Chapter 9 Solutions.docx

8/19/2019 Chapter 9 Solutions.docx

1/41

. Required return Answer: e Diff: E

. Required return Answer: d Diff: E

. Required return Answer: a Diff: E

The total return is made up of a dividend yield and capital gains yield.

For Stock A, the total required return is 10 percent and its capital gains

yield (g is ! percent. Therefore, A"s dividend yield must #e $ percent.

For Stock %, the required return is 1& percent and its capital gains yield

(g is ' percent. Therefore, %"s dividend yield must also #e $ percent.

Therefore, statement a is true. Statement # is false. arket efficiency

)ust means that all of the kno*n information is already reflected in the

price, and you can"t earn a#ove the required return. This *ould depend on

#etas, dividends, and the num#er of shares outstanding. +e don"t have any

of that information. Statement c is false. The epected returns of the

t*o stocks *ould #e the same only if they had the same #etas.

. Constant growth model Answer: a Diff: E

Statement a is true- the other statements are false. The constant gro*th

model is not appropriate for stock valuation in the a#sence of a constant

gro*th rate. f the required rate of return differs for the t*o firms due

to risk differences, then the firms" stock prices *ould differ.

. Constant growth model Answer: a Diff: E

Statement a is true- the other statements are false. f a stock"s

required return is 1& percent and its capital gains yield is / percent,

then its dividend yield is 1& / 2 !. The epected future dividends

should #e discounted at the required rate of return.

. Constant growth model Answer: c Diff: E

Statement c is true- the others are false. Statement a *ould #e true only

if the dividend yield *ere 3ero. Statement # is false- *e"ve #een given

no information a#out the dividend yield. Statement c is true- the

constant rate at *hich dividends are epected to gro* is also the epected

gro*th rate of the stock"s price.

. Constant growth model Answer: e Diff: E

Statement a is false4 50 2 617(ks g. g is different for the t*o stocks,

#ut the required return and epected dividend are the same, so the prices

*ill #e different also. Statement # is false4 ks 2 61750 8 g. A has a

higher g, so its dividend yield must #e lo*er #ecause the firms have the

same required rate of return. Statement c is false. Therefore, statement

e is the correct ans*er.


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. Constant growth model Answer: c Diff: E N

The correct ans*er is statement c.

For Stock 9, ks 2 61750 8 g

0.1& 2 61750 8 0.0:, or 61750 2 0.0:.

For Stock ;, ks 2 61750 8 g 0.10 2 61750 8 0.0

2 =/0(1.0:10 2

=?'./


3/41

. Constant growth model and CAPM Answer: a Diff: E N

The correct ans*er is statement a. From the information given and the

A5 equation, *e kno* that Stock A"s and Stock %"s required returns are

1&.' and 11.!, respectively. The required return is equal to a dividend

yield and a capital gains yield. Since these are constant gro*th stocks,

their capital gains yields are equivalent to their dividend gro*th ratesof !. Therefore, the dividend yields for Stock A and Stock % are /.'

and


4/41

. Efficient mar!ets h"pothesis Answer: e Diff: E

Statement a is false- riskier securities have higher required returns.

Statement # is false for the same reason as statement a. Statement c is

false- semistrongform efficiency says that you cannot make a#normal

profits #y trading off pu#licly availa#le information. So statement e is

the correct ans*er.

. Efficient mar!ets h"pothesis Answer: e Diff: E

+eakform efficiency means that you cannot profit from recent trends in

stock prices (that is, technical analysis doesn"t *ork. Therefore,

statement a must #e false. Semistrongform efficiency means that all

pu#lic information is already accounted for in the stock price. %ecause

#onds and stocks have different risk levels and ta implications, there is

no reason to epect them to have the same return. Therefore, statement #

must #e false. Similarly, #ecause different stocks have different risk

levels, there is no reason to epect all stocks to have the same return.

Therefore, statement c is also false. The correct choice is statement e.

. Efficient mar!ets h"pothesis Answer: c Diff: E

Statement c is true- the other statements are false. Semistrongform

market efficiency implies that only pu#lic information, not private, is

rapidly incorporated into stock prices. arkets can #e efficient yet

still price securities differently depending on their risks.

