Chapter

McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved.

6 Common Stock Valuation

6-2

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.

4. Price ratio analysis.

6-3

Common Stock Valuation

• 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 three categories:– Dividend discount models– Residual Income models– Price ratio models

6-4

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.

6-5

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

TT

33

221

0k1

D

k1

D

k1

D

k1

DP

6-6

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?

$515.42

0.081

$200

0.081

$200

0.081

$200P

k1

D

k1

D

k1

DP

320

33

221

0

6-7

The Dividend Discount Model: the Constant Growth Rate Model

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

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

g k if D T P

g k if k1

g11

gk

g)(1DP

00

T

10

g)(1g)(1D g)(1 D D So,

g1DD

012

t1t

6-8

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?

$243.86

1.08

1.101

.10.08

1.10$10P

k1

g11

gk

g)(1DP

20

0

T

00

6-9

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:

k)g :(Important

gk

D

gk

g1DP 10

0

6-10

Example: Constant Perpetual Growth Model

• Think about the electric utility industry. • In 2007, the dividend paid by the utility company, DTE Energy Co.

(DTE), was $2.12.

• Using D0 =$2.12, k = 6.7%, and g = 2%, calculate an estimated value for DTE.

Note: the actual mid-2007 stock price of DTE was $47.81.

What are the possible explanations for the difference?

$46.01

.02.067

1.02$2.12P0

6-11

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.

6-12

The Historical Average Growth Rate

• Suppose the Broadway Joe Company paid the following dividends:

– 2002: $1.50 2005: $1.80– 2003: $1.70 2006: $2.00– 2004: $1.75 2007: $2.20

• The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.

Year: Dividend: Pct. Chg:2007 $2.20 10.00%2006 $2.00 11.11%2005 $1.80 2.86% Grown at2004 $1.75 2.94% Year: 7.96%:2003 $1.70 13.33% 2002 $1.502002 $1.50 2003 $1.62

2004 $1.758.05% 2005 $1.89

2006 $2.047.96% 2007 $2.20

Arithmetic Average:

Geometric Average:

6-13

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

Ratio) Payout - (1 ROE

Ratio Retention ROE Rate Growth eSustainabl

6-14

Example: Calculating and Using the Sustainable Growth Rate

• In 2007, American Electric Power (AEP) had an ROE of 10.17%, projected earnings per share of $2.25, and a per-share dividend of $1.56. What was AEP’s:– Retention rate?– Sustainable growth rate?

• Payout ratio = $1.56 / $2.25 = .693

• So, retention ratio = 1 – .693 = .307 or 30.7%

• Therefore, AEP’s sustainable growth rate = .1017 .307 = .03122, or 3.122%

6-15

Example: Calculating and Using the Sustainable Growth Rate, Cont.

• What is the value of AEP stock, using the perpetual growth model, and a discount rate of 6.7%?

• The actual mid-2007 stock price of AEP was $45.41.

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

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

$44.96

.03122.067

1.03122$1.56P

0

6-16

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 grow at a rate g2 < k during a perpetual second

stage of growth.

• The Two-Stage Dividend Growth Model formula is:

2

20

T

1

T

1

1

10

gk

)g(1D

k1

g1

k1

g11

gk

)g(1DP

0

6-17

Using the Two-Stage Dividend Growth Model, I.

• 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?

6-18

Using the Two-Stage Dividend Growth Model, II.

• 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.

$46.03.

$31.78 $14.25

0.040.10

0.04)$5.00(1

0.101

0.90

0.101

0.901

0.10)(0.10

)$5.00(0.90P

gk

)g(1D

k1

g1

k1

g11

gk

)g(1DP

55

2

20

T

1

T

1

1

10

0

0

6-19

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

• 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.?

6-20

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

• 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

6-21

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

• Therefore, 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:

million. $87.58

$69.93$6.36$5.87$5.42

0.201

$120.835

0.201

$10.985

0.201

$8.45

0.201

$6.50P

k1

P

k1

D

k1

D

k1

DP

332

33

33

221

0

0

6-22

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

6-23

Observations on Dividend Discount Models, I.

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.

6-24

Observations on Dividend Discount Models, II.

