges. (A procedure that may be used to choose between loans that differ in amount and interest rates was presented in detail in Chapter 7.)

Underwriting Standards—FHA-Insured Mortgages If the borrower in our example is considering an FHA-insured mortgage, a similar approach is used to underwriting, with some notable exceptions. To begin our general discussion of FHA underwriting, we point out that unlike the conventional underwriting process, which provides for loan amounts as a percentage of appraised value (80%, 95%, etc.), FHA has a specific procedure that is used to establish the maximum insurable loan

7 Examples of various closing costs to be discussed later in the chapter include origination fees, appraisal fees, credit report fees, and transfer taxes.

Conventional Insured Conventional

  FRMs ARMs FRMs ARMs

Maximum ratios allowed (%):   Loan-to-value 80% 80% 95% 90*–95%   Payment-to-income 28 25†–28 28 25†–28   Total obligations to income 36 33†–36 36 33†–36

*Conventional ARMs with loan-to-value ratios in excess of 90 percent are generally not available, although some lenders will loan in excess of 90 percent at a higher interest rate. Graduated payment mortgages (GPMs) are usually limited to 90 percent loan-to-value ratios because of scheduled negative amortization. †Generally, the higher ratios are allowed; however, if the conventional ARM or GPM allows for the possibility of maximum increases in monthly payments beyond prescribed limits, the lower ratios must be met for the loan to be insured. See: Bankrate.com for current information on underwriting standards.

EXHIBIT 8–2 General Industry Standards for Underwriting Conventional and Insured Conventional Loans

Final PDF to printer

Chapter 8 Underwriting and Financing Residential Properties 235

bru19684_ch08_222-253.indd 235 11/01/17 04:06 PM

amount for which it is willing to issue an insurance binder.8 This process is generally described in Exhibit 8–4.

It should be stressed that FHA has historically established its own standards for both of these qualifying ratios (see bottom of the exhibit), which it uses uniformly for FRM, GPM, and ARM loans. This practice of computing ratios based on current income at the time of loan origination is followed even though monthly payments with a GPM or ARM may change in future periods.

As in the case of conventional lending, the underwriter is likely to take into account other assets, credit history, and offsetting factors when deciding to accept or reject a loan application. Qualifying ratios used as standards in determining the adequacy of borrower income are based on FHA’s loss experience in the operation of its insurance fund. Our hypothetical borrower-applicants, then, would likely qualify for an FHA- insured loan. FHA uses one additional underwriting test, however, which is discussed in the next section.

Underwriting Standards—VA-Guaranteed Mortgages The underwriting process followed by the Veterans Administration (VA) differs consider- ably in its approach to establishing the adequacy of borrower income in relation to the loan request. The VA procedure stresses the notion of residual income, which is a process, whereby gross income is reduced by all monthly outlays for housing, expenses, taxes, all debt obligations, and recurring job-related expenses (see Exhibit 8–5). The difference, or residual income, is then examined to establish whether VA deems it adequate for support- ing the borrower’s family.

A few items are of particular importance. The mortgage loan amount is equal to the sale price, $76,700, plus a funding fee ranging from .5 percent to 3.0 percent of the loan request

8 The maximum loan-to-value limits are subject to change at any time.

  Conventional Insured Conventional

Loan amount requested $61,360 $72,865 Terms FRM 30 years 9.25% FRM 30 years 9.5% Loan-to-value ratio 80% 95% Borrower income (A) $ 3,542 $ 3,542 Housing expenses:  Principal and interest $ 505 $ 613  Property taxes 66 66  Hazard insurance 46 46  Mortgage insurance − 21

Housing expense (B) 617 746 Add:  Installment debt* 181 181  Credit cards 50 50

 Total obligations (C) $ 848 $ 977 Housing expense ratio (B ÷ A) 17% 21% Total obligation ratio (C ÷ A) 24% 28%

*Usually defined as an obligation with at least 11 remaining monthly payments. However, any obligation that in the judgment of the underwriter requires a large monthly outlay relative to income may be included, even if the number of remaining payments is less than 11.

