Application of Concepts/Time Value of Money, APA Format 400 to 600 words. All required files attached.
Logan_9
Chapter5-PowerPoint-Notes1.pptFinance 3rd Edition Cornett, Adair, and Nofsinger
5
Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
Time Value of Money 2: Analyzing Annuity Cash Flows
5-*
Introduction
Time Value of Money calculations
Can deal with either single cash flows
Or multiple cash flows over time
5-*
Future Value of Multiple Cash Flows
Multiple cash flows
Regular, evenly-spaced
Car loans and home mortgage loans
Saving for retirement
Companies paying interest on debt
Companies paying dividends
5-*
Future Value – Several Cash Flows
Concept: Compounding
Value in the future
Different cash flows paid in at different times
...
5-*
Finding FV – Several Cash Flows Example
Assumptions
Invest $100 today (compounds for 3 years)
Invest $125 at end of year 2 (compounds for 2 years)
Invest $150 at end of year 3 (compounds for 1 year)
Interest rates: 7%
...
5-*
FV Several Cash Flows Time Line Example
...
Several (Different) Cash Flow Values
5-*
Future Value – Level Cash Flows
Concept: Compounding
Also called “annuities”
Value in the future
Same cash flows paid in every period
...
5-*
Finding FV – Level Cash Flows/Annuity Example
Assumptions
Invest $100 at the end of each year for 5 years
Interest rates: 8%
...
5-*
Level Cash Flows Time Line Example
...
Level (same) Cash Flows Each Period
5-*
Future Value – Multiple Annuities
Concept: Compounding – annuity equation to compute future value – two levels of cash flows
To solve for multiple annuities, compute FV for each separately and add them together
...
5-*
Finding FV – Multiple Annuities Example
Assumptions
Invest $100 at end of years 1 - 3 at 8%
Invest $150 at end of years 4 - 5 at 8%
...
5-*
Future Value – Multiple Annuities
Step 1 (same as FV of Level Cash Flows Calculation)
Step 2
Add two sums together – FV of both is $690.66
Step 3
5-*
Present Value of Multiple Cash Flows
Multiple cash flows
Car loans and home mortgage loans
Determining value of business opportunities
5-*
Present Value – Several Cash Flows
Concept: Discounting
Value of future sum today
Different cash flows paid in at different times
...
5-*
Finding PV – Several Cash Flows Example
Assumptions
Deposit $100 today
Deposit $125 next year
Deposit $150 at end of year 2
Interest rates: 7%
...
5-*
PV Several Cash Flows Time Line Example
...
5-*
Present Value – Level Cash Flows
Concept: Discounting
Value of future sum today
Level cash flows paid in at different times
Most loans set up with even payments throughout life of loan
...
5-*
Finding PV – Level Cash Flows Example
Assumptions
$100 payments at end of each year for 5 years
Interest rates: 8% per year
...
5-*
PV Level Cash Flows Time Line Example
...
5-*
Present Value – Multiple Annuities
Concept: Discounting
Changing level cash flows
Ex: Alex Rodriguez’s baseball contract
...
5-*
PV – Multiple Annuities Example
Assumptions (Alex Rodriguez’s Contract)
$10 million signing bonus
$21 million per year from 2001 – 2004
$25 million per year in 2005 and 2006
$27 million per year in 2007 – 2010
Interest rates: 8% per year
...
5-*
PV – Multiple Annuities Example (cont.)
5-*
Perpetuity – Special Annuity
Concept: Discounting
Stream of level cash flows paid forever
Preferred stocks are an example
Value of investment is present value of all future annuity payments
...
5-*
Ordinary Annuities vs. Annuities Due
Ordinary Annuity
Payment occurs at the end of each period
Annuity Due
Payment occurs at the beginning of each period
5-*
Annuity Due Time Line Example
Cash flows at beginning, not at end of period
Five annuity-due cash flows basically same as payment today plus 4-year ordinary annuity
Payments occur one period sooner than ordinary annuity -- earn extra period of interest
...
5-*
Future Value of Annuity Due
Concept: Compounding
Value of future sum today
Cash flows at beginning of each period
...
5-*
Future Value of Annuity Due
Assumptions
Assumes cash flows at the beginning of each period
5 annuity-due cash flows of $100 each
First cash flow compounds for 5 years
Last cash flow compounds for 1 year
Interest rates: 8%
...
5-*
Present Value of Annuity Due
Concept: Discounting
Today’s value of future sum
Cash flows at beginning of each period
...
5-*
Present Value of Annuity Due
Assumptions
Cash flows at beginning of period
5 annuity-due cash flows of $100
First cash flow paid today – not discounted
Last cash flow discounted 4 years
All cash flows discounted for one year less than ordinary annuity
Interest rates: 8%
...
5-*
Compounding Frequency
Used in situations that do not use yearly time periods
Semiannual bond payments
Quarterly stock dividends
Consumer loans – monthly payments
5-*
Effect of Compounding Frequency
Assumptions
$100 deposit today
12% annual interest rate
Bank compounds interest at six months instead of end of year
Interest is earned on interest
...
5-*
EARS and APRS
Quoted, or nominal rate called annual percentage rate (APR)
Rate that incorporates compounding called effective annual rate (EAR)
Relationship between APR and EAR
...
5-*
EARS vs. APR Example
Assumptions
Borrow $100 today
12% annual interest rate
APR: Loan compounds annually -- you pay 12.00%
EARS: Loan compounds monthly -- you pay 12.68%
...
5-*
Annuity Loans
Compares payments
Compares implied interest rate
5-*
Finding Payments on Amortized Loan
Concept
Rearrange PV of annuity formula to solve for payment
...
5-*
Payments on Amortized Loan Example
Assumptions
Need $10,000 to buy car
Loan term: 4 years
Interest rate: 9% APR
Use interest rate of 0.75 % (=9%/12) and 48 periods (=4 X 12)
...
