09 answers to all problems.doc

8/19/2019 09 answers to all problems.doc

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Chapter 9 (13E)Stocks and Their Valuation

Answers to End-of-Chapter Questions

9-1 a The average investor of a rm traded on the NYSE is not really interested inmaintaining his or her proportionate share of ownership and control. If theinvestor wanted to increase his or her ownership, the investor could simply buymore stoc on the open maret. !onse"uently, most investors are not concernedwith whether new shares are sold directly #at about maret prices$ or throughrights o%erings. &owever, if a rights o%ering is being used to e%ect a stoc split,or if it is being used to reduce the underwriting cost of an issue #by substantialunderpricing$, the preemptive right may well be benecial to the rm and to itsstocholders.

! The preemptive right is clearly important to the stocholders of closely held#private$ rms whose owners are interested in maintaining their relative controlpositions.

9-" No. The correct e"uation has '( in the numerator and a minus sign in thedenominator.

9-3 Yes. If a company decides to increase its payout ratio, then the dividend yieldcomponent will rise, but the e)pected long*term capital gains yield will decline.

9-# Yes. The value of a share of stoc is the + of its e)pected future dividends. If thetwo investors e)pect the same future dividend stream, and they agree on the stoc-srisiness, then they should reach similar conclusions as to the stoc-s value.

9-$ perpetual bond is similar to a no*growth stoc and to a share of perpetual preferredstoc in the following ways/

(. ll three derive their values from a series of cash in0ows1coupon payments fromthe perpetual bond, and dividends from both types of stoc.

2. ll three are assumed to have indenite lives with no maturity value #3$ for theperpetual bond and no capital gains yield for the stocs.

&owever, there are preferreds that have a stated maturity. In this situation,the preferred would be valued much lie a bond with a stated maturity. 4othderive their values from a series of cash in0ows1coupon payments and amaturity value for the bond and dividends and a stoc price for the preferred.

9-% The discounted dividend model uses the rm-s cost of e"uity as the discount rate to

discount future dividends per share an investor e)pects to receive starting at t 5 ( to

calculate the rm-s intrinsic value, 6+7 , today. The corporate valuation model uses the

rm-s weighted average cost of capital as the discount rate to discount the rm-s future

free cash 0ows starting at t 5 ( to arrive at the rm-s corporate value. #8ree cash 0ows

represent cash generated from current operations less the cash that must be spent on

Chapter 9& Stocks and Their Valuation Answers and Solutions 1

' "13 Cenae *earnin All +ihts +eser,ed a. not !e copied/ scanned/ or duplicated/ in whole or in part/ e0ceptfor use as peritted in a license distri!uted with a certain product or ser,ice or otherwise on a password-protectedwe!site for classroo use


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investments and woring capital to support future growth. 8ree cash 0ows are funds

available to all capital investors and thus are discounted at the rm-s 9!!.$ :nce the

corporate value is determined the current maret value of debt and preferred is subtracted

to arrive at the rm-s e"uity value. The rm-s e"uity value is divided by the number of

shares outstanding to calculate the rm-s intrinsic value, 6+7 . The corporate valuation

model can be used to value divisions and rms that do not pay dividends. The discounted

dividend model could not be used in those situations.

9-2 The +;E approach can be used as a starting point in stoc valuation. If a stoc-s +;Eratio is well above its industry average and if the stoc-s growth potential and ris aresimilar to other rms in the industry, the stoc-s price may be too high. To estimate aball*par value multiply the rm-s E+S by the industry*average +;E ratio.

n alternative approach is based on the concept of Economic alue dded #E$.


3/31


4/31

c The rm-s intrinsic value is calculated as the sum of the present value of alldividends during the supernormal growth period plus the present value of theterminal value. Msing your nancial calculator, enter the following inputs/ !86 5 6,!8( 5 (.@6, !82 5 (.6 F BC.6 5 BJ.G6, I;Y< 5 (6, and then solve for N+ 5?BH.6J.

9-$ The rm-s free cash 0ow is e)pected to grow at a constant rate, hence we can apply aconstant growth formula to determine the total value of the rm.

8irm value 5 8!8(;#9!! = g8!8$5 ?(@6,666,666;#6.(6 = 6.6@$5 ?B,666,666,666.

To nd the value of an e"uity claim upon the company #share of stoc$, we mustsubtract out the maret value of debt and preferred stoc. This rm happens to beentirely e"uity funded, and this step is unnecessary. &ence, to nd the value of ashare of stoc, we divide e"uity value #or in this case, rm value$ by the number ofshares outstanding.

E"uity value per share 5 E"uity value;Shares outstanding5 ?B,666,666,666;@6,666,6665 ?G6.

Each share of common stoc is worth ?G6, according to the corporate valuation model.

9-% 'p 5 [email protected] p 5 ?G6A rp 5

rp 5p

p

,

' 5

?G6.6

[email protected] 5 .BBD.