EXHIBIT 8–3 General Approaches to Computation of Borrower Qualification (Conventional and Insured Conventional Loan Examples)

Final PDF to printer

bru19684_ch08_222-253.indd 236 11/01/17 04:06 PM

236 Part 3 Residential Housing

First-time homeowners often use FHA loans to finance their home. Go to www.fha-home-loans.com and find out the current requirements to qualify for an FHA loan. They may differ slightly from that described in

the book because the underwriting requirements fre- quently change. Summarize the types of loans that are currently available. What is the highest loan-to-value ratio that you could obtain?

Web App

SECTION I. Maximum Loan Amount Calculation

First Calculation Lower of price or appraised value $ 76,700 Plus: Closing cost allowance* 1,350

Acquisition cost $ 78,050 97 percent of the first $25,000 $ 24,250 95 percent of the remainder 50,397

Maximum loan amount under first calculation $ 74,647 Second Calculation Lower of price or appraised value $ 76,700 Times: Maximum loan-to-value ratio—Value > $50,000 97.75%

Maximum loan amount under second calculation $ 74,974 Maximum loan amount†—lesser of the first or second calculation $ 74,647 Plus: Financed mortgage insurance premium† of 2.25 percent‡ 1,679

Amount financed $ 76,326

SECTION II. Computation of Qualifying Ratios

Gross income (monthly) (A) $ 3,542 Housing Expense Principal, interest, and up-front mortgage insurance premium ($76,326, 9.5%, 30 years) $ 642 Property taxes 66 Hazard insurance 46 Annual mortgage insurance premium‡ 31

Total housing expense (B) $ 785

Other Obligations Installment debt§ $ 181 Credit cards 50

Total obligations (C) $ 1,016

EXHIBIT 8–4 General Approach in the Determination of Maximum Loan Amount and Borrower Qualification Ratios (General FHA Example)

Qualifying Ratios (percent)

Applicant Ratios (%)

FHA Maximum Ratios (%)

Housing expense ratio B/A 22 29 Total obligations ratio C/A 29 41

*The FHA may provide a closing cost allowance in determining the loan amount. Limits on this amount vary by region. †The maximum loan amount may not exceed limits set by FHA regulations. These limits vary by city and change over time. ‡The mortgage insurance premium is composed of two components, an up-front insurance premium, which may be financed or paid in cash, and an annual fee, which varies in terms of amount and term according to the loan-to-value ratio. See U.S. Department of Housing and Urban Development Mortgagee Letter 94–14 and revisions for a complete discussion on mortgage insurance premiums. §Usually, debt with 10 installments remaining. However, the underwriter can increase or decrease the number of installments depending on the total number of obligations outstanding and the relationship to borrower income.