. Efficient mar!ets h"pothesis Answer: a Diff: E

. Efficient mar!ets h"pothesis Answer: e Diff: E N

The correct ans*er is statement e. f prices rapidly reflect all

availa#le pu#lic information, then the market is semistrongform efficient

not *eakform efficient. Therefore, statement a is incorrect. f the

market is *eakform efficient, then you cannot #eat the market #y using

technical analysis or charting. Therefore, statement # is incorrect.

6ifferent stocks *ill have different risk and *ill have different required

and epected returns, so statement c is incorrect.

. Efficient mar!ets h"pothesis Answer: a Diff: E

Statement a is true- the other statements are false. Bistorical

information cannot #e used to #eat the market under *eakform efficiency.

5u#lic information cannot #e used to #eat the market under semistrongform

efficiency.

. Preferred stoc! concepts Answer: e Diff: E

. Preferred stoc! concepts Answer: e Diff: E

%oth statements a and # are true- therefore, statement e is the correct

choice. !0 percent of dividends received, not paid out, are ta

deducti#le.. Common stoc! concepts Answer: d Diff: E

Statements # and c are true- therefore, statement d is the correct choice.


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A greater proportion of common stock in the capital structure increases

the likelihood of a takeover #id.

. Common stoc! concepts Answer: e Diff: E

+e don"t kno* anything a#out the dividends of either stock. Stock ; could

have a dividend yield of 0 percent and a capital gains yield of 1&

percent, *hile Stock 9 has a dividend yield of 10 percent and a capital

gains yield of 0 percent. Therefore, statement a is false. f the t*o

stocks have the same dividend yield, Stock ; must have a higher epected

capital gains yield than 9 #ecause ; has the higher required return.

Therefore, statement # is false. Cemem#er the 6F formula4 50 2 617(ks

g. f 61 and g are the same, and *e kno* that ; has a higher required

return than 9, then ;"s dividend yield must #e larger than 9"s. n order

for this to #e true ;"s price must #e lo*er than 9"s. Therefore,

statement c is false. Since statements a, #, and c are false, then the

correct ans*er is statement e.

. Declining growth stoc! Answer: e Diff: E

Statement e is the correct choice- all the statements are true. Statementa is true- 50 2 =&7(0.1/ 8 0.0/ 2 =10. Statement # is true- 6iv yield/ 2

6:75/ or =&.00(0.'//G7=10.00(0.'//G 2 =1./

c is true- =10(0.'// 2 =!.!


6/41

epected return does not equal the required return, then markets are not

in equili#rium. f you are epecting a higher return than you require

(given the level of risk for a stock, then the stock *ill #e a H#argain.I

;ou *ill #e getting a higher return than you require. This disequili#rium

*ill not last, and the stock price *ill ad)ust until its epected return

equals its required return. Therefore, statement # is correct. 6ifferent

investments should have different epected returns. ;ou *ill have adifferent epected return for an oil company stock than you *ould for an

airline company stock, depending on *hat is happening to oil prices.

There is no reason for you to epect the same returns on all of your

investments. Therefore, statement c is incorrect. nvestments should not

have the same reali3ed returns. Ceali3ed returns are historical, and all

stocks have different price histories. Therefore, statement d is

incorrect.

. Mar!et efficienc" and stoc! returns Answer: c Diff: M

Statement c is true- the other statements are false. f #eta increased,

#ut g remained the same, the ne* stock price *ould #e lo*er. arket

efficiency says nothing a#out the relationship #et*een epected andreali3ed rates of return.

. Efficient mar!ets h"pothesis Answer: e Diff: M

Statement e is true- the other statements are false. f the stock market

is *eakform efficient, you could use private information to outperform

the market. Semistrongform efficiency means that current market prices

reflect all pu#licly availa#le information.

. Efficient mar!ets h"pothesis Answer: c Diff: M

. Efficient mar!ets h"pothesis Answer: e Diff: M

Statement e is the correct choice. Semistrongform efficiency implies

that past stock prices cannot #e used to forecast future returns.

. Efficient mar!ets h"pothesis Answer: d Diff: M

. Mar!et equilirium Answer: a Diff: M

. #wnership and going pulic Answer: c Diff: M

. Dividend "ield and g Answer: Diff: M

Statement # is true- the other statements are false. The stock"s required

return must equal the sum of its epected dividend yield and constant

gro*th rate. A stock"s dividend yield can eceed the epected gro*th

rate.. Constant growth model Answer: d Diff: M

Statement d is true- the other statements are false. ks 2 6ividend yield

8 apital gains. 1


7/41

. Preferred stoc! value Answer: d Diff: E

Ep 2 6p7kp 2 =/70.&0 2 =&/.