9-2 p 5 'p;rpA therefore, rp 5 'p;p.

a rp 5 ?;?G6 5 (B.BBD.

! rp 5 ?;?6 5 (6.6D.

c rp 5 ?;?(66 5 .6D.

d rp 5 ?;?(H6 5 @.C(D.

9-4 a .(2@?6I.6

(6?

r

'

,p

p

p ===

! .BB.IB?(2.6

(6?p ==

# Answers and Solutions Chapter 9& Stocks and Their Valuation



5/31

9-9 a The preferred stoc pays ? annually in dividends. Therefore, its nominal rate ofreturn would be/

Nominal rate of return 5 ?;?6 5 (6D.

:r alternatively, you could determine the security-s periodic return and multiply byH.

+eriodic rate of return 5 ?2;?6 5 2.@D.

Nominal rate of return 5 2.@D × H 5 (6D.

! E< 5 #( F rN:3;H$H = (5 #( F 6.(6;H$H = (5 6.(6B(B 5 (6.B(BD.

9-1 [email protected]?26.6

[email protected]?

[email protected](@.6

[email protected]#@?

[email protected]#(@.6

[email protected]#(O@?

gr

$g(#'

gr

'+7

s

6

s

(

6 ==+=

−−−+

=−+

=−

=

9-11 8irst, solve for the current price.

6+7 5 '(;#rs = g$

5 ?6.@6;#6.(2 = 6.6C$5 ?(6.66.

If the stoc is in a constant growth state, the constant dividend growth rate is also thecapital gains yield for the stoc and the stoc price growth rate. &ence, to nd theprice of the stoc four years from today/

H+7 5 +6#( F g$H

5 ?(6.66#(.6C$H

5 ?(B.(6CJG P ?(B.((.

9-1" a (. [email protected]?26.6

J6.(?


[email protected](#2?+7

6 ==

+−=

2.6+7 5 ?2;6.(@ 5 ?(B.BB.

B. .66.2(?(6.6

(6.2?


$6@.(#2?+7

6 ==−=

H. [email protected]

26.2?

(6.6(@.6

$(6.(#2?+7

6 ==−=

! (.6+7 5 ?2.B6;6 5 Mndened.

2.6+7 5 ?2.H6;#*6.6@$ 5 *?H, which is nonsense.

Chapter 9& Stocks and Their Valuation Answers and Solutions $



6/31

These results show that the formula does not mae sense if the re"uired rate ofreturn is e"ual to or less than the e)pected growth rate.

c No, the results of +art b show this. It is not reasonable for a rm to grow indenitelyat a rate higher than its re"uired return. Such a stoc, in theory, would become solarge that it would eventually overtae the whole economy.

9-13 The problem ass you to determine the value ofB+7 , given the following facts/ '( 5 ?2,

b 5 6.J, r


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@+7 5 'G;#rs = g$ 5 ?2.HB;#6.(@ = 6.6$ 5 ?BH.C(H. This is the stoc price at the end of

Year @.

!86 5 6A !8(*2 5 6A !8B 5 (.6A !8H 5 (.@A !8@ 5 BG.JGHA I;Y< 5 (@. 9ith these cash 0owsin the !8Q: register, press N+ to calculate the value of the stoc today/ N+ 5?(J.J.

9-1$ a &oriKon value 56C.6(B.6

$6C.(#H6?

−

56G.6

I6.H2?5 ?C(B.BB million.

! 6 ( 2 B HL L L L L

*26 B6 H6 H2.6#? (C.C6$

2B.HJBop

5 C(B .BB @22 .(6 C@B .BB?@2C .J

Msing a nancial calculator, enter the following inputs/ !86 5 6A !8( 5 *26A !82 5B6A !8B 5 [email protected] I;Y< 5 (BA and then solve for N+ 5 [email protected] million.

c Total valuet56 5 [email protected] million.

alue of common e"uity 5 [email protected] = ?(66 5 ?H2C.J million.

+rice per share 566.(6

IJ.H2C? 5 ?H2.CJ.

9-1% The value of any asset is the present value of all future cash 0ows e)pected to begenerated from the asset. &ence, if we can nd the present value of the dividends

during the period preceding long*run constant growth and subtract that total from thecurrent stoc price, the remaining value would be the present value of the cash 0ows tobe received during the period of long*run constant growth.

