Corporate Finance Thirteenth Edition

Stephen A. Ross / Randolph W. Westerfield / Jeffrey F. Jaffe /

Bradford D. Jordan

Chapter 9 (Topic 3)

• Stock Valuation

• © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.
Key Concepts and
Skills
•Understand how stock prices
depend on future dividends
and dividend growth
•Be able to compute stock
prices using the dividend
growth model
•Understand valuation
comparable
•Understand the basics of the
stock market

© 2019 McGraw-Hill Education. 9-2

9.1 The Present Value of Common
Stocks

Stock
ownership • Dividends
produces cash • Capital Gains
flows from:

Valuation of • Zero Growth

Different Types • Constant Growth
of Stocks • Differential Growth

© 2019 McGraw-Hill Education. 9-3

 Case 1: Zero Growth

Assume that dividends will remain at the same level

forever
D1 D2 D3 
• Since future cash flows are constant, the value of a
zero growth stock is the present value of a perpetuity:
D1 D2 D3
P0 = + + + 
1+ R 1+ R  1+ R 
2 3

D
P0 =
R

© 2019 McGraw-Hill Education. 9-4

 Case 2: Constant Growth

Assume that dividends will grow at a constant rate, g,

forever, i.e.,
D1 D0 (1  g )
D2 D1 (1  g ) D0 (1  g ) 2
D3 D2 (1  g ) D0 (1  g ) 3
Since future cash flows grow at a constant rate
forever, the value of a constant growth stock is the
present value of a growing perpetuity:
D1
P0 
R g
© 2019 McGraw-Hill Education. 9-5
 Constant Growth Example

Suppose Big D, Inc., just paid a dividend of $.50. It is

expected to increase its dividend by 2% per year. If the
market requires a return of 15% on assets of this risk
level, how much should the stock be selling for?

P0 = .50 1 + .02  .15 – .02  = $3.92

D1=D0*(1+g) R-g

© 2019 McGraw-Hill Education. 9-6

 Case 3: Differential Growth – I

Assume that dividends will grow at different rates in the

foreseeable future and then will grow at a constant
rate thereafter.
To value a differential growth stock, we need to:
• Estimate future dividends in the foreseeable future.
• Estimate the future stock price when the stock
becomes a constant growth stock (Case 2).
• Compute the total present value of the estimated
future dividends and future stock price at the
appropriate discount rate.

© 2019 McGraw-Hill Education. 9-8

 Case 3: Differential Growth – II

Assume that dividends will grow at rate g1 for N years

and grow at rate g2 thereafter.

D1 = D0 1+ g1 
D2 = D1 1+ g1  = D0 1 + g1 
2


DN = DN -1 1+ g1  = D0 1 + g1 
N

DN+1 = DN 1+ g 2  = D0 1 + g1  1 + g 2 
N

© 2019 McGraw-Hill Education. 9-9

 Case 3: Differential Growth – III

Dividends will grow at rate g1 for N years and grow at

rate g2 thereafter

© 2019 McGraw-Hill Education. 9-10

 Case 3: Differential Growth – IV

We can value this as the sum of:

a T-year annuity growing at rate g1
 1 + g1  
T
C
PA = 1  
1  R 
T
R  g1  

plus the discounted value of a perpetuity growing at
rate g2 that starts in year T+1
 DT 1 
 
 R  g2 
PB 
(1  R)T
© 2019 McGraw-Hill Education. 9-11
 Case 3: Differential Growth - V

Consolidating gives:
D1
 DT 1 
 
C  (1  g1 )   R  g 2 
T
P 1  T 

R  g1  (1  R )  (1  R )T

Or, we can “cash flow” it out.

Not applicable for the case: R ≤ g1

© 2019 McGraw-Hill Education. 9-12

 A Differential Growth Example

A common stock just paid a dividend of $2. The

dividend is expected to grow at 8% for 3 years, then it
will grow at 4% in perpetuity.
What is the stock worth? Assume the discount rate is
12%.