Final PDF to printer

• Cover
• Real Estate Finance and Investments
• Preface
• Brief Contents
• Table of Contents
• PART ONE: OVERVIEW OF REAL ESTATE FINANCE AND INVESTMENTS
• Chapter 1: Real Estate Investment: Basic Legal Concepts
• Property Rights and Estates
• Definition of Estate
• Two General Classifications of Estates
• Examples of Freehold Estates
• Estates Not Yet in Possession (Future Estates)
• Examples of Leasehold Estates
• Interests, Encumbrances, and Easements
• Assurance of Title
• The Meaning of Title
• Deeds
• Methods of Title Assurance
• Abstract and Opinion Method
• The Title Insurance Method
• Recording Acts
• Limitations on Property Rights
• Chapter 2: Real Estate Financing: Notes and Mortgages
• Notes
• The Mortgage Instrument
• Definition of a Mortgage
• Relationship of Note to Mortgage
• Interests That Can Be Mortgaged
• Minimum Mortgage Requirements
• Important Mortgage Covenants
• Assumption of Mortgage
• Acquiring Title “Subject to” a Mortgage
• Property Covered by a Mortgage
• Junior Mortgages
• Recording of Mortgages
• Other Financing Sources
• Seller Financing
• Land Contracts
• Default
• What Constitutes Default?
• Alternatives to Foreclosure: Workouts
• Restructuring the Mortgage Loan
• Transfer of Mortgage to a New Owner
• Voluntary Conveyance
• Friendly Foreclosure
• Prepackaged Bankruptcy
• Short Sale
• Foreclosure
• Judicial Foreclosure
• Redemption
• Sales of Property
• Effect of Foreclosure on Junior Lienors
• Deficiency Judgment
• Taxes in Default
• Bankruptcy
• Chapter 7 Liquidation
• Chapter 11
• Chapter 13
• PART TWO: MORTGAGE LOANS
• Chapter 3: Mortgage Loan Foundations: The Time Value of Money
• Compound Interest
• Compound or Future Value
• Calculating Compound Interest Factors
• Using Financial Functions: Calculators and Spreadsheets
• Present Value
• A Graphic Illustration of Present Value
• Expanding the Use of Calculators for Finding Present Values
• Compound or Future Value of an Annuity
• Use of Compound Interest Factors for Annuities
• Present Value of an Annuity
• Use of the Present Value of an Annuity Factors
• Accumulation of a Future Sum
• Determining Yields, or Internal Rates of Return, on Investments
• Investments with Single Receipts
• Yields on Investment Annuities
• Equivalent Nominal Annual Rate (ENAR): Extensions
• Solving for Annual Yields with Partial Periods: An Extension
• Chapter 4: Fixed Interest Rate Mortgage Loans
• Determinants of Mortgage Interest Rates: A Brief Overview
• The Real Rate of Interest: Underlying Considerations
• Interest Rates and Inflation Expectations
• Interest Rates and Risk
• A Summary of Factors Important in Mortgage Loan Pricing
• Understanding Fixed Interest Rate Mortgage (FRM) Loan Terms
• Calculating Payments and Loan Balances—Fixed Interest Rate Loans
• The Importance of Accrued Interest and Loan Payments
• Loan Amortization Patterns
• Fully Amortizing, Constant Payment Mortgage (CPM) Loans
• Partially Amortizing, Constant Payment Mortgage (CPM) Loans
• Zero Amortizing, or Interest-Only—Constant Payment Mortgage (CPM) Loans
• Negative Amortizing, Constant Payment Mortgage (CPM) Loans
• Summary and Comparisons: Fixed Interest Rate, Constant Payment Mortgage (CPM) Loans with Various Amortization Patterns
• Determining Loan Balances
• Finding Loan Balances—Other Amortization Patterns
• Loan Closing Costs and Effective Borrowing Costs
• Loan Fees and Early Repayment: Fully Amortizing Loans
• Charging Fees to Achieve Yield, or When “Pricing” FRMs
• Financing Loan Fees and Other Closing Costs
• Other FRM Loan Patterns—Declining Payments and Constant Amortization Rates
• Amortization Schedules and Callable Loans
• “Reverse Mortgages”
• Appendix Inflation, Mortgage Pricing, and Payment Structuring
• Chapter 5: Adjustable and Floating Rate Mortgage Loans
• The Price Level Adjusted Mortgage (PLAM)
• PLAM: Payment Mechanics
• ARMs and Floating Rate Loans: An Overview
• Variations: ARM and Floating Rate Loans
• Risk Premiums, Interest Rate Risk, and Default Risk
• Expected Yield Relationships and Interest Rate Risk
• More Complex Features
• ARM Payment Mechanics