'( 5 ?2.66 × #(.2@$( 5 ?2.@6 +#'($ 5 ?2.@6;#(.(2$( 5 ?2.2B2(

'2 5 ?2.66 × #(.2@$2 5 ?B.(2@ +#'2$ 5 ?B.(2@;#(.(2$

2 5 ?2.HJ(B

'B 5 ?2.66 × #(.2@$B 5 ?B.J6G2@ +#'B$ 5 ?B.J6G2@;#(.(2$B 5 ?2.C6H

Σ +#'( to 'B$ 5?C.@6B

Therefore, the + of the remaining dividends is/ [email protected] = ?C.@6B 5 ?@(.BCG2.!ompounding this value forward to Year B, we nd that the value of all dividends

received during constant growth is ?C2.(. O?@(.BCG2#(.(2$B 5 ?C2.(CJJ ≈ ?C2.(.pplying the constant growth formula, we can solve for the constant growth rate/

B+7 5 'B#( F g$;#rs = g$

?C2.( 5 ?B.J6G2@#( F g$;#6.(2 = g$?.GG(G = ?C2.(g 5 ?B.J6G2@ F ?B.J6G2@g

?H.C@@H 5 [email protected]@ 5 g



gn 5 CD

9!! 5 (BD

× (;(.(B

× (;#(.(B$2

× (;#(.(B$B


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G.2@D 5 g.

4 Answers and Solutions Chapter 9& Stocks and Their Valuation



9/31

9-12 6 ( 2 B HL L L L L

'6 5 2.66 '( '2 'B 'H

B+7

a '( 5 ?2#(.6@$ 5 ?2.(6A '2 5 ?2#(.6@$2 5 ?2.26@6A 'B 5 ?2#(.6@$

B 5 ?2.B(@2@.

! 8inancial calculator solution/ Input 6, 2.(6, 2.26@6, and 2.B(@2@ into the cash 0owregister, input I;Y< 5 (2, and solve for N+ 5 + 5 [email protected].

c 8inancial calculator solution/ Input 6, 6, 6, and BH.CB into the cash 0ow register,I;Y< 5 (2, and solve for N+ 5 + 5 ?2H.C2.

d ?2H.C2 F [email protected] 5 ?B6.66 5 3a)imum price you should pay for the stoc.

e [email protected](2.6

(6.2?

gr

'

gr

$g(#'+7

s

(

s

6

6 =−=

−=

−+

=

f No. The value of the stoc is not dependent upon the holding period. The valuecalculated in +arts a through d is the value for a B*year holding period. It is e"ual

to the value calculated in +art e. ny other holding period would produce the same

value of6+7 A that is,

6+7 5 ?B6.66.

9-14 a +art (/ Rraphical representation of the problem/

Supernormal Normalgrowth growth

6 ( 2 B ∞L L L L L

'6 '( #'2 F 2+7 $ 'B '∞

+'(+'2

2+7+,

+6

'( 5 '6#( F gs$ 5 ?(.G#(.26$ 5 ?(.J2.

'2 5 '6#( F gs$2 5 ?(.G6#(.26$2 5 ?2.B6H.

.6G.G(?

6.6G6.(6

$6G.(#B6H.2?

gr

$g(#'

gr

'+7

ns

n2

ns

B2 =

−

=

−

+=

−

=

6+7 5 +#'($ F +#'2$ F +# 2+7 $

52

s

2

2

s

2

s

(

$r(#

+7

$r(#

'

$r(#

'

++

++

+

5 ?(.J2;(.(6 F ?2.B6H;#(.(6$2 F ?G(.6G;#(.(6$2 5 ?@H.((.



rs 5 (2D

g 5 @D


10/31

8inancial calculator solution/ Input 6, (.J2, GB.BGH#2.B6H F G(.6G$ into the cash0ow register, input I;Y< 5 (6, and solve for N+ 5 + 5 ?@H.((.

+art 2/ E)pected dividend yield/

'(;+6 5 ?(.J2;?@H.(( 5 B.@@D.

!apital gains yield/ 8irst, nd (+7 , which e"uals the sum of the present values of'2 and 2+7 discounted for one year.

.G6.@C?$(6.(#

6G.G(?B6H.2?+7

(( =+=

8inancial calculator solution/ Input 6, GB.BGH#2.B6H F G(.6G$ into the cash 0owregister, input I;Y< 5 (6, and solve for N+ 5 + 5 [email protected].

Second, nd the capital gains yield/

[email protected]((.@H?

((.@H?G6.@C?

+

++7

6

6( =−

=−

'ividend yield 5 B.@@D!apital gains yield 5 G .H@

(6 .66D 5 rs.