. Preferred stoc! value Answer: d Diff: E

The dividend is calculated as 10 × =1&0 2 =1&. +e kno* that the cost of

preferred stock is equal to the dividend divided #y the stock price or ?

2 =1&75rice. Solve this epression for 5rice 2 =1/0. (Dote4 Don

participating preferred stockholders are entitled to )ust the stated

dividend rate. There is no gro*th in the dividend.

. Preferred stoc! "ield Answer: c Diff: E

Annual dividend 2 =&./0(


8/41

. %uture stoc! price&&constant growth Answer: a Diff: E

Step 14 Find g4

50 2 617(ks g

=&0 2 =&7(0.1/ g

g 2 /.

Step &4 Find 5 at t 2 !4

! 2 50(1 8 g!

! 2 =&0(1.0/!

! 2 =&?.1< ≈ =&?.

. %uture stoc! price&&constant growth Answer: a Diff: E

Step 14 6etermine the constant gro*th rate, g4

ks 2 61750 8 g

' 2 =&7=


9/41

. Constant growth stoc! Answer: c Diff: E

50 2 617(ks g

=$0 2 =$7(0.1: L g

=


10/41

2 =0.


11/41

0.1& 2 0.0: 8 0.0:(#

# 2 1.

. New issues and dilution Answer: Diff: E

alculate current and ne* market value of firm after ne* stock issue4

1,000 shares× =100 per share 2 =100,000

5lus 1,000 ne* shares Q ='0 each 8 '0,000

De* firm market value =1'0,000

alculate ne* market share price4

=1'0,0007&,000 shares 2 ='/.00 per share

6ilution4 @ld shareholders lose =100 ='/ 2 =/.00 per share.

. %C% model for valuing stoc! Answer: d Diff: E N

Firm value 2 =&/,000,0007(0.10 L 0.0! 2 =?$$,$$$,$$$. This is the value

of the *hole company, including de#t, preferred stock, and common stock.

From this, *e su#tract the =&00,000,000 in de#t and preferred stock. This

leaves an equity value of =?$$,$$$,$$$ =&00,000,000 2 =:$$,$$$,$$$.

So, the price7share 2

000,000,$0

$$$,$$$,:$$=

2 =&1.11.

. %C% model for valuing stoc! Answer: d Diff: E N

FF1 2 =$00,000,000, gro*th rate 2 !, and +A 2 11.

Firm value 2 FF17(+A L g

2 =$00,000,0007(0.11 L 0.0! 2 =!,/00,000,000.

Total E assets 2 E de#t 8 E pref. stock 8 E common equity =!,/00,000,000 2 =/00,000,000 8 E common equity

=!,000,000,000 2 E common equity.

2 E equity7R of shares

2 =!,000,000,00071/0,000,000

2 =


12/41

Step Step :. Solve for 50 2 61 7(ks g 2 =1.:':07(0.1$

50 2

0.0


13/41

Do*, that *e have the constant gro*th rate, *e can find the stock"s

epected price in ;ear /4

2 50(1 8 gt

2 =


14/41

Det, determine the dividends during the nonconstant gro*th period4

61 2 =1.00 × 1.& 2 =1.&0.

6& 2 =1.&0 × 1.1/ 2 =1.$?.

Finally, determine the company"s current stock price4

Dumerical solution4

.:!.1?=1&.1(

!0.&0=$?.1=

1&.1

&0.1=5

&0 =

++=

Financial calculator solution4

Onter in FP@ register F0 2 0, F1 2 1.&0, and F& 2 &&.0?. Then enter

2 1&, and press D5E to get D5E 2 50 2 =1?.:!.

. Nonconstant growth stoc! Answer: a Diff: M

ks 2 kCF 8 C5(#

2 ? 8 :(1./

2 1!.

61 2 =0.!/(1.

6(1.1!

=11?.$$/8=&.0/?$

2 =!!.1


15/41

50 2

$1$.1(

100=

2 =:'.$0/ ≈ =:'.$1.

. Nonconstant growth stoc! Answer: e Diff: M

To find ks, the return on the stock, *e use the A5.ks 2 : 8 (11 : × 1.& 2 1&.

The value of the dividends for ;ears 1 < are4

61 2 =$.00.