© 2019 McGraw-Hill Education. 9-13

 With the Formula
g1
 $2(1.08) 3 (1.04) 
 
$2 (1.08)  (1.08)  3
.12  .04  g2
P  1  3

.12  .08  (1.12)  (1.12) 3
$32.75 N
P $54 1  .8966 
(1.12) 3
P $5.58  $23.31
P $28.89

© 2019 McGraw-Hill Education. 9-14

 With Cash Flows

The constant growth

phase beginning in year
4 can be valued as a
growing perpetuity at
time 3.
$2.16 $2.33 $2.52  $32.75
P0    $28.89
   
2 3
1.12 1.12 1.12

Access the text alternative for slide images

© 2019 McGraw-Hill Education. 9-15
 Variable Dividend Growth Rate

It may be unreasonable to assume that a firm will

grow at the same rate forever.
Firm grow at different rates over different time
periods.
Example: Current dividend is $1.50 per share.
Expected to grow at 15% rate for next 3 years.
After 3-years, dividends are expected to grow at
more normal rate of 8% per year indefinitely. If
required return on the stock is 12%, what price
would you willing to pay for a share of the stock?

Copyright© 2008 John Wiley & Sons, Inc . 16

 Variable Dividend Growth Rate ( continued)

First, calculate the dividends in the above-normal

period of growth and in the first period of normal
growth.
Calculate the dividends for the first 4 years.
D1 = $1.50 (1.15)1 = $1.72
CF1=1.72
D2 = $1.50 (1.15) = S1.98 CF2=1.98
2 D1=D0(1+g)
CF3=2.28
D3 = $1.50 (1.15) = S2.28 I=12
3

D4 = $2.28(1.08) = $2.46 NPV=4.74

Calculate the price at the end of the above-normal

growth period.

Copyright© 2008 John Wiley & Sons, Inc . 17

 Variable Dividend Growth Rate ( continued)

Calculate the price at the end of the above-normal

growth period.
P0  D1 /( r  g )
P3 = D4 FV=61.6
r-g N=3
I=12
= $2.46 PV=43.85
0.12-0.08

= $61.60

Substitute the values for D1, D2, D3 and P3 into

equation in order to calculate current stock price
Current stock price = 4.74+ 43.85= $ 48.58
If currently selling at $49—OVERPRICED, SELL
If currently selling at $48—UNDERPRICED, BUY
Copyright© 2008 John Wiley & Sons, Inc . 18
 9.2 Estimates of Parameters in
the Dividend Discount Model
The value of a firm depends upon its growth rate, g,
and its discount rate, R.
• Where does g come from?
g = Retention ratio × Return on retained earnings
(ROE)

How much the How much the

company kept company earned

© 2019 McGraw-Hill Education. 9-19

 Where Does R Come From?

The discount rate can be broken into two parts.

• The dividend yield
• The growth rate (in dividends)

In practice, there is a great deal of estimation error

involved in estimating R.

© 2019 McGraw-Hill Education. 9-20

 Using the DGM to Find R

Start with the DGM:

D0 (1  g ) D1
P0  
R–g R–g

Rearrange and solve for R:

D0 (1  g ) D1
R  g  g
P0 P0

Market price

© 2019 McGraw-Hill Education. 9-21

 9.3 Comparables

Comparables are used to value companies based

primarily on multiples.

Common multiples include:

• Price-Earnings Ratios
• Enterprise Value Ratios

© 2019 McGraw-Hill Education. 9-22

 Price-Earnings Ratio

The price-earnings ratio is calculated as the current

stock price divided by annual EPS.

Normally similar firms have similar PE ratios.

This is useful to estimate the price per share if we

have the industry average PE ratio.

