CHAPTER 12 Stock Valuation

8/3/2019 CHAPTER 12 Stock Valuation

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STOCK VALUATION

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Principles Used in This Chaptery Money Has a Time Value

y There is a Risk-Return Tradeoff

y Cash Not Profits-is King

y The Agency Problem

y Managers wont work for the owners unless it is in their

best interest.

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Security Valuation

yIn general, the intrinsic value of an

asset = thepresent value of thestream of expected cash flows

discounted at an appropriate

required rate of return.

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Differences Between Debt and Equity

y Debt

y Not an ownership interest

y Creditors do not have votingrights

y Interest is considered a cost ofdoing business and is taxdeductible

y Creditors have legal recourse ifinterest or principal paymentsare missed

y Excess debt can lead tofinancial distress andbankruptcy

y Equity

y Ownership interest

y Common stockholders vote forthe board of directors and other

issuesy Dividends are not considered a

cost of doing business and arenot tax deductible

y Dividends are not a liability ofthe firm and stockholders haveno legal recourse if dividendsare not paid

y An all equity firm can not gobankrupt

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Cash Flows forS

tockholdersy If you buy a share of stock, you can receive cash in two

ways

yThe company pays dividends

y You sell your shares, either to another investor in the

market or back to the company

y (you receive capital gain/loss)

y As with bonds, the price of the stock is the present value

of these expected cash flows

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PreferredStock

A hybridsecurity

y Its like common stock- no fixed maturity.

y Technically, its part of equity capital.

y Its like debt- preferred dividends are fixed.

y Missing a preferred dividend does not

constitute default.

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y Firms may have multiple classes of preferred, each

with different features.

yPriority of claim: lower than debt, higher than common

stock.

y Cumulative feature: all past unpaid preferred stock

dividends must be paid before any common stock

dividends are declared.

PreferredStock Features

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y Protective provisions are common.

y Convertibility: many preferred stocks are convertible

into common shares.

y Adjustable ratepreferred stocks have dividends tied

to interest rates.

y Participation: some (very few) preferred stocks have

dividends tied to the firms earnings.

PreferredStock Features-cont

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y PIKPreferred:Pay-in-kindpreferred stocks pay

additional preferred shares to investors rather than cash

dividends.

y Retirement: Most preferred stocks are callable, and

many include a sinking fund provision to set cash aside

for the purpose of retiring preferred shares.

PreferredStock Features-cont

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PreferredS

tock ValuationyA preferred stock can usually be

valued like a perpetuity:

=VpsD

kps

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Example

y If we know XYZs preferred stock is selling at

RM40, and the preferred dividend is RM4.125,

the expected return is:

kps = = = .10314.12540DPo

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ySuppose our required rate of return on

XYZs preferred is 9.5%.

Vps ==4.125

.095= RM43.42

Should we purchase XYZs preferred stocks?

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Common Stock

y Is a variable-income security.

yDividends may be increased or decreased,

depending on earnings.

yRepresents equity orownership.

y Includes voting rights.

yLimited liability: liability is limited to amount of

owners investment.

yPriority of claim: lower than debt and preferred.

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Common Stock Characteristics

y Claim on Income - a stockholder has a claim on thefirms residual income.

y

Claim on Assets-

a stockholder has a residual claimon the firms assets in case of liquidation.

yPreemptive Rights - stockholders may share

proportionally in any new stock issues.

y Voting Rights - right to vote for the firms board of

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y You plan to purchase XYZ stock and hold it for only

ONE year. XYZ is expected to pay a RM2.50 dividend

at the end of the year. The stock price is expected to be

RM15 at that time.

y If you require a 15% rate of return, how much would

you pay for the stock now?

Common Stock Valuation(Single Holding Period)

0 1 year

? RM2.50 + RM15

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Common Stock Valuation(Single Holding Period)

Solution:

Vcs = (RM2.50/1.15) + (RM15/1.15)

= RM2.17 + RM13.04

= RM15.21

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Common Stock Valuation(Two Holding Period)

y Now what if you decide to hold the stock for two years? In

addition to the dividend in one year, you expect a dividend

of RM3 in two years and a stock price of RM16 at the endof year 2. Now how much would you be willing to pay?

Vcs = RM2.50/(1.15) + RM3/(1.15)2 + RM16/(1.15)2

= RM2.17 + RM2.27 + RM12.10

= RM16.54

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Common Stock Valuation

(Three Holding Period)

y What if you decide to hold the stock for three years? In

addition to the dividends at the end of years 1 and 2, you

expect to receive a dividend of RM4.00 at the end of year 3and the stock price is expected to be RM17.50 in year 3.

Now how much would you be willing to pay today?

VCS = RM2.50/(1.15) + RM3/(1.15)2

+ (RM4 + RM17.50) / (1.15)3

= RM2.17 + RM2.27 + RM14.14

= RM18.58

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yYou could continue to push back when youwould sell the stock

yYou would find that the price of the stock isreally just thepresent value of all expected

future dividends

ySo, how can we estimate all future dividend

payments?