6& 2 =$.00 × 1.&/ 2 =$.!/.

6$ 2 =$.!/ × 1.&/ 2 =


16/41

2 =:$./&/.

Step $4 Find the current stock price4

The current stock price (at t 2 0 is the present value of the

dividends 61, 6&, 6$, and the present value of$5

. 6iscount these

values at 11 percent.

50 2

$&11.1(

/&/.:$=:$.$=11.1($0.$=

11.100.$= +++

2 =/


17/41

Step &4 Find the stock"s value at ;ear /4

2 6:7(ks g

2 =/.&&


18/41

Step $4 6etermine the value of the stock at ;ear ?4

2 6'7(ks L g

2 (=1.'/$1&/ × 1.0/7(0.10$ L 0.0/

2 =$?.:'


19/41

ks 2 kCF 8 (k kCF#

2 / 8 (


20/41

2 ='!.&0.

Step


21/41

.'0:&/.1&?=10.01/.0

10.1(?/'$!/./(=

gk

g1(65>

s

$$ =

−=

−+

=

Step $4 Find the D5E of the cash flo*s, the stock"s value4

F0 2 0- F1 2 $.!/00- F& 2


22/41

.?!/.1!1=5>

10.011.0

!1?!/.1=5>

gk

65>

!

!

s

?!

=

−

=

−

=

Step $4 6etermine the price of the stock today4

As an investor today, you *ould #e entitled to 6/, 6:, 6!, and .

Onter the follo*ing input data in your calculator4

F0 2 0- F1


23/41

constant.

2 6/7(ks L g

2 =&./:$/7(0.1& L 0.0/

2 =$:.:&11.

Step $4 Msing your financial calculator, enter the cash flo*s to

determine the stock"s current price.F0 2 0- F1 2 1.&/- F& 2 1./:&/- F$ 2 1.'/$1- F


24/41

nputs4 F0 2 0- F1 2 $.:0- F& 2 ''.$:- 2 1/.

@utput4 D5E 2 =!?.&:.

6ividend yield 2 =$.:07=!?.&: 2 0.0


25/41

.&0.

1/:&/./0=$

2

0.1:

=1.'0

2 =11.?!/.

2 =11.?!/(0.'/$ 2 =10.1?.

. $toc! growth rate Answer: d Diff: M

Cequired rate of return4 ks 2 11 8 (1


26/41

=


27/41

=&0.00

=&0.00=&?./!

2

=&0.00

=?./!

2 0.


28/41

Step &4 alculate the current market price4

./0.&!=0.100.1:

=1./0(1.1050 =

−=

Step $4 alculate the earnings and 57O ratio461 2 =1./0(1.10 2 =1.:/ 2 0.$0O1.

O1 2 =1.:/70.$0 2 =/./0.

O

5

1

0

2

=/./0

=&!./0

2 /.0×.

. $toc! price Answer: d Diff: M

Step 14 Set up an income statement to find net income4

Sales =100,000 =10 × 10,000

Earia#le costs /0,000 =/ × 10,000

Fied costs 10,000 (Niven

O%T =


29/41

Dote4 %ecause these pro)ections are for the coming year, this

dividend is 61, or the dividend for the coming year.

Step &4 Mse the A5 equation to find the required return on the stock4

kS 2 kCF 8 (k kCF# 2 0.0/ 8 (0.0' 0.0/1.< 2 0.10: 2 10.:.

Step $4 alculate stock price450 2 617(kS g

2 =1.$':?7(0.10: 0.0?

2 =/$.!&.

. 'eta coefficient Answer: c Diff: M

alculate old required return and #eta4

ks(old 2

=

ks(De* 2

=$0

8 0.10/ 2 0.1!/&.

0.1!/& 2 0.0? 8 (0.0$#De*- #De* 2 $.1!& ≈ $.1!.

. Ris! and stoc! value Answer: d Diff: M

alculate required return on market and stock4

k 2 0.0/(! 8 0.$0(? 8 0.$0(' 8 0.$0(10 8 0.0/(1& 2 '.0/.

ks 2 :.0/ 8 ('.0/ :.0/&.0 2 1&.0/.

alculate epected equili#rium stock price4

.$?.0 =

−=

. %uture stoc! price&&constant growth Answer: Diff: M

First, find ks 2 : 8 /(0.? 2 10. Then, find 50 2 617(ks g. 50 2

=$.007(0.10 L 0.0/ 2 =:0. Finally, compound this at the / gro*th rate

for / years to find/5>

./5>

2 =:0(1.0// 2 =!:./?.