! 'ue to the longer period of supernormal growth, the value of the stoc will behigher for each year. lthough the total return will remain the same, rs 5 (6D, thedistribution between dividend yield and capital gains yield will di%er/ The dividendyield will start o% lower and the capital gains yield will start o% higher for the @*yearsupernormal growth condition, relative to the 2*year supernormal growth state. The dividend yield will increase and the capital gains yield will decline over the @*year period until dividend yield 5 HD and capital gains yield 5 GD.

c Throughout the supernormal growth period, the total yield, rs, will be (6D, but thedividend yield is relatively low during the early years of the supernormal growthperiod and the capital gains yield is relatively high. s we near the end of thesupernormal growth period, the capital gains yield declines and the dividend yieldrises. fter the supernormal growth period has ended, the capital gains yield wille"ual gn 5 GD. The total yield must e"ual rs 5 (6D, so the dividend yield muste"ual (6D = GD 5 HD.

d Some investors need cash dividends #retired people$, while others would prefergrowth. lso, investors must pay ta)es each year on the dividends received duringthe year, while ta)es on the capital gain can be delayed until the gain is actuallyrealiKed. !urrently #26(($, dividends to individuals are now ta)ed at the lower

capital gains rate of (@DA however, as we wor on these solutions, this is set toe)pire at the end of 26(2 and ta)ation of dividends is set to increase to pre*266Blevels.

9-19 a 6 ( 2 B HL L L L L

B,666,666 G,666,666 (6,666,666 (@,666,666

1 Answers and Solutions Chapter 9& Stocks and Their Valuation


9!! 5 (2D


11/31

Msing a nancial calculator, enter the following inputs/ !86 5 6A !8( 5 B666666A !82 5 G666666A !8B 5 (6666666A !8H 5 (@666666A I;Y< 5 (2A and then solve for N+ 5?2H,((2,B6.

! The rm-s horiKon value is calculated as follows/

.666,666,B2(?6C.6(2.6

$6C.(#666,666,(@? =

−

c The rm-s total value is calculated as follows/

6 ( 2 B H @L L L L L L

B,666,666 G,666,666 (6,666,666 (@,666,666 (G,6@6,666

+ 5 B2(,666,666 56C.6(2.6

666,6@6,(G

−

Msing your nancial calculator, enter the following inputs/ !86 5 6A !8( 5 B666666A

!82 5 G666666A !8B 5 (6666666A !8H 5 (@666666 F B2(666666 5 BBG666666AI;Y< 5 (2A and then solve for N+ 5 ?22,((B,G(2.

d To nd 4arrett-s stoc price, you need to rst nd the value of its e"uity. The valueof 4arrett-s e"uity is e"ual to the value of the total rm less the maret value of itsdebt and preferred stoc.

Total rm value ?22,((B,G(23aret value, debt F preferred G6,666,666 #given in problem$3aret value of e"uity ?(G,((B,G(2

4arrett-s price per share is calculated as/

.I(.(G?666,666,(6

G(2,((B,(GI?=

9-" 8!8(5 E4IT#( = T$ F 'epreciation = ese)penditur!apital

= ∆

capitalworingoperatingNet

5 ?@66,666,666 F ?(66,666,666 = ?266,666,666 = ?65 ?H66,666,666.

8irm value 58!8

(

g9!!

8!8

−

56G.6(6.6

666,666,H66?

−

56H.6

666,666,H66?

5 ?(6,666,666,666.

This is the total rm value. Now nd the maret value of its e"uity.

3 Total 5 3E"uity F 3'ebt



gn 5 CD9!! 5 (2D


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?(6,666,666,666 5 3E"uity F ?B,666,666,6663E"uity 5 ?C,666,666,666.

This is the maret value of all the e"uity. 'ivide by the number of shares to nd theprice per share. ?C,666,666,666;266,666,666 5 [email protected].

9-"1 a End of Year/ (2 (B (H (@ (G (C (L L L L L L L

'6 5 (.C@ '( '2 'B 'H '@ 'G

't 5 '6#( F g$t.

'26(B 5 ?(.C@#(.(@$( 5 ?2.6(.

'26(H 5 ?(.C@#(.(@$2 5 ?(.C@#(.B22@$ 5 ?2.B(.

'26(@ 5 ?(.C@#(.(@$B 5 ?(.C@#(.@26J$ 5 ?2.GG.

'26(G 5 ?(.C@#(.(@$

H

5 ?(.C@#(.CHJ6$ 5 ?B.6G.

'26(C 5 ?(.C@#(.(@$@ 5 ?(.C@#2.6((H$ 5 ?B.@2.

! Step (/

+ of dividends 5 ∑= +

@

(tt

s

t

$r(#

'.

+ '26(B 5 ?2.6(;#(.(2$ 5 ?(.CJ+ '26(H 5 ?2.B(;#(.(2$2 5 ?(.H+ '26(@ 5 ?2.GG;#(.(2$B 5 ?(.J+ '26(G 5 ?B.6G;#(.(2$H 5 ?(.JH

+ '26(C 5 ?B.@2;#(.(2$@

5 ?2.66+ of dividends 5 ?J.HG

Step 2/

.I6.@2?6C.6

C6.B?

[email protected](2.6

$6@.(#@2.B?

gr

$g(#'

gr

'+7

ns

26(C

ns

26(I26(C ==−

=−

+=

−=

This is the price of the stoc @ years from now. The + of this price, discountedbac @ years, is as follows/

+ of26(C+7 5 [email protected];#(.(2$@ 5 ?2J.JG

Step B/ The price of the stoc today is as follows/

6+7 5 + dividends Years 26(B*26(C F + of

26(C+7

5 ?J.HG F ?2J.JG 5 ?BJ.H2.