• Expected Yields on ARMs: A Comparison
• Chapter 6: Mortgages: Additional Concepts, Analysis, and Applications
• Incremental Borrowing Cost
• Early Repayment
• Origination Fees
• Incremental Borrowing Cost versus a Second Mortgage
• Relationship between the Incremental Cost and the Loan-to-Value Ratio
• Differences in Maturities
• Loan Refinancing
• Early Repayment: Loan Refinancing
• Effective Cost of Refinancing
• Borrowing the Refinancing Costs
• Other Considerations
• Early Loan Repayment: Lender Inducements
• Market Value of a Loan
• Effective Cost of Two or More Loans
• Second Mortgages and Shorter Maturities
• Effect of Below-Market Financing on Property Prices
• Assuming a Lower Loan Balance
• Cash Equivalency
• Cash Equivalency: Smaller Loan Balance
• Cash Equivalency: Concluding Comments
• Wraparound Loans
• Buydown Loans
• Appendix After-Tax Effective Interest Rate
• PART THREE: RESIDENTIAL HOUSING
• Chapter 7: Single-Family Housing: Pricing, Investment, and Tax Considerations
• Overview
• House Prices
• Income and Employment
• Renting versus Owning
• Analyzing Expected House Prices
• Economic Base Analysis—Location Quotients
• Housing Supply: An Overview
• Submarkets: Neighborhoods/Municipalities
• Capitalization Effects: Price Premiums
• Pricing Property in Specific Submarkets/Locations
• Investing in “Distressed Properties”
• Financial Framework for Analyzing Distressed Properties
• Acquisition Phase
• Holding Period Phase
• Disposition Phase—Exit Strategies
• Chapter 8: Underwriting and Financing Residential Properties
• Underwriting Default Risk
• Classification of Mortgage Loans
• Conventional Mortgage Loans
• Insured Conventional Mortgage Loans
• FHA-Insured Mortgage Loans
• VA-Guaranteed Mortgage Loans
• The Underwriting Process
• Borrower Income
• Verification of Borrower Assets
• Assessment of Credit History
• Estimated Housing Expense
• Other Obligations
• Compensating Factors
• The Underwriting Process Illustrated
• Underwriting Standards—Conventional and Insured Conventional Mortgages
• Underwriting Standards—FHA-Insured Mortgages
• Underwriting Standards—VA-Guaranteed Mortgages
• Underwriting and Loan Amounts—A Summary
• The Closing Process
• Fees and Expenses
• Prorations, Escrow Costs, and Payments to Third Parties
• Statutory Costs
• Requirements under the Real Estate Settlement and Procedures Act (RESPA)
• Settlement Costs Illustrated
• Federal Truth-in-Lending (FTL) Requirements
• Truth-in-Lending Sample Disclosure
• Establishing the APR under Federal Truth-in-Lending Requirements
• ARMs and Truth-in-Lending Disclosure
• PART FOUR: INCOME-PRODUCING PROPERTIES
• Chapter 9: Income-Producing Properties: Leases, Rents, and the Market for Space
• Property Types
• Supply and Demand Analysis
• Local Market Studies of Supply and Demand
• Location and User-Tenants
• The Business of Real Estate
• The “Market” for Income-Producing Real Estate
• Income Potential—Real Estate Assets
• Vacancy
• Underwriting Tenants
• General Contents of Leases
• Leases and Rental Income
• Leases and Responsibility for Expenses (Recoveries)
• Comparing Leases: Effective Rent
• Other Financial Considerations
• Developing Statements of Operating Cash Flow
• Case Example: Office Properties
• Rent Premiums and Discounts for Office Space
• Pro Forma Statement of Cash Flow—Office Properties
• Case Example: Industrial and Warehouse Properties
• Pro Forma Statement of Cash Flow—Industrial/Warehouse Properties
• Case Example: Retail Properties
• The Retail Leasing Environment
• CAM Charges—Recoveries
• Pro Forma Statement of Cash Flow—Retail Properties
• Case Example: Apartment Properties
• Chapter 10: Valuation of Income Properties: Appraisal and the Market for Capital
• Introduction
• Valuation Fundamentals
• Appraisal Process and Approaches to Valuation
• Sales Comparison Approach
• Income Approach
• Capitalization Rate
• Capitalization Rates—A Note of Caution
• Discounted Cash Flow Techniques
• Land Values: Highest and Best Use Analysis
• Volatility in Land Prices
• “Highest and Best Use” Analysis—Vacant Site
• “Highest and Best Use” Analysis—Improved Property
• Mortgage-Equity Capitalization
