Fundamental of Corporate Finance,chpt8

8/3/2019 Fundamental of Corporate Finance,chpt8

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Chapter 8

Stock Valuation

Prepared and Taught by Lecturer : YIN SOKHNG

E-mail: [email protected]

Tel:(855) 16889872 / 17989972

2Instructed by YIN SOKHENG, Master in Finance

Chapter Outline

8.1 Common Stock Valuation

8.2 The Present Value of Common Stock

8.3 Estimates of Parameters in the Dividend-

Discount Model

8.4 Growth Opportunities

8.5 The Dividend Growth Model and the

NPVGO Model (Advanced)

8.6 Price Earnings Ratio8.7 The Stock Markets

3

Valuation of Bonds and Stock

First Principles: Value of financial securities = PV of expected future

cash flows

To value bonds and stocks we need to:

Estimate future cash flows: Size (how much) and

Timing (when)

Discount future cash flows at an appropriate rate: The rate should be appropriate to the risk presented by the

security.

Instructed by YIN SOKHENG, Master in Finance


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4

Cash Flows to Stockholders

If you buy a share of stock, you can receive cash

in two ways

The company pays dividends

You sell your shares, either to another investor in the

market or back to the company

As with bonds, the price of the stock is the

present value of these expected cash flows


5

Common stock valuation for one period

P0 = D1/(1 + r) + P1/(1 + r)

P0 = Value of stock at time 0

P1 = Price of stock at the end of the period

D1 = Dividend at the end of the period

8.1 Common stock valuation


6

One Period Example

Suppose you are thinking of purchasing the stock of

Moore Oil, Inc. and you expect it to pay a $2 dividend

in one year and you believe that you can sell the stock

for $14 at that time. If you require a return of 20% on

investments of this risk, what is the maximum you

would be willing to pay?

P0 = D1/(1 + r) + P1/(1 + r)

P0 = 2/(1.2) + 14/(1.2) = $13.33



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Common stock valuation for two period

P0 = D1/(1 + r) + D2/(1 + r)t +P2/(1 + r)

t

Now what if you decide to hold the stock for twoyears? In addition to the dividend in one year,you expect a dividend of $2.10 in and a stock

price of $14.70 at the end of year 2. Now how

much would you be willing to pay?

P0 = 2/(1.2) + 2.1/(1.2)2 +14.7/(1.2)2 = $13.33


8

Three Period Example

Finally, what if you decide to hold the stock for three

periods? In addition to the dividends at the end of years

1 and 2, you expect to receive a dividend of $2.205 at

the end of year 3 and a stock price of $15.435. Now

how much would you be willing to pay?

PV = 2 / 1.2 + 2.10 / (1.2)2 + (2.205 + 15.435) / (1.2)3 =

13.33

Or CF0 = 0; C01 = 2; F01 = 1; C02 = 2.10; F02 = 1; C03

= 17.64; F03 = 1; NPV; I = 20; CPT NPV = 13.33


9

Three Period Example

Finally, what if you decide to hold the stock for

three periods? In addition to the dividends at the

end of years 1 and 2, you expect to receive a

dividend of $2.205 at the end of year 3 and a

stock price of $15.435. Now how much would

you be willing to pay? P0 = 2 / 1.2 + 2.10 / (1.2)

2 + 2.205/ (1.2)3+ 15.435 /(1.2)3 = $13.33



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Multiple-Period Dividend Valuation Model

P0 = D1/(1+R) + D2/(1+R)2 + D3/(1+R)

3 +..or

P0 = D1/(1+R) + D2/(1+R)2 +.+ D n/(1+R)

n

Suppose that theinvestoris consideringpurchasing a share of this stock

andholdingit for 5 years. Assume that theinvestor's required rate of

returnis still 14%. Dividends from the stock are expectedto be$1 in the

first year, $1 inthe secondyear, $1 inthe third year, $1.25 inthe fourth

year, and$1.25 in thefifth year. The expectedselling price of thestockat

the end of5 years is $41.