1" Answers and Solutions Chapter 9& Stocks and Their Valuation


rs 5 (2D

gs 5 (@D gn 5 @D


13/31

This problem could also be solved by substituting the proper values into thefollowing e"uation/

@@

(t sns

G

t

s

t

s6

6r(

(

gr

'

$r(#

$g(#'+7 ∑

=

+

−

+++

= .

!alculator solution/ Input 6, 2.6(, 2.B(, 2.GG, B.6G, @G.B2 #B.@2 F @2.6$ into thecash 0ow register, input I;Y< 5 (2, and solve for N+ 5 + 5 ?BJ.HB.

c 26(B'(;+6 5 ?2.6(;?BJ.HB 5 @.(6D!apital gains yield 5 G .J6

E)pected total return 5 (2.66D

9e now that rs is (2D, and the dividend yield is @.(6DA therefore, the capitalgains yield must be G.J6D.

26('G;+@ 5 ?B.C6;[email protected] 5 C.66D

!apital gains yield 5 @ .66E)pected total return 5 (2.66D

The main points to note here are as follows/

(. The total yield is always (2D #e)cept for rounding errors$.

2. The capital gains yield starts relatively high, then declines as the supernormalgrowth period approaches its end. The dividend yield rises.

B. fter (2;B(;(C, the stoc will grow at a @D rate. The dividend yield will e"ualCD, the capital gains yield will e"ual @D, and the total return will be (2D.

d +eople in high*income ta) bracets will be more inclined to purchase UgrowthV

stocs to tae the capital gains and thus delay the payment of ta)es until a laterdate. The rm-s stoc is UmatureV at the end of 26(C.

e Since the rm-s supernormal and normal growth rates are lower, the dividends and,hence, the present value of the stoc price will be lower. The total return from thestoc will still be (2D, but the dividend yield will be larger and the capital gainsyield will be smaller than they were with the original growth rates. This resultoccurs because we assume the same last dividend but a much lower current stocprice.

f s the re"uired return increases, the price of the stoc declines, but both thecapital gains and dividend yields increase initially. :f course, the long*term capitalgains yield is still HD, so the long*term dividend yield is (6D.




14/31

Coprehensi,e5Spreadsheet ro!le

Note to Instructors:The solutions for arts a throuh c of this pro!le are pro,ided at the !ack of the

te0t6 howe,er/ the solution to art d is not 7nstructors can access the Excel 8le onthe te0t!ooks we!site or the 7nstructors +esource C:

9-"" a (. 8ind the price today.

2. 8ind the e)pected dividend yield.


15/31

! (. 8ind the price today.

2. 8ind the e)pected dividend yield.

B. 8ind the e)pected capital gains yield.

c 9e used the @ year supernormal growth scenario for this calculation, but ultimatelyit does not matter which e)ample you use, as they both yield the same result.

Chapter 9& Stocks and Their Valuation Comprehensive/Spreadsheet Problem 1$



16/31

Mpon re0ection, we see that these calculations were unnecessary because theconstant growth assumption holds that the long*term growth rate is the dividendgrowth rate and the capital gains yield, hence we could have simply subtracted thelong*run growth rate from the re"uired return to nd the dividend yield.

d

The price as estimated by the corporate valuation method di%ers from thediscounted dividends method because di%erent assumptions are built into the twosituations. If we had pro>ected nancial statements, found both dividends and freecash 0ow from those pro>ected statements, and applied the two methods, then theprices produced would have been identical. s it stands, though, the two priceswere based on somewhat di%erent assumptions, hence di%erent prices wereobtained. Note especially that in the 8!8 model we assumed a 9!! of JD versusa cost of e"uity of (6D for the discounted dividend model. That would obviouslytend to raise the price.

1% Comprehensive/Spreadsheet Problem Chapter 9& Stocks and Their Valuation



17/31

7nterated Case

9-"3

utual of Chicao 7nsurance Copan.Stock Valuation

+o!ert ;alik and Carol


18/31

" Coon stockholders often ha,e the riht/ called the

preepti,e riht/ to purchase an. additional shares

sold !. the 8r 7n soe states/ the preepti,e riht

is autoaticall. included in e,er. corporate charter6 in

others/ it is necessar. to insert it speci8call. into the

charter

; (1) Frite a forula that can !e used to ,alue an. stock/

reardless of its di,idend pattern

Answer& BShow S9-3 throuh S9-% here The ,alue of an. stock is

the present ,alue of its e0pected di,idend strea&

(G H

)r1(

:

)r1(

:

)r1(

:

)r1(

:

s

3

s

3

s

"

t

s

1

∞

∞

Iowe,er/ soe stocks ha,e di,idend rowth patterns that

allow the to !e ,alued usin short-cut forulas

; (") Fhat is a constant rowth stockJ Iow are constant rowth

stocks ,aluedJ

Answer& BShow S9-2 and S9-4 here A constant rowth stock is one

whose di,idends are e0pected to row at a constant rate

fore,er KConstant rowthL eans that the !est estiate

of the future rowth rate is soe constant nu!er/ not that

we reall. e0pect rowth to !e the sae each and e,er.