• Reconciliation: Sales Comparison and Income Capitalization Approaches
• Exploring the Relationships between Changing Market Conditions, Cap Rates, and Property Values
• A Closing Note on Cap Rates and Market Conditions
• A Word of Caution—Simultaneous Effects of Real Market Forces and Interest Rates on Property Values
• Leases: Valuation of a Leased Fee Estate
• Cost Approach
• Valuation Case Study—Oakwood Apartments
• RealNex Solution
• Appendix RealNex Inputs and Output for Apartment Analysis
• Chapter 11 Investment Analysis and Taxation of Income Properties
• Motivations for Investing
• Real Estate Market Characteristics and Investment Strategies
• The Real Estate Cycle
• Investment Strategies
• Market Analysis
• Supply of Space
• Market Rents
• Forecasting Supply, Demand, Market Rents, and Occupancy
• Making Investments: Projecting Cash Flows
• Office Building Example
• Base Rent
• Market Rent
• Expense Stops
• Net Operating Income
• Expected Outlays for Replacements and Capital Improvements
• Estimated Sale Price
• Introduction to Investment Analysis
• Internal Rate of Return (IRR)
• Present Value
• Introduction to Debt Financing
• Measures of Investment Performance Using Ratios
• Before-Tax Cash Flow from Sale
• Summary of Investment Analysis Calculations
• Taxation of Income-Producing Real Estate
• Taxable Income from Operation of Real Estate
• Depreciation Allowances
• Loan Points
• Tax Liability and After-Tax Cash Flow
• Taxable Income from Disposal of Depreciable Real Property
• After-Tax Investment Analysis
• After-Tax Cash Flow from Operations
• After-Tax Cash Flow from Sale
• After-Tax IRR
• Effective Tax Rate
• A Note about Passive Losses
• Special Exceptions to PAL Rules
• Appendix A Approaches to Metro Area Market Forecasting
• Appendix B RealNex Office Example
• Chapter 12 Financial Leverage and Financing Alternatives
• Introduction to Financial Leverage
• Conditions for Positive Leverage—Before Tax
• Conditions for Positive Leverage—After Tax
• Break-Even Interest Rate
• Risk and Leverage
• Underwriting Loans on Income Properties
• Market Study and Appraisal
• Borrower Financials
• The Loan-to-Value Ratio
• The Debt Coverage Ratio
• Other Loan Terms and Mortgage Covenants
• Alternatives to Fixed Rate Loan Structures
• Participation Loans
• Lender Motivations
• Investor Motivations
• Participation Example
• Sale-Leaseback of the Land
• Effective Cost of the Sale-Leaseback
• Interest-Only Loans
• Accrual Loans
• Structuring the Payment for a Target Debt Coverage Ratio
• Convertible Mortgages
• Lender’s Yield on Convertible Mortgages
• Comparison of Financing Alternatives
• Other Financing Alternatives
• Chapter 13 Risk Analysis
• Introduction
• Comparing Investment Returns
• Types of Risk
• Due Diligence in Real Estate Investment Risk Analysis
• Sensitivity Analysis
• Partitioning the IRR
• Variation in Returns and Risk
• Retail Case Study—Westgate Shopping Center
• Westgate Shopping Center Scenario Analysis
• Lease Rollover Risk
• Market Leasing Assumptions with Renewal Probabilities
• Market Rent
• Months Vacant
• Leasing Commissions
• Tenant Improvements
• Industrial Case Study—Worthington Distribution Center
• Risk and Leverage
• Monte Carlo Simulation
• Example
• Extensions of Monte Carlo Simulation
• Participation Example
• A “Real Options” Approach to Investment Decisions
• Traditional Approach to Land Valuation
• Real Option Approach to Land Valuation
• Real Options Extensions and Strategy
• Chapter 14 Disposition and Renovation of Income Properties
• Disposition Decisions
• A Decision Rule for Property Disposition
• IRR for Holding versus Sale of the Property
• Return to a New Investor
• Marginal Rate of Return
• Refinancing as an Alternative to Disposition
• Incremental Cost of Refinancing
• Leveraged Return from Refinancing and Holding an Additional Five Years
• Refinancing at a Lower Interest Rate
• Other Disposition Considerations—Portfolio Balancing
• Tax-Deferral Strategies upon Disposition
• Installment Sales
• Tax-Deferred Exchanges
• Renovation as an Alternative to Disposition
• Renovation and Refinancing