P0 = 1/ (1 + 0.14) + 1/ (1 + 0.14)2 + 1/ (1 + 0.14) 3 + 1.25/ (1 + 0.14) 4 +

1.25/ (1 + 0.14) 5 + 41/ (1+ 0.14) 5

P0 = $24.99 or25


11

8.2 The Present Value

of Common Stocks

Dividends versus Capital Gains

Valuation of Different Types of Stocks

Zero Growth

Constant Growth

Differential Growth


12

Estimating Dividends: Special Cases

Zero growth /Constant dividend

The firm will pay a constant dividend forever This is like preferred stock

The price is computed using the perpetuity formula

Constant dividend growth

The firm will increase the dividend by a constant percentevery period

Differential /Supernormal growth

Dividend growth is not consistent initially, but settlesdown to constant growth eventually



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Case 1: Zero Growth Assume that dividends will remain at the same level

forever

rrrP

)1(

Div

)1(

Div

)1(

Div3

32

21

10 ++

++

++

= L

L===321 DivDivDiv

Since future cash flows are constant, the value of a zerogrowth stock is the present value of a perpetuity:

Suppose stock is expected to pay a $0.50 dividendevery quarter and the required return is 10% withquarterly compounding. What is the price?

P0 = .50 / (.1 / 4) = $20

r

Div=


14

Case 2: Constant Growth

)1(DivDiv 01 g+=

Since future cash flows grow at a constant rate forever,the value of a constant growth stock is the presentvalue of a growing perpetuity:

Assume that dividends will grow at a constant rate, g,forever. i.e.

2

012 )1(Div)1(DivDiv gg +=+=

.

.

3

023 )1(Div)1(DivDiv gg +=+=

.

g-rDiv

g-rg)1(DivP 100


15

CGDMExample 1

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, how much should the stock be

selling for?

P0 = .50(1+.02) / (.15 - .02) = $3.92



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Case 3: Differential Growth

Assume that dividends will grow at differentrates in the foreseeable future and then will growat a constant rate thereafter.

To value a Differential Growth Stock, we needto:

Estimate future dividends in the foreseeable future.

Estimate the future stock price when the stockbecomes a Constant Growth Stock (case 2).

Compute the total present value of the estimatedfuture dividends and future stock price at theappropriate discount rate.


17


)(1DivDiv 101 g+=

Assume that dividends will grow at rate g1 forNyears and grow at rate g2 thereafter

2

10112 )(1Div)(1DivDiv gg +=+=

N

NN gg )(1Div)(1DivDiv 1011 +=+= -

)(1)(1Div)(1DivDiv 21021 ggg

N

NN ++=+=+


18


Dividends will grow at rate g1 forNyears and grow at

rate g2 thereafter)(1Div 10 g+

2

10 )(1Div g+

0 1 2

Ng )(1Div 10 + )(1)(1Div

)(1Div

210

2

gg

gN

N

++=

+

N N+1



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To value a Differential Growth Stock, we can use

Or we can cash flow it out.

NT

T

r

gr

r

g

gr

CP

)1(

Div

)1(

)1(1 2

1N

1

1

-

--


20

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? The discount rate is

12%.


21

With the Formula

NT

T

rgr

rg

grCP

)1(

Div

)1()1(1 2

1N

1

1

-

--

3

3

3

3

)12.1(

04.12.

)04.1()08.1(2$

)12.1(

)08.1(1

08.12.

)08.1(2$

-

-

-x

P

[ ] ( )3)12.1(

75.32$8966.154$ -xP

31.23$58.5$ P 89.28$P



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A Differential Growth Example (continued)

08).2(1$ 208).2(1$

0 1 2 3 4

308).2(1$ )04.1(08).2(1$

3

16.2$ 33.2$08.

62.2$52.2

89.28$)12.1(

75.32$52.2$

)12.1(

33.2$

12.1

16.2$320

P

75.32$08.

62.2$3

P

The constantgrowth phase

beginning in year 4can be valued as agrowing perpetuity

at time 3.

$


23

Supernormal Growth Problem Statement

Suppose a firm is expected to increase

dividends by 20% in one year and by 15% in

two years. After that dividends will increase at

a rate of 5% per year indefinitely. If the lastdividend was $1 and the required return is

20%, what is the price of the stock?

Remember that we have to find the PV ofall

expected future dividends.