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The Growth Factor

y Growth is an expansion of a company as a result of

investment through :

I. External Financing

y

Borrowing moneyy Issuing new shares

II. Internal Financing

y Internal Funds ~(i.e reinvestment through retainedearnings)

y INTERNAL GROWTH (g) = ROE x r

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Common Stock Valuation

(Multiple Holding Period)y Constant dividend

y The firm will pay a constant dividend forever

y This is like preferred stock

The price is computed using the perpetuity formula

y Constant dividend growth

y The firm will increase the dividend by a constant percentevery

period

y Supernormal growth

y Dividend growth is not consistent initially, but settles down to

constant growth eventually

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ConstantDividend(Zero Growth)

y Assume that dividends will remain at the same levelforever

cs

cscscs

k

kkk

CS

CS

DivV

)1(

Div

)1(

Div

)1(

DivV

3

3

2

2

1

1

!

! .

.!!!321

DivDivDiv

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

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Zero Growth

y If dividends are expected at regular intervals forever, then this

is a perpetuity and the present value of expected future

dividends can be found using the perpetuity formula

y

P0 = D / kcs

y Suppose stock is expected to pay a RM0.50 dividend every

quarter and the required return is 10% with quarterly

compounding.W

hat is the price?y P0 = RM0.50 / 0.025= RM20

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Constant Growth(Dividend Growth Model)

)1(DivDiv01

g!

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 !!

.

.

.

Dividends are expected to grow at a constant percent per period.

Vcs = D1 /(1+kcs) + D2 /(1+kcs)2 + D3 /(1+kcs)

3 +

Vcs= D0(1+g)/(1+kcs) + D0(1+g)2/(1+kcs)

2 + D0(1+g)3/(1+kcs)

3 +

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Assumes common stock dividends will grow

at a constant rate into the future.

gk

g

cs

cs

!

)(1DV

0

gkcscs

!1

DV

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y Assumes common stock dividends will grow at aconstant rate into the future.

y D1 = the dividend at the end of period 1.

y kcs = the required return on the common stock.

yg = the constant, annual dividend growth rate.

y provided kcs>g


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Example 1:

y XYZ stock recently paid a RM5.00 dividend. The

dividend is expected to grow at 10% per year

indefinitely. What would we be willing to pay if our required return on XYZ stock is 15%?

Vcs = = = RM110D0(1+g) 5(1.10)

kcs - g .15 - .10

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Constant Growth

(Dividend Growth Model)

Example 2:

y Suppose ABC is expected to pay a RM2 dividend in one

year. If the dividend is expected to grow at 5% per yearand the market required return is 20%, what is the price?

yP0 = 2 / (.2 - .05) = RM13.33

**Notice that the RM2 in the numerator is already an

expected dividend (i.e. D1),

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Stock Price Sensitivity to Dividend Growth, gAs the growth rate approaches the required return, the stock price

increases dramatically.

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2

Growth Rate

Stock

Price

D1 = RM2; kcs = 20%

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Stock Price Sensitivity to Required Return, kcsAs the required return approaches the growth rate, the price increases

dramatically.

0

50

100

150

200

250

0 0.05 0.1 0.15 0.2 0.25 0.3

Growth Rate

Stock

Price

D1 = RM2; g = 5%

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Nonconstant Growth

(S

upernormal growth)Example:

y 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

last dividend was RM1 and the required return is 20%,

what is the price of the stock?

yRemember that we have to find the PV of all expected

future dividends!!!

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Nonconstant Growth

Example Solution

y Compute the dividends until growth levels off

y D1 = 1(1.2) = RM1.20

y D2 = 1.20(1.15) = RM1.38

y D3 = 1.38(1.05) = RM1.449

y Find the expected future price

y P2 = D3 / (kcs g) = 1.449 / (.2 - .05) = RM9.66

y Find the present value of the expected future cash flows

y P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = RM8.67

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Expected Return on Common Stock

Just adjust the valuation model!

Vcs =D

kcs - g

k = + gD1

Po

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Example 1:

y If you purchase a stock that will pay a RM3.00 dividend at

time 1, at a price of RM27 and an expected growth rate of

5%. How much is your expected return on this stock?

kcs = ( ) + gD1

Po

kcs = ( ) + .05 = 16.11%3.00

27

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Example 2:

y If you purchase a stock that paid a RM3.00 dividend

recently, at a price of RM27 and an expected growth rate

of 5%. How much is your expected return on this stock?

kcs = ( ) + gD1

Po

kcs = ( ) + .05 = 16.67%3.00 (1.05)

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Example 3:

y If you purchase a stock that will pay a fixed dividend of

RM3.00 (i.e. growth =0), at a price of RM27. How much

is your expected return on this stock?

kcs =D1

Po

kcs = = 11.11%3.00

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CHAPTER 12 Stock Valuation