• Rehabilitation Investment Tax Credits
• Low-Income Housing
• Chapter 15 Financing Corporate Real Estate
• Lease-versus-Own Analysis
• Leasing versus Owning—An Example
• Cash Flow from Leasing
• Cash Flow from Owning
• Cash Flow from Owning versus Leasing
• Return from Owning versus Leasing
• Importance of the Residual Value of Real Estate
• The Investor’s Perspective
• A Note on Project Financing
• Factors Affecting Own-versus-Lease Decisions
• The Role of Real Estate in Corporate Restructuring
• Sale–Leaseback
• Refinancing
• Investing in Real Estate for Diversification
• Appendix Real Estate Asset Pricing and Capital Budget Analysis: A Synthesis
• PART FIVE: FINANCING REAL ESTATE DEVELOPMENT
• Chapter 16: Financing Project Development
• Introduction
• Overview: The Planning and Permitting Process
• The Development of Income-Producing Property
• Market Risks and Project Feasibility
• Project Risks
• Project Development Financing—An Overview
• Lender Requirements in Financing Project Development
• Interest Rates and Fees
• Project Development Illustrated
• Project Description and Project Costs
• Market Data and Tenant Mix
• Pro Forma Construction Costs and Cash Flow Projections
• Feasibility, Profitability, and Risk—Additional Issues
• Profitability before and after Taxes
• Sensitivity Analysis, Risk, and Feasibility Analysis
• Chapter 17: Financing Land Development Projects
• Characterization of the Land Development Business
• The Land Development Process—An Overview
• Acquisition of Land—Use of the Option Contract
• Financing and Development
• Lender Requirements in Financing Land Development
• Detailed Cost Breakdowns
• General Contracts and Subcontracts
• Residential Land Development Illustrated
• Market Conditions and Site Plan
• Estimating Development Cost and Interest Carry
• Estimating Release Prices per Parcel Sold
• Loan Request and Repayment Schedule
• Project Feasibility and Profitability
• Project IRR and Net Present Value
• Entrepreneurial Profits
• Sensitivity Analysis
• PART SIX: ALTERNATIVE REAL ESTATE FINANCING AND INVESTMENT VEHICLES
• Chapter 18: Structuring Real Estate Investments: Organizational Forms and Joint Ventures
• Introduction
• Sole Proprietorships
• Partnerships
• Limited Liability Companies
• Corporations
• Joint Ventures
• Organizational Forms
• Profit Sharing
• Initial Capital Contributions
• Sharing Cash Flow from Operations
• Sharing of Cash Flow from Sale
• Summary of Cash Flows Distributed in Each Operating Year
• Cash Flow from Sale
• IRR to Each Joint Venture Party
• Variation on the Preferred IRR—“The Lookback IRR”
• Syndications
• Use of the Limited Partnership in Private and Public Syndicates
• Private Syndication Problem Illustrated
• Financial Considerations—Partnership Agreement
• Operating Projections
• Statement of Before-Tax Cash Flow (BTCF)
• Calculation of Net Income or Loss
• Calculation of Capital Gain from Sale
• Capital Accounts
• Distribution of Cash from Sale of Asset
• Calculation of After-Tax Cash Flow and ATIRR on Equity
• Partnership Allocations and Substantial Economic Effect
• Capital Accounts and Gain Charge-Backs
• Use of the Limited Partnership in Private and Public Syndicates
• Use of Corporate General Partners
• Private versus Public Syndicates
• Accredited Investors—Regulation D
• Regulation of Syndicates
• Investment Objectives and Policies
• Promoters’ and Managers’ Compensation
• Investor Suitability Standards
• Federal and State Securities Authorities
• Chapter 19: The Secondary Mortgage Market:Pass-Through Securities
• Introduction
• Evolution of the Secondary Mortgage Market
• Early Buyers of Mortgage Loans
• The Secondary Market after 1954
• FNMA’s Changing Role
• The Government National Mortgage Association
• Mortgage-Backed Securities and the GNMA Payment Guarantee
• The Federal Home Loan Mortgage Corporation
• Operation of the Secondary Mortgage Market
• Direct Sale Programs
• The Development of Mortgage-Related Security Pools
• Mortgage-Backed Bonds
• Pricing Mortgage-Backed Bonds
• Subsequent Prices
• Mortgage Pass-Through Securities
• Important Characteristics of Mortgage Pools