.ear an. copanies ha,e di,idends that are e0pected to

row steadil. into the foreseea!le future/ and suchcopanies are ,alued as constant rowth stocks

Mor a constant rowth stock&

:1 H :(1 N )/ :" H :1(1 N ) H :(1 N )"/ and so on

14 Interated Case Chapter 9& Stocks and Their Valuation



19/31

Fith this reular di,idend pattern/ the eneral stock

,aluation odel can !e sipli8ed to the followin ,er.

iportant e=uation&

(G H

r:s

1

Hr)1(:

s

This is the well-known KOordon/L or Kconstant-rowthL

odel for ,aluin stocks Iere :1 is the ne0t e0pected

di,idend/ which is assued to !e paid 1 .ear fro now/ rs is

the re=uired rate of return on the stock/ and is the

constant rowth rate

; (3) Fhat are the iplications if a copan. forecasts a constant

that e0ceeds its rsJ Fill an. stocks ha,e e0pected P rs

in the short run (that is/ for the ne0t few .ears)J 7n the

lon run (that is/ fore,er)J

Answer& BShow S9-9 here The odel is deri,ed atheaticall./ and

the deri,ation re=uires that rs P 7f is reater than rs/ the

odel i,es a neati,e stock price/ which is nonsensicalThe odel sipl. cannot !e used unless (1) rs P / (") is

e0pected to !e constant/ and (3) can reasona!l. !e

e0pected to continue inde8nitel.

Stocks a. ha,e periods of supernoral rowth/ where

s P rs6 howe,er/ this rowth rate cannot !e sustained

inde8nitel. 7n the lon-run/ rs

C Assue that ;on Teps has a !eta coecient of 1"/ that

the risk-free rate (the .ield on T-!onds) is 2R/ and that the

re=uired rate of return on the arket is 1"R Fhat is ;on

Tepss re=uired rate of returnJ

Chapter 9& Stocks and Their Valuation Interated Case 19



20/31

Answer& BShow S9-1 here Iere we use the S* to calculate ;on

Tepss re=uired rate of return&

rs H r+M N (r r+M)!;on Teps

H 2R N (1"R 2R)(1")

H 2R N ($R)(1")

H 2R N %R H 13R

: Assue that ;on Teps is a constant rowth copan.

whose last di,idend (:/ which was paid .esterda.) was

" and whose di,idend is e0pected to row inde8nitel.

at a %R rate

(1) Fhat is the 8rs e0pected di,idend strea o,er the ne0t 3.earsJ

Answer& BShow S9-11 here ;on Teps is a constant rowth stock/

and its di,idend is e0pected to row at a constant rate of

%R per .ear E0pressed as a tie line/ we ha,e the

followin setup Uust enter " in .our calculator6 then keep

ultipl.in !. 1 N H 1% to et :1/ :"/ and :3&

1 " 3

"1" ""#2 "34"14412%1%$

: (") Fhat is its current stock priceJ

Answer& BShow S9-1" here Fe could e0tend the tie line on out

fore,er/ 8nd the ,alue of ;on Tepss di,idends for e,er.

.ear on out into the future/ and then the V of each

" Interated Case Chapter 9& Stocks and Their Valuation


rs H 13R

H %R

15113

15(113)"

15(113)3


21/31

di,idend discounted at rs H 13R Mor e0aple/ the V of :1

is 142%16 the V of :" is 12$996 and so forth Wote that

the di,idend pa.ents increase with tie/ !ut as lon as rs

P / the present ,alues decrease with tie 7f we e0tended

the raph on out fore,er and then sued the Vs of the

di,idends/ we would ha,e the ,alue of the stock Iowe,er/

since the stock is rowin at a constant rate/ its ,alue can

!e estiated usin the constant rowth odel&

(G H

r

:

s

1

H%13

1""T

H2

1""T H 3"9

: (3) Fhat is the stocks e0pected ,alue 1 .ear fro nowJ

Answer& BShow S9-13 here After one .ear/ :1 will ha,e !een paid/

so the e0pected di,idend strea will then !e :"/ :3/ :#/ and

so on Thus/ the e0pected ,alue one .ear fro now is

3"1&

1G H

r

:

s

"

