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Chapter 7

Brief History of Risk and Return

Ayşe Yüce – Ryerson University

1.pdf

VALUATION AND MANAGEMENT

Investments

JORDAN MILLER DOLVIN YÜCE

third canadian edition

fundamentals of

Ayşe Yüce – Ryerson University

Learning Objectives

Separate yourself from the commoners by having a good

understanding of these security valuation methods:

1. The basic dividend discount model.

2. The two-stage dividend growth model.

3. The residual income model and free cash flow
model.

4. Price ratio analysis.

Common Stock Valuation

Ayşe Yüce – Ryerson University

Our goal in this chapter is to examine the methods commonly used by financial analysts to assess the economic value of common stocks.

These methods are grouped into four categories:
Dividend discount models
Residual Income model
Free Cash Flow model
Price ratio models

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Security Analysis: Be Careful Out There

Fundamental analysis is a term for studying a company’s accounting statements and other financial and economic information to estimate the economic value of a company’s stock.
The basic idea is to identify “undervalued” stocks to buy and “overvalued” stocks to sell.
In practice however, such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst.

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The Dividend Discount Model

The Dividend Discount Model (DDM) is a method to estimate the value of a share of stock by discounting all expected future dividend payments. The basic DDM equation is:

In the DDM equation:
P0 = the present value of all future dividends
Dt = the dividend to be paid t years from now
k = the appropriate risk-adjusted discount rate

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Example: The Dividend Discount Model

Suppose that a stock will pay three annual dividends of $200 per year, and the appropriate risk-adjusted discount rate, k, is 8%.
In this case, what is the value of the stock today?

The Dividend Discount Model:

The Constant Growth Rate Model

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Assume that the dividends will grow at a constant growth rate g. The dividend in the next period, (t + 1), is:

For constant dividend growth for “T” years, the DDM formula becomes:

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Example: The Constant Growth Rate Model

Suppose the current dividend is $10, the dividend growth rate is 10%, there will be 20 yearly dividends, and the appropriate discount rate is 8%.

What is the value of the stock, based on the constant growth rate model?

Ayşe Yüce – Ryerson University

The Dividend Discount Model:

The Constant Perpetual Growth Model

Assuming that the dividends will grow forever at a constant growth rate g.

For constant perpetual dividend growth, the DDM formula becomes:

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Example: Constant Perpetual Growth Model

Think about the electric utility industry.
In 2009, the dividend paid by the utility company, DTE Energy Co. (DTE), was $2.12.
Using D0 =$2.12, k = 5.75%, and g = 2%, calculate an estimated value for DTE.

Note: the actual mid-2009 stock price of DTE was $40.29.

What are the possible explanations for the difference?

Ayşe Yüce – Ryerson University

The Dividend Discount Model:

Estimating the Growth Rate

The growth rate in dividends (g) can be estimated in a number of ways:
Using the company’s historical average growth rate.
Using an industry median or average growth rate.
Using the sustainable growth rate.

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The Historical Average Growth Rate

Suppose the Broadway Joe Company paid the following dividends:
2005: $1.50 2008: $1.80
2006: $1.70 2009: $2.00
2007: $1.75 2010: $2.20
The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.

Sheet1

Year:	Dividend:	Pct. Chg:
2010	$2.20	10.00%
2009	$2.00	11.11%
2008	$1.80	2.86%		Grown at
2007	$1.75	2.94%	Year:	7.96%:
2006	$1.70	13.33%	2005	$1.50
2005	$1.50		2006	$1.62
			2007	$1.75
Arithmetic Average:		8.05%	2008	$1.89
			2009	$2.04
Geometric Average:		7.96%	2010	$2.20

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The Sustainable Growth Rate

Return on Equity (ROE) = Net Income / Equity
Payout Ratio = Proportion of earnings paid out as dividends
Retention Ratio = Proportion of earnings retained for investment

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Example: Calculating and Using the Sustainable Growth Rate

In 2009, American Electric Power (AEP) had an ROE of 10%, projected earnings per share of $2.90, and a per-share dividend of $1.64. What was AEP’s:
Retention rate?
Sustainable growth rate?
Payout ratio = $1.64 / $2.90 = .566 or 56.6%
So, retention ratio = 1 – .566 = .434 or 43.4%
Therefore, AEP’s sustainable growth rate = .10  .434 = .0434, or 4.34%

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Example: Calculating and Using the Sustainable Growth Rate

What is the value of AEP stock using the perpetual growth model and a discount rate of 5.75%?

The actual late-2009 stock price of AEP was $31.83.