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.

6-25

Residual Income Model (RIM), I.

• 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.

6-26

Residual Income Model (RIM), II.

• 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:

gk

gBEPSP

or

gk

kBg)(1EPSBP

010

0000

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

6-27

Using the Residual Income Model.

• Superior Offshore International, Inc. (DEEP)• It is July 1, 2007—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 sayabout the marketprice of DEEP?

$19.46..04

$.7652$1.308$5.886P

.09.13

.13$5.886.09)(1$1.20$5.886P

gk

kBg)(1EPSBP

0

0

0000

6-28

DEEP Growth

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

3.55%. or .0355g

6.254g.2222

.43481.20g5.054g$.6570

.76521.20g1.20g)(.13$5.054

g.13

.13$5.886g)(1$1.20$5.886$10.94

gk

kBg)(1EPSBP 00

00

6-29

Price Ratio Analysis, I.

• 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.

6-30

Price Ratio Analysis, II.

• 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.

6-31

Price Ratio Analysis, III.

• 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.

6-32

Price/Earnings Analysis, Intel Corp.

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

5-year average P/E ratio 27.30Current EPS $.86EPS growth rate 8.5%

Expected stock price = historical P/E ratio projected EPS

$25.47 = 27.30 ($.86 1.085)

Mid-2007 stock price = $24.27

6-33

Price/Cash Flow Analysis, Intel Corp.

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

5-year average P/CF ratio 14.04Current CFPS $1.68CFPS growth rate 7.5%

Expected stock price = historical P/CF ratio projected CFPS

$25.36 = 14.04 ($1.68 1.075)

Mid-2007 stock price = $24.27

6-34

Price/Sales Analysis, Intel Corp.

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

5-year average P/S ratio 4.51Current SPS $6.14SPS growth rate 7%

Expected stock price = historical P/S ratio projected SPS

$29.63 = 4.51 ($6.14 1.07)

Mid-2007 stock price = $24.27

6-35

An Analysis of theMcGraw-Hill Company

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

6-36

The McGraw-Hill Company Analysis, I.

6-37

The McGraw-Hill Company Analysis, II.

6-38

The McGraw-Hill Company Analysis, III.

• Based on the CAPM, k = 3.1% + (.80 9%) = 10.3%

• Retention ratio = 1 – $.66/$2.65 = .751

• Sustainable g = .751 23% = 17.27%

• Because g > k, the constant growth rate model cannot be used. (We would get a value of -$11.10 per share)

6-39

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

• Let’s assume that “today” is January 1, 2008, g = 7.5%, and k = 12.6%.

• 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.

End of 2007 2008 (VL) 2008 (CSR)

Beginning BV per share NA $6.50 $6.50

EPS $3.05 $3.45 $3.2788

DIV $.82 $.82 $2.7913

Ending BV per share $6.50 $9.25 $6.9875

1.0753.05 1.0756.50

6.50)- (6.9875-3.2788 Plug""

6-40

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

• Using the CSR assumption:

• Using Value Line numbers for EPS1=$3.45, B1=$9.25B0=$6.50; 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)

$54.73.P

.075.126

.126$6.50.075)(1$3.05$6.50P

gk

kBg)(1EPSBP

0

0

0000

$20.23P

.075.126

6.50)-($9.25$3.45$6.50P

gk

kBg)(1EPSBP

0

0

0000

Stock price at the time = $57.27.What can we say?

6-41

The McGraw-Hill Company Analysis, IV.

6-42

Useful Internet Sites

• www.nyssa.org (the New York Society of Security Analysts)• www.aaii.com (the American Association of Individual

Investors)• www.eva.com (Economic Value Added)• www.valueline.com (the home of the Value Line Investment

Survey)

• Websites for some companies analyzed in this chapter:• www.aep.com • www.americanexpress.com • www.pepsico.com • www.intel.com • www.corporate.disney.go.com • www.mcgraw-hill.com

6-43

Chapter Review, I.

• 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

6-44

Chapter Review, II.

• The Two-Stage Dividend Growth Model– Discount Rates for Dividend Discount Models

– Observations on Dividend Discount Models

• Residual Income Model (RIM)

• 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