H%13

"#2"T

H2

"#2"T H 3"1

: (#) Fhat are the e0pected di,idend .ield/ capital ains .ield/

and total return durin the 8rst .earJ

Answer& BShow S9-1# here The e0pected di,idend .ield in an. @ear

W is

:i,idend .ield H1W

W

3G

:

/

Fhile the e0pected capital ains .ield is

Capital ains .ield H1W

1WW

3G

)3G3G(

H rs 1W

W

3

:

Chapter 9& Stocks and Their Valuation Interated Case "1



22/31

Thus/ the di,idend .ield in the 8rst .ear is 2R/ while the

capital ains .ield is %R&

Total return H 13R

:i,idend .ield H "1"53"9H 2R

Capital ains .ield H %R

E Wow assue that the stock is currentl. sellin at 3"9

Fhat is its e0pected rate of returnJ

Answer& The constant rowth odel can !e rearraned to this for&

srG H

:

1

Iere the current price of the stock is known/ and we sol,e

for the e0pected return Mor ;on Teps&

srG H "1"53"9 N % H 2 N % H 13R

M Fhat would the stock price !e if its di,idends were e0pected

to ha,e ?ero rowthJ

Answer& BShow S9-1$ here 7f ;on Tepss di,idends were not

e0pected to row at all/ then its di,idend strea would !e a

perpetuit. erpetuities are ,alued as shown !elow&

1 " 3

" " "1221$2139

(G H1$ 34

(G H :5rs H "513 H 1$34

"" Interated Case Chapter 9& Stocks and Their Valuation


rs H 13R

H R

15(113)"

15(113)3

15113


23/31

Wote that if a preferred stock is a perpetuit./ it a. !e

,alued with this forula

Chapter 9& Stocks and Their Valuation Interated Case "3



24/31

O Wow assue that ;on Teps is e0pected to e0perience

nonconstant rowth of 3R for the ne0t 3 .ears/ then

return to its lon-run constant rowth rate of %R Fhat is

the stocks ,alue under these conditionsJ Fhat are its

e0pected di,idend and capital ains .ields in @ear 1J @ear

#J

Answer& BShow S9-1% throuh S9-14 here ;on Teps is no loner a

constant rowth stock/ so the constant rowth odel is not

applica!le Wote/ howe,er/ that the stock is e0pected to

!ecoe a constant rowth stock in 3 .ears Thus/ it has a

nonconstant rowth period followed !. constant rowthThe easiest wa. to ,alue such nonconstant rowth stocks is

to set the situation up on a tie line as shown !elow&

1 " 3 #

"% 334 #39# #%$2%#

"31 "%#2 3#$

#% 11# 3G H %%$# H

$# 12 H (G

Sipl. enter " and ultipl. !. (13) to et :1 H "%6

ultipl. that result !. 13 to et :" H 334/ and so forth

Then reconi?e that after @ear 3/ ;on Teps !ecoes a

constant rowth stock/ and at that point 3G can !e found

usin the constant rowth odel 3G is the present ,alue

as of t H 3 of the di,idends in @ear # and !e.ond and is also

called the hori?on/ or continuin/ ,alue

Fith the cash ows for :1/ :"/ :3/ and 3G shown on the

tie line/ we discount each ,alue !ack to @ear / and the

"# Interated Case Chapter 9& Stocks and Their Valuation


rs H 13R

s H 3R s H 3R s H 3R n H %R

%13

%$2%##

15(113)"

15(113)3

15(113)3

15113


25/31

su of these four Vs is the ,alue of the stock toda./ H

$#12

The di,idend .ield in @ear 1 is #4R/ and the capital

ains .ield is 4"R&

:i,idend .ield H12$#T

%"T H #4 H #4R

Capital ains .ield H 13R #4R H 4"R

:urin the nonconstant rowth period/ the di,idend .ields

and capital ains .ields are not constant/ and the capital

ains .ield does not e=ual Iowe,er/ after @ear 3/ the

stock !ecoes a constant rowth stock/ with H capitalains .ield H %R and di,idend .ield H 13R %R H

2R

I Suppose ;on Teps is e0pected to e0perience ?ero rowth

durin the 8rst 3 .ears and then resue its stead.-state

rowth of %R in the fourth .ear Fhat would !e its ,alue

thenJ Fhat would !e its e0pected di,idend and capital

ains .ields in @ear 1J 7n @ear #J

Answer& BShow S9-19 and S9-" here Wow we ha,e this situation&

1 " 3 #

" " " "1"

1221$2139

" 99 3G H 3"9 H"$ 2" H (G

:urin @ear 1&

:i,idend .ield H2""$T

"T H 224 H 224R

Chapter 9& Stocks and Their Valuation Interated Case "$


rs H 13R

H R H R H R n H %R

2

1""

15(113)"