Price per share

P E ratio =
EPS

© 2019 McGraw-Hill Education. 9-23

 Enterprise Value Ratios

The PE ratio focuses on equity, but what if we want the

value of the firm?
Use enterprise value:
• EV = market value of equity + market value of
debt – cash
Like PE, we compare the value to a measure of
earnings. From a firm level, this is EBITDA, or earnings
before interest, taxes, depreciation, and amortization.
• EBITDA represents a measure of total firm cash flow
The Enterprise Value Ratio = EV EBITDA

The valuation for a company 9-24

© 2019 McGraw-Hill Education.
© 2019 McGraw-Hill Education. 9-25
9.4 Valuing Stocks Using Free Cash
Flows
In Chapters 5 and 6 you learned that the value of a
project (i.e., its NPV) was the discounted value of the
cash flows it generates.
The firm value is the consolidated present value of the
cash flow from all of its projects.

© 2019 McGraw-Hill Education. 9-26

Common Stock Valuation:
Free Cash Flow Valuation Model
A free cash flow valuation model determines the value of an entire
company as the present value of its expected free cash flows
discounted at the firm’s weighted average cost of capital, which is its
expected average future cost of funds over the long run.
VC =value of the entire company
FC =free cash flow expected at the
Ft end of year t end of year t
ra =the firm’s weighted average
cost of capital

Free cash flow (FCF) represents the cash available for the company to
repay creditors or pay dividends and interest to investors.

© Pearson Education Limited, 2015. 7-27

Common Stock Valuation:
Free Cash Flow Valuation Model (cont.)
Because the value of the entire company, VC, is the
market value of the entire enterprise (that is, of all
assets), to find common stock value, VS, we must
subtract the market value of all of the firm’s debt, VD,
and the market value of preferred stock, VP, from VC.

© Pearson Education Limited, 2015. 7-28

Common Stock Valuation:
Free Cash Flow Valuation Model
Dewhurst, Inc. wishes to determine the value of its
stock by using the free cash flow valuation model. The
firm’s CFO developed the following data:

Table 7.4 Dewhurst, Inc.’s, Data for the Free

Cash Flow Valuation Model

© Pearson Education Limited, 2015. 7-29

Common Stock Valuation:
Free Cash Flow Valuation Model (cont.)
Step 1. Calculate the present value of the free cash
flow occurring from the end of 2021 to infinity,
measured at the beginning of 2021.

© Pearson Education Limited, 2015. 7-30

Common Stock Valuation:
Free Cash Flow Valuation Model (cont.)
Step 2. Add the present value of the FCF from 2021 to infinity,
which is measured at the end of 2020, to the 2020 FCF value to
get the total FCF in 2020.

Total FCF2020 = $600,000 + $10,300,000 = $10,900,000

Step 3. Find the sum of the present values of the FCFs for 2016
through 2020 to determine the value of the entire company, VC.
This step is detailed in Table 7.5 on the following slide.

© Pearson Education Limited, 2015. 7-31

Table 7.5 Calculation of the Value of the
Entire Company for Dewhurst, Inc.

CF0=0, CF1=400000, CF2=450000, CF3=520000,

CF4=560000, CF5=10900000, I=9, NPV=8628234
© Pearson Education Limited, 2015. 7-32
Common Stock Valuation:
Free Cash Flow Valuation Model (cont.)
Step 4. Calculate the value of the common stock.

VS = $8,626,426 – $3,100,000 – $800,000 =

$4,726,426

The value of Dewhurst’s common stock is therefore

estimated to be $4,726,426. By dividing this total by
the 300,000 shares of common stock that the firm has
outstanding, we get a common stock value of $15.76
per share ($4,726,426 ÷ 300,000).

© Pearson Education Limited, 2015. 7-33

Basics of the Stock Market

• The primary market is the financial market in

which securities are initially issued; the only market
in which the issuer is directly involved in the
transaction.
• Secondary markets are financial markets in which
preowned securities (those that are not new issues)
are traded.