. %uture stoc! price&&constant growth Answer: e Diff: M


30/41

The gro*th rate is the required return minus the dividend yield.

g 2 0.1$ 0.0/ 2 0.0?.

+hat is 61K

0.0/ 2 617=&?

61 2 =1.

0.0/(1.& 2 0.1&.

t follo*s that4 5/ 2 =&.?0/17(0.1& 0.0! 2 =/:.10.


To find the gro*th rate4

ks 2 61750 8 g

Therefore ks 61750 2 g

0.1& =&7=&0 2 0.0&.

To find *e can use the follo*ing formula4

2 6:7ks g.

+e therefore need 6:.

6: 2 61(1 8 g/

2 =&(1.0&/ 2 =&.&0?.

Therefore 2 6:7ks g 2 =&.&0?70.1& 0.0& 2 =&&.0?.


Step 14 Find the cost of equity4

ks 2 : 8 (1& :1.< 2 1


31/41

Step &4 alculate the stock"s price today4

50 2 617(ks g

2 =&.007(0.1< 0.0'

2 =


32/41

2

0/.0

$&0=

2 =:,


33/41

Ealue of equity 2 Ealue of firm L Ealue of de#t and preferred stock

Ealue of equity 2 =10,000 L (='00 8 =/00

Ealue of equity 2 =?,:00 million.

To find the value per share of stock, *e must divide the total value of

the firm"s equity #y the num#er of shares outstanding.

Ealue per share 2 Ealue of equity7R of shares

Ealue per share 2 =?,:007&00

Ealue per share 2 =


34/41

50 2 EO7R shares

2 =1,&/07&0

2 =:&./0.

. New equit" and equilirium price Answer: c Diff: M

alculate ne* equili#rium price and determine change4

50, @ld 2

0.0:0.1&:

(1.0:60

2

0.0::

=1.00(1.0:

2 =1:.0:.

50, De* 2

gk>

g8=1.00(1

De*De*s,

De*

2

0.0:/0.1$/

/=1.00(1.0:

2

0.0!

=1.0:/

2 =1/.&1.

hange in price 2 =1/.&1 =1:.0: 2 =0.?/.

. Ris! and stoc! price Answer: a Diff: *

alculate the required rate of return4

60 2 O0(5ayout ratio 2 =alculate the ne* epected equili#rium stock price4

05>

2

0:.01$


35/41

Time line4

0 1 & $ < ;ears

J J J J J

O0 2 &.00 O1 2 &.


36/41

nputs4 F0 2 0- F1 2 0./&/- F& 2 $0.?!0&/- 2 1&.

@utput4 D5E 2 =&/.0?. 2 =&/.0?.

. Nonconstant growth stoc! Answer: e Diff: *

Time line4

0 1 & $ < ;earsJ J J J J

50 2

2

.0.100.1/

06(1.0/(1.1 1

−

.?/.&=6

1!./0

1

11111

$

1

$

1

&

11

==+++=

−+++=

. Nonconstant growth stoc! Answer: c Diff: *

Mse the SP equation to solve for ks4

ks 2 0.0:&/ 8 (0.0/(1.!/ 2 0.1/ 2 1/.

alculate dividend per share4

60 2 (O5S0(5ayout ratio 2 (=&./0(0.


37/41

Time line40 1 & $ < ;earsJ J J J J

1.00 1.&/00 1./000 1.!&/0 1.?


38/41

Step $4 alculate the present value of these dividends4

5Ediv 2 =1.0071.10 8 =1.&/7(1.10& 8 =1./:&/7(1.10$ 8

=1.'/$1&/7(1.10<

5Ediv 2 =0.'0'1 8 =1.0$$1 8 =1.1!$' 8 =1.$$


39/41

nputs4 D 2 /- 2 :.1?$1$- 5T 2 0- FE 2 /000.

@utput4 5E 2 =$,!0


40/41

Alternatively, enter all of the dividend cash flo*s along *ith the

terminal value of the stock into the cash flo* register and enter the 10

cost of equity to solve for the price of the stock today4

F0 2 0- F1 2 0.!/- F& 2 0.'$!/- F$ 2 1.&:/:&/ 8 $$./$'0:&/ 2

$


41/41

05>

2 =1./

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