In this case, using the sustainable growth rate to value the stock gives a reasonably poor estimate.

What can we say about g and k in this example?

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Analyzing ROE

To estimate a sustainable growth rate, you need the (relatively stable) dividend payout ratio and ROE.
Changes in sustainable growth rate likely stem from changes in ROE.
The DuPont formula separates ROE into three parts (profit margin, asset turnover, equity multiplier)

Managers can increase the sustainable growth rate by:
Decreasing the dividend payout ratio
Increasing profitability (Net Income / Sales)
Increasing asset efficiency (Sales / Assets)
Increasing debt (Assets / Equity)

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The Two-Stage Dividend Growth Model

The two-stage dividend growth model assumes that a firm will initially grow at a rate g1 for T years, and thereafter, it will grow at a rate g2 < k during a perpetual second stage of growth.

The Two-Stage Dividend Growth Model formula is:

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Using the Two-Stage Dividend Growth Model

Although the formula looks complicated, think of it as two parts:
Part 1 is the present value of the first T dividends (it is the same formula we used for the constant growth model).
Part 2 is the present value of all subsequent dividends.
So, suppose MissMolly.com has a current dividend of
D0 = $5, which is expected to shrink at the rate, g1 = 10%, for 5 years but grow at the rate, g2 = 4%, forever.
With a discount rate of k = 10%, what is the present value of the stock?

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Using the Two-Stage Dividend Growth Model

The total value of $46.03 is the sum of a $14.25 present value of the first five dividends, plus a $31.78 present value of all subsequent dividends.

Ayşe Yüce – Ryerson University

Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth

Chain Reaction, Inc., has been growing at a phenomenal rate of 30% per year.
You believe that this rate will last for only three more years.
Then, you think the rate will drop to 10% per year.
Total dividends just paid were $5 million.
The required rate of return is 20%.
What is the total value of Chain Reaction, Inc.?

Ayşe Yüce – Ryerson University

Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth

First, calculate the total dividends over the “supernormal” growth period:

Using the long run growth rate, g, the value of all the shares at Time 3 can be calculated as:

P3 = [D3 x (1 + g)] / (k – g)

P3 = [$10.985 x 1.10] / (0.20 – 0.10) = $120.835

Year	Total Dividend: (in $millions)
1	$5.00 x 1.30 = $6.50
2	$6.50 x 1.30 = $8.45
3	$8.45 x 1.30 = $10.985

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Example: Using the DDM to Value a Firm Experiencing “Supernormal” Growth

To determine the present value of the firm today, we need the present value of $120.835 and the present value of the dividends paid in the first 3 years:

If there are 20 million shares outstanding, the price per share is $4.38.

Ayşe Yüce – Ryerson University

The H-Model

For Chain Reaction, Inc., we assumed a supernormal growth rate of 30 percent per year for three years, and then growth at a perpetual 10 percent.
The growth rate is more likely to start at a high level and then fall over time until reaching its perpetual level.
Many possible ways to assume how the growth rate declines
A popular way is the H-model: which assumes a linear growth rate decline

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The H-Model

Let’s revisit Chain Reaction, Inc.
Suppose the growth rate begins at 30% and reaches 10% in year 4 and beyond.
Using the H-model, we would assume that the company’s growth rate would decline by 20% from the end of year 1 to the beginning of year 4.
If we assume a linear decline:
the growth rate falls by 6.67% per year (20%/3 years).
Growth estimates would be: 30%, 23.33%, 16.66%, and 10%
Using these growth estimates, you will find that the firm value is $75.93 million, or $3.80 per share.
The value is lower than before because of the lower growth rates in years 2 and 3.

Ayşe Yüce – Ryerson University

Discount Rates for Dividend Discount Models

The discount rate for a stock can be estimated using the capital asset pricing model (CAPM ).
We will discuss the CAPM in a later chapter.
However, we can estimate the discount rate for a stock using this formula:
Discount rate = time value of money + risk premium = U.S. T-bill Rate + (Stock Beta x Stock Market Risk Premium)

T-bill Rate:	return on 90-day U.S. T-bills
Stock Beta:	risk relative to an average stock
Stock Market Risk Premium:	risk premium for an average stock

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Observations on Dividend Discount Model

Constant Perpetual Growth Model:

Simple to compute
Not usable for firms that do not pay dividends
Not usable when g > k
Is sensitive to the choice of g and k
k and g may be difficult to estimate accurately.
Constant perpetual growth is often an unrealistic assumption.