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Supernormal GrowthExample Solution

Compute the dividends until growth levels off

D1 = 1(1.2) = $1.20

D2 = 1.20(1.15) = $1.38

D3 = 1.38(1.05) = $1.449

Find the expected future price

P2 = D3/ (Rg) = 1.449 / (.2 - .05) = 9.66

Find the present value of the expected futurecash flows

P0 = 1.20 / (1.2) + 1.38/ (1.2)2 + 9.66/ (1.2)2 = $8.67



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Using the DGM to Find R

Start with the DGM:

gP

Dg

P

g)1(DR

Rforsolveandrearrange

g-RD

g-Rg)1(DP

0

1

0

0

100


26

Finding the Required Return - Example

Suppose a firms stock is selling for $10.50.They just paid a $1 dividend and dividends areexpected to grow at 5% per year. What is therequired return?

R = [1(1.05)/10.50] + .05 = 15%

What is the dividend yield?

1(1.05) / 10.50 = 10%

What is the capital gains yield?g =5%


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8.3 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?

Where does rcome from?

Where does g come from?

g = Retention ratio Return on retained earnings



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Where does rcome 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.


29

8.4 Growth Opportunities

Growth opportunities are opportunities to

invest in positive NPV projects.

The value of a firm can be conceptualized as

the sum of the value of a firm that pays out

100-percent of its earnings as dividends and

the net present value of the growth

opportunities.

NPVGOr

EPSP +=


30

8.5 The Dividend Growth Model and the

NPVGO Model (Advanced)

We have two ways to value a stock:

The dividend discount model.

The price of a share of stock can be calculated as

the sum of its price as a cash cow plus the per-

share value of its growth opportunities.



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Consider a firm that has EPS of $5 at the end of the

first year, a dividend-payout ratio of 30%, a discount

rate of 16-percent, and a return on retained earnings of

20-percent.

The dividend at year one will be $5 .30 = $1.50 pershare.

The retention ratio is .70 ( = 1 -.30) implying a growth

rate in dividends of 14% = .70 20%

From the dividend growth model, the price of a share is:

75$14.16.

50.1$Div10

-

-

gr

P


32

The NPVGO Model

First, we must calculate the value of the firm as acash cow.

25.31$16.

5$Div10

===r

P

Second, we must calculate the value of the growth

opportunities.

Finally, 75$75.4325.310 =+=P

75.43$14.16.

875$.16.

20.50.350.3

0

-

-

x-

gr

P


33

8.6 Price Earnings Ratio

Many analysts frequently relate earnings per share to

price. The price earnings ratio is a.k.a. the multiple

Calculated as current stock price divided by annual EPS

The Wall Street Journal uses last 4 quarters earnings

EPS

shareperPriceratioP/E =



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Other Price Ratio Analysis

Many analysts frequently relate earnings pershare to variables other than price, e.g.:

Price/Cash Flow Ratio cash flow = net income + depreciation = cash flow

from operations or operating cash flow

Price/Sales current stock price divided by annual sales per share

Price/Book (a.k.a. Market to Book Ratio) price divided by book value of equity, which is

measured as assetsliabilities


35

8.7 Stock Market Reporting52 WEEKS YLD VOL NET

HI LO STO CK SY M D IV % PE 10 0s HI LO C LO SE C HG

52.75 19.06 Gap Inc GPS 0.09 0.5 15 65172 20.50 19 19.25 -1.75

Gap has

been as

high as$52.75 in

the last

year.

Gap has been

as low as$19.06 in the

last year.

Given the current

price, the PE ratio

is 15 times earnings

6,517,200 sharestraded hands in the

last days trading

Gap ended trading

at $19.25, down

$1.75 from

yesterdays close

Gap pays a

dividend of 9

cents/share

Given the

current price,

the dividend

yield is %


36

Stock Market Reporting52 WEEKS YLD VOL NET

HI LO STO CK S YM D IV % P E 10 0s HI LO C LO SE C HG

52.75 19.06 Gap Inc GPS 0.09 0.5 15 65172 20.50 19 19.25 -1.75

Gap Incorporated is having a tough year, trading near their 52-

week low. Imagine how you would feel if within the past year you

had paid $52.75 for a share of Gap and now had a share worth

$19.25! That 9-cent dividend wouldnt go very far in making

amends.

Yesterday, Gap had another rough day in a rough year. Gap

opened the day down beginning trading at $20.50, which was

down from the previous close of $21.00 = $19.25 + $1.75

Looks like cargo pants arent the only things on sale at Gap.


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Fundamental of Corporate Finance,chpt8