© Pearson Education Limited, 2015. 7-34

The Money Market

• The money market is created by a financial

relationship between suppliers and demanders of
short-term funds.
• Most money market transactions are made in
marketable securities which are short-term debt
instruments, such as:
• U.S. Treasury bills issues by the federal government
• commercial paper issued by businesses
• negotiable certificates of deposit issued by financial
institutions
• Investors generally consider marketable securities
to be among the least risky investments available.

© Pearson Education Limited, 2015. 7-35

The Capital Market

• The capital market is a market that enables

suppliers and demanders of long-term funds to
make transactions.
• The key capital market securities are bonds (long-
term debt) and both common and preferred stock
(equity, or ownership).
– Bonds are long-term debt instruments used by businesses
and government to raise large sums of money, generally
from a diverse group of lenders.
– Common stock are units of ownership interest or equity in
a corporation.
– Preferred stock is a special form of ownership that has
features of both a bond and common stock.

© Pearson Education Limited, 2015. 7-36

Broker Markets and
Dealer Markets
Broker markets are securities exchanges on which
the two sides of a transaction, the buyer and seller,
are brought together to trade securities.
– Trading takes place on centralized trading floors of national
exchanges, such as NYSE Euronext, as well as regional
exchanges.

© Pearson Education Limited, 2015. 7-37

Broker Markets and
Dealer Markets (cont.)
• Dealer markets, such as Nasdaq, are markets in
which the buyer and seller are not brought together
directly but instead have their orders executed by
securities dealers that “make markets” in the given
security.
– The dealer market has no centralized trading floors.
Instead, it is made up of a large number of market makers
who are linked together via a mass-telecommunications
network.
• As compensation for executing orders, market
makers make money on the spread (bid price – ask
price).

© Pearson Education Limited, 2015. 7-38

© Pearson Education Limited, 2015. 7-39
© Pearson Education Limited, 2015. 7-40
© Pearson Education Limited, 2015. 7-41
The Role of Capital Markets

• From a firm’s perspective, the role of capital

markets is to be a liquid market where firms can
interact with investors in order to obtain valuable
external financing resources.
• From investors’ perspectives, the role of capital
markets is to be an efficient market that allocates
funds to their most productive uses.
• An efficient market allocates funds to their most
productive uses as a result of competition among
wealth-maximizing investors and determines and
publicizes prices that are believed to be close to
their true value.

© Pearson Education Limited, 2015. 7-42

The Role of Capital Markets (cont.)

• Advocates of behavioral finance, an emerging

field that blends ideas from finance and psychology,
argue that stock prices and prices of other
securities can deviate from their true values for
extended periods.
• Examples of the principle that stock prices
sometimes can be wildly inaccurate measures of
value include:
• the huge run up and subsequent collapse of the prices of
Internet stocks in the late 1990s
• the failure of markets to accurately assess the risk of
mortgage-backed securities in the more recent financial
crisis

© Pearson Education Limited, 2015. 7-43

The Financial Crisis: Financial Institutions
and Real Estate Finance
• Securitization is the process of pooling mortgages
or other types of loans and then selling claims or
securities against that pool in a secondary market.
• Mortgage-backed securities represent claims on
the cash flows generated by a pool of mortgages
and can be purchased by individual investors,
pension funds, mutual funds, or virtually any other
investor.
• A primary risk associated with mortgage-back
securities is that homeowners may not be able to,
or may choose not to, repay their loans.

© Pearson Education Limited, 2015. 7-44

The Financial Crisis: Falling Home Prices
and Delinquent Mortgages
• Rising home prices between 1987 and 2006 kept
mortgage default rate low.
• Lenders relaxed standards for borrowers and
created subprime mortgages.
• As housing prices fell from 2006 to 2009, many
borrowers had trouble making payments, but were
unable to refinance.
• As a result, there was a sharp increase in the
number of delinquencies and foreclosures.

© Pearson Education Limited, 2015. 7-45

© Pearson Education Limited, 2015. 7-46