Observations on Dividend Discount Models

Ayşe Yüce – Ryerson University

Two-Stage Dividend Growth Model:

More realistic in that it accounts for two stages of growth
Usable when g > k in the first stage
Not usable for firms that do not pay dividends
Is sensitive to the choice of g and k
k and g may be difficult to estimate accurately.

Residual Income Model (RIM)

Ayşe Yüce – Ryerson University

We have valued only companies that pay dividends.

But, there are many companies that do not pay dividends.
What about them?
It turns out that there is an elegant way to value these companies, too.

The model is called the Residual Income Model (RIM).

Major Assumption (known as the Clean Surplus Relationship, or CSR): The change in book value per share is equal to earnings per share minus dividends.

Residual Income Model (RIM)

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Inputs needed:
Earnings per share at time 0, EPS0
Book value per share at time 0, B0
Earnings growth rate, g
Discount rate, k

There are two equivalent formulas for the Residual Income Model:

BTW, it turns out that the RIM is mathematically the same as the constant perpetual growth model.

Using the Residual Income Model

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Duckwall—Alco Stores, Inc. (DUCK)
It is July 1, 2010—shares are selling in the market for $10.94.
Using the RIM:
EPS0 = $1.20
DIV = 0
B0 = $5.886
g = 0.09
k = .13

What can we say
about the market
price of DUCK?

The Growth of DUCK

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Using the information from the previous slide, what growth rate results in a DUCK price of $10.94?

Free Cash Flow

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We can value companies that do not pay dividends using the residual income model.
Note: We assume positive earnings when we use the residual income model.
But, there are companies that do not pay dividends and have negative earnings.
Negative earnings = little value?
We calculate earnings based on accounting rules and tax codes.
It is possible that a company has:
negative earnings
positive cash flows
a positive value.

Free Cash Flow

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Depreciation—the key to understand how a company can have negative earnings and positive cash flows
Depreciation reduces earnings because it is counted as an expense (more expenses = lower taxes paid).

Most stock analysts, however, use a relatively simple formula to calculate Free Cash Flow, FCF:

FCF = Net Income + Depreciation – Capital Spending

We can see that it is possible for: Net Income < 0 and FCF > 0
Depreciation and Capital Spending matter in FCF.

DDMs Versus FCF

Ayşe Yüce – Ryerson University

The DDMs calculate a value of the equity only.
DDMs use dividends, a cash flow only to equity holders
DDMs use the CAPM to estimate required return
DDMs use an equity beta to account for risk

Using the FCF model, we calculate a value for the firm.
Free cash flow can be paid to debt holders and to stockholders.
We can still calculate the value of equity using FCF
Calculate the value of the entire firm
Subtract out the value of debt
We need a beta for assets, not the equity, to account for risk

Asset Betas

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Asset betas measure the risk of the company’s industry.
Firms in an industry should have about the same asset betas.
Their equity betas, however, could be quite different.
Investors can increase portfolio risk by using margin (i.e., borrowing money to buy stock).
A business can increase risk by using debt.
So, to value the company, we must “convert” reported equity betas into asset betas by adjusting for leverage.
The following conversion formula is widely used:

What happens when a firm has no debt?

tax rate.

The FCF Approach, Example

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Inputs
An estimate of FCF:
Net Income
Depreciation
Capital Expenditures
The growth rate of FCF
The proper discount rate
Tax rate
Debt/Equity ratio
Equity beta

Calculate value using a “DDM” formula

“DDM” because we are using FCF, not dividends.

Valuing Landon Air: A New Airline

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An estimate of FCF:
Net Income: $25 million
Depreciation: $10 million
Capital Expenditures: $3 million
Growth rate of FCF: 3%
Tax rate: 35%
Debt/Equity ratio: .40
Equity beta: 1.2

Asset Beta:

1.2 = BAsset x [1+.4 x (1-.35)]

1.2 = BAsset x 1.26

BAsset = 0.95

The proper discount rate: k = 4.00 + (7.00 × 0.95) = 10.65%

Assume:

No dividends

Risk-free rate = 4%

Market risk premium = 7%

Price Ratio Analysis

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Price-earnings ratio (P/E ratio)
Current stock price divided by annual earnings per share (EPS)
Earnings yield
Inverse of the P/E ratio: earnings divided by price (E/P)
High-P/E stocks are often referred to as growth stocks, while low-P/E stocks are often referred to as value stocks.

Price Ratio Analysis

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Price-cash flow ratio (P/CF ratio)
Current stock price divided by current cash flow per share
In this context, cash flow is usually taken to be net income plus depreciation.
Most analysts agree that in examining a company’s financial performance, cash flow can be more informative than net income.
Earnings and cash flows that are far from each other may be a signal of poor quality earnings.