• Mortgage Pass-Through Securities: A General Approach to Pricing
• Mortgage Pass-Through Payment Mechanics Illustrated
• Prepayment Patterns and Security Prices
• Prepayment Assumptions
• The Effects of Prepayment Illustrated
• Security Prices and Expected Yields
• Market Interest Rates and Price Behavior on Mortgage Pass-Throughs
• A Note on MBBs and MPTs
• Chapter 20: The Secondary Mortgage Market: CMOs and Derivative Securities
• Introduction
• Mortgage Pay-Through Bonds (MPTBs)
• Collateralized Mortgage Obligations
• CMOs Illustrated
• CMO Mechanics
• CMOs: Pricing and Expected Maturities
• CMO Price Behavior and Prepayment Rates
• CMO Tranche Variations
• Subprime Mortgage-Backed Securities
• Derivatives Illustrated
• Yield Enhancement
• IO and PO Strips
• Convexity
• Residential Mortgage-Related Securities: A Summary
• Residential Mortgage-Related Securities: Some Closing Observations
• Commercial Mortgage-Backed Securities (CMBSs)
• Rating Commercial Mortgage-Backed Securities
• Collateralized Debt Obligations (CDOs)
• Mortgage-Related Securities and REMICs
• REMICs: Other Considerations
• Appendix Duration—An Additional Consideration in Yield Measurement
• Chapter 21: Real Estate Investment Trusts (REITs)
• Introduction
• Legal Requirements
• Tax Treatment
• Violation Penalties and Status Termination
• Taxable REIT Subsidiaries
• TYPES of REITs
• Equity REITs
• The Investment Appeal of Equity REITs
• Public Nonlisted REITs
• Importance of FFO (Funds from Operations)
• REIT Expansion and Growth
• Important Issues in Accounting and Financial Disclosure: Equity REITs
• Tenant Improvements and Free Rents: Effects on FFO
• Leasing Commissions and Related Costs
• Use of Straight-Line Rents
• FFO and Income from Managing Other Properties
• Types of Mortgage Debt and Other Obligations
• Existence of Ground Leases
• Lease Renewal Options and REIT Rent Growth
• Occupancy Numbers: Leased Space or Occupied Space?
• Retail REITs and Sales per Square Foot
• Additional Costs of Being a Public Company
• The Investment Appeal of Mortgage REITs
• Financial Analysis of an Equity REIT Illustrated
• Valuing REITs as Investments
• Valuation of Midwestern America Property Trust
• PART SEVEN: PORTFOLIO ANALYSIS AND REAL ESTATE FUNDS
• Chapter 22: Real Estate Investment Performance and Portfolio Considerations
• Introduction
• The Nature of Real Estate Investment Data
• Sources of Data Used for Real Estate Performance Measurement
• REIT Data: Security Prices
• Hybrid and Mortgage REITs
• NCREIF Property Index: Property Values
• Data Sources for Other Investments
• Cumulative Investment Return Patterns
• Computing Holding Period Returns
• Comparing Investment Returns
• Risk, Return, and Performance Measurement
• Risk-Adjusted Returns: Basic Elements
• Elements of Portfolio Theory
• Calculating Portfolio Returns
• Portfolio Risk
• Portfolio Weighting: Trading Off Risk and Return
• Real Estate Returns, Other Investments, and the Potential for Portfolio Diversification
• Portfolio Diversification: EREITs and Other Investments
• Public versus Private Real Estate Investments
• Real Estate Performance and Inflation
• Diversification by Property Type and Location
• Global Diversification
• Risks of Global Investment
• Use of Derivatives to Hedge Portfolio Risk
• Example—Swap Office for Retail
• Up Shares and Down Shares
• Chapter 23: Real Estate Investment Funds: Structure, Performance, Benchmarking, and Attribution Analysis
• Investor Goals and Objectives
• General Explanation of Possible Provisions in Fund Offerings
• Reporting Fund Performance
• Measuring and Reporting Investment Returns
• Summary of Major Activity during Quarter
• Calculating Returns
• Calculating Returns at the Property Level
• Comparing Returns: Fund Level versus Property Level
• Returns: Before and After Fees
• Calculating Historical Returns
• Time-Weighted Returns
• Choosing IRR versus TWR for Performance Measurement
• Target Returns and Benchmarks
• Investment Multiple
• Attribution Analysis
• Attribution Analysis Mathematics
• Interpreting Sector Allocation
• Evaluating Risk Differences
• Jensen’s Alpha
• Indexes