15(113)3

15(113)3

15113


26/31

Capital ains .ield H 13R 224R H $""R

Aain/ in @ear # ;on Teps !ecoes a constant rowth

stock6 hence H capital ains .ield H %R and di,idend

.ield H 2R

7 Minall./ assue that ;on Tepss earnins and di,idends

are e0pected to decline at a constant rate of %R per .ear/

that is/

H -%R Fh. would an.one !e willin to !u. such a stock/

and at what price should it sellJ Fhat would !e its di,idend

and capital ains .ields in each .earJ

Answer& BShow S9-"1 and S9-"" here The copan. is earnin

soethin and pa.in soe di,idends/ so it clearl. has a

,alue reater than ?ero That ,alue can !e found with the

constant rowth forula/ !ut where is neati,e&

(3 Hr

:

S

1

Hr

)1(:

S

H)%(13

)9#("T H

19

441T H 949

Since it is a constant rowth stock& H Capital ains .ield H -%R/

Ience&

:i,idend .ield H 13R (-%R) H 19R

As a check&

:i,idend .ield H499T

441T H 19 H 19R

The di,idend and capital ains .ields are constant o,er

tie/ !ut a hih (19R) di,idend .ield is needed to oXset

the neati,e capital ains .ield

"% Interated Case Chapter 9& Stocks and Their Valuation



27/31

U Suppose ;on Teps e!arked on an aressi,e e0pansion

that re=uires additional capital anaeent decided to

8nance the e0pansion !. !orrowin # illion and !.

haltin di,idend pa.ents to increase retained earnins

7ts FACC is now 1R/ and the pro>ected free cash ows for

the ne0t 3 .ears are -$ illion/ 1 illion/ and "

illion After @ear 3/ free cash ow is pro>ected to row at

a constant %R Fhat is ;on Tepss total ,alueJ 7f it has

1 illion shares of stock and # illion of de!t and

preferred stock co!ined/ what is the price per shareJ

Answer& BShow S9-"3 throuh S9-"9 here

1 " 3 #

-$ 1 " "1"

-#$#$4"%#

1$"%394 192 $3 H

#1% 9#" H Total ,alue

Value of e=uit. H Total ,alue :e!t

H #1%9# # H 32%9# illion

rice per share H 32%9#51 H 32%9


28/31

Answer& BShow S9-3 and S9-31 here

prG Hp

p

V

:

H $T$T

H 1R

7f the preferred has a "-.ear aturit. its ,alue would !e

calculated as follows&

Enter the followin inputs into .our 8nancial calculator& W

H "6 75@+ H 16 T H $6 MV H $6 and then sol,e for V H

$

Iowe,er/ to 8nd the ,alue of the perpetual preferreds

di,idends after @ear " we can enter the followin data& W

H "6 75@+ H 16 T H $6 MV H 6 and then sol,e for V H

#"$2 Thus/ di,idends in @ears "1 to in8nit. account for

$ #"$2 H 2#3 of the perpetual preferreds ,alue

"4 Interated Case Chapter 9& Stocks and Their Valuation



29/31

Appendi0 9AStock arket E=uili!riu

Answers to End-of-Chapter Questions

9A-1 8or a stoc to be in e"uilibrium, two related conditions must hold/

(. stoc-s e)pected rate of return as seen by the marginal investor must e"ual its

re"uired rate of return/ ii rr7 = .

2. The actual maret price of the stoc must e"ual its intrinsic value as estimated by

the marginal investor/ 66 +7+ = .

9A-" Some individual investors may believe that ii rr7 > and 66 ++7 > #hence they would

invest most of their funds in the stoc$, while other investors might have an opposite viewand sell all of their shares. &owever, investors at the margin establish the actual maret

priceA and for these investors, we must have ii rr7 = and 66 ++7 = . If these conditions donot hold, trading will occur until they do.

Appendi0 9A& Stock arket E=uili!riu Answers and Solutions "9



30/31

Solutions to End-of-Chapter ro!les

9A-1 a ri 5 r


31/31

9A-3 a :ld rs 5 rected. The decrease in ris is not suWcient to o%set the decline inprotability and the reduced growth rate.

! +:ld 5 [email protected]. +New 56H.6r

$6H.(#2?

s −

.

Solving for rs we have the following/

[email protected] 56H.6r

6I.2?

s −

?2.6 5 [email protected]#rs$ = ?2.B@@G?H.HB@G 5 [email protected]#rs$

rs 5 6.6C@B2.

Solving for b/

C.@B2D 5 GD F BD#b$(.@B2D 5 BD#b$

b 5 6.@(6C.

!hec/ rs 5 GD F #BD$6.@(6C 5 C.@B2D.

6+7 5

[email protected]

6I.2?

−

5 [email protected].

Therefore, only if management-s analysis concludes that ris can be lowered to b 56.@(6C, should the new policy be put into e%ect.

Appendi0 9A& Stock arket E=uili!riu Answers and Solutions 31

Documents

09 answers to all problems.doc