Price Ratio Analysis

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Price-sales ratio (P/S ratio)
Current stock price divided by annual sales per share
A high P/S ratio suggests high sales growth, while a low P/S ratio suggests sluggish sales growth.
Price-book ratio (P/B ratio)
Market value of a company’s common stock divided by its book (accounting) value of equity
A ratio bigger than 1.0 indicates that the firm is creating value for its stockholders.

Price/Earnings Analysis, Intel Corp.

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Intel Corp (INTC) - Earnings (P/E) Analysis

5-year average P/E ratio 20.96

Current EPS $.92

EPS growth rate 8.5%

Expected stock price = historical P/E ratio  projected EPS

$20.92 = 20.96  ($.92  1.085)

Late-2009 stock price = $19.40

Price/Cash Flow Analysis, Intel Corp.

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Intel Corp (INTC) - Cash Flow (P/CF) Analysis

5-year average P/CF ratio 10.85

Current CFPS $1.74

CFPS growth rate 7.5%

Expected stock price = historical P/CF ratio  projected CFPS

$20.29 = 10.85  ($1.74  1.075)

Late-2009 stock price = $19.40

Price/Sales Analysis, Intel Corp.

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Intel Corp (INTC) - Sales (P/S) Analysis

5-year average P/S ratio 3.14

Current SPS $6.76

SPS growth rate 7%

Expected stock price = historical P/S ratio  projected SPS

$22.71 = 3.14  ($6.76  1.07)

Late-2009 stock price = $19.40

An Analysis of the McGraw-Hill Company

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The next few slides contain a financial analysis of the McGraw-Hill Company, using data from the Value Line Investment Survey.

The McGraw-Hill Company Analysis

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The McGraw-Hill Company Analysis

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The McGraw-Hill Company Analysis, III

Based on the CAPM, k = 4.0% + (1.2  7%) = 12.4%
Retention ratio = 1 – $.90/$2.55 = .65
Sustainable g = .65  36.5% = 23.73%

(Value Line reports a projected ROE of 36.5%)

Because g > k, the constant growth rate model cannot be used. (We would get a value of -$9.83 per share)

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The McGraw-Hill Company Analysis
(Using the Residual Income Model)

Let’s assume that “today” is January 1, 2010, g = 8.5%, and k = 12.4%.
Using the Value Line Investment Survey (VL), we can fill in column two (VL) of the table below.
We use column one and our growth assumption for column three (CSR) of the table below.

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End of 2009	2010 (VL)	2010 (CSR)
Beginning BV per share	NA	$5.95	$5.95
EPS	$2.30	$2.55	$2.4955
DIV	$.90	$.90	$1.9897
Ending BV per share	$5.95	$7.05	$6.4558

The McGraw-Hill Company Analysis
(Using the Residual Income Model)

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Using the CSR assumption:

Using Value Line numbers for EPS1=$2.55, B1=$7.05
B0=$5.95; and using the actual change in book value instead of an estimate of the new book value, (i.e., B1-B0 is = B0 x k)

Stock price at the time = $28.73.
What can we say?

The McGraw-Hill Company Analysis

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Useful Internet Sites

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www.nyssa.org (The New York Society of Security Analysts)
www.aaii.com (The American Association of Individual Investors)
www.valueline.com (the home of the Value Line Investment Survey)
Websites for some companies analyzed in this chapter:
www.aep.com
www.intel.com
www.mcgraw-hill.com

Ayşe Yüce – Ryerson University

Chapter Review

Security Analysis: Be Careful Out There

The Dividend Discount Model
Constant Dividend Growth Rate Model
Constant Perpetual Growth
Applications of the Constant Perpetual Growth Model
The Sustainable Growth Rate

The Two-Stage Dividend Growth Model
Discount Rates for Dividend Discount Models
Observations on Dividend Discount Models

40.pdf

VALUATION AND MANAGEMENT

Investments

JORDAN MILLER DOLVIN YÜCE

third canadian edition

fundamentals of

Ayşe Yüce – Ryerson University

Chapter Review

Residual Income Model (RIM)

Free Cash Flow Model

Price Ratio Analysis
Price-Earnings Ratios
Price-Cash Flow Ratios
Price-Sales Ratios
Price-Book Ratios
Applications of Price Ratio Analysis
An Analysis of the McGraw-Hill Company

41.pdf

VALUATION AND MANAGEMENT

Investments

JORDAN MILLER DOLVIN YÜCE

third canadian edition

fundamentals of

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