FIN 301 B Porter Rachna Exam III - Review II Soln

8/18/2019 FIN 301 B Porter Rachna Exam III - Review II Soln.

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Exam III: Review II Soln.

Use the following information for Questions 1 and 2:A stock has a required return on 11 percent. The risk-free is 7 percent and the marketrisk premium is ! percent.

1. "hat is the stock#s $eta%

A. 1.2&. 1.1'. 1.()*. (.+

2. ,f the market risk premium increases to percent what will happen to the stock#srequired rate of return%

A. .((&. 7.(('. 11.((*. 1/.(()

/. 0tock has a $eta of 1. 0tock 0 has a $eta of (.7 the e3pected rate of returnon an a4erage stock is 1/ percent and the risk-free rate of return is 7 percent. &5how much does the required return on the riskier stock e3ceed the required returnon the less risk5 stock%

A. 2.&. /.('. /.*. !.)

!. An in4estment has a ( chance of producing a 2( return a 2 chance of producing an 6 return and a 2 chance of producing a -12 return. "hat isits e3pected return% +8

. 0tocks 9 ; ha4e the following pro$a$ilit5 distri$utions of e3pected futurereturns:

Probability X Y

(.1 1(8 /8 (.2 2 ( (.! 12 2(

(.2 2( 2 (.1 /6 !

a. 'alculate the e3pected rate of return r; for stock ;. r9 < 128 $. 'alculate the standard de4iation of e3pected returns for 0tock 9. ; < 2(./8 =ow calculate the coefficient of 4ariation for 0tock ;.

a. rY= 0.1(-35%) + 0.2(0%) + 0.4(20%) + 0.2(25%) + 0.1(45%)= 14% versus 12% for X.

b. σ2 = (-10% – 12%)2(0.1) + (2% – 12%)2(0.2) + (12% – 12%)2(0.4)

+ (20% – 12%)2(0.2) + (38% – 12%)2(0.1) = 148.8%.

σX = 12.20% versus 20.35% for Y.

CVX = σX/ rX = 12.20%/12% = 1.02, wh!e


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CV Y = 20.35%/14% = 1.45.

. 0uppose 5ou are the mone5 manager of a >! million in4estment fund. The fundconsists of ! stocks with the following in4estments and $etas:

Stock Investment Beta

A >!((((( 1.(

& ((((( .(8 ' 1(((((( 1.2 * 2(((((( (.7

,f the market#s required rate of return is 1! and the risk-free rate is what is thefunds required rate of return%

"or#fo!o $e# = &400,000/4,000,000'(1.50) + &00,000/4,000,000' (-0.50) + &1,000,000/4,000,000' (1.25) + &2,000,000/4,000,000' (0.5)$* = (0.1)(1.5) + (0.15)(-0.50) + (0.25)(1.25) + (0.5)(0.5)= 0.15 – 0.05 + 0.3125 + 0.35 = 0.25.

r* = r + (r – r)($*) = % + (14% – %)(0.25) = 12.1%.

7. "arr 'orporation ?ust paid a di4idend of >1.( a share that is *( 1.(8. The di4idend is e3pected to grow 7 a 5ear for / 5ears and then at a5ear thereafter. "hat is the e3pected di4idend per share for each of the ne3t 5ears%

*( < >1.(@ g1-/ < 7@ gn < @ *1 through * < %*1 < *(1 g18 < >1.(1.(78 < >1.((.*2 < *(1 g181 g28 < >1.(1.(782 < >1.717!.*/ < *(1 g181 g281 g/8 < >1.(1.(78/ < >1.6/7.*! < *(1 g181 g281 g/81 gn8 < >1.(1.(78/1.(8 < >1.+2+!.* < *(1 g181 g281 g/81 gn82 < >1.(1.(78/1.(82 < >2.(2+.

6. Thomas &rothers is e3pected to pa5 >(.( per share di4idend at the end ofthe 5ear that is *1 < >(.(8. The di4idend is e3pected to grow at a constant rateof 7 a 5ear. The required rate of return on the stock s is 1. "hat is thestock#s 4alue per share%

*1 < >(.(@ g < 7@ rs < 1@ Bhat8 ( < %

+. Carrison 'lothiers# stock currentl5 sells for >2( a share. ,t ?ust paid adi4idend of >1.(( a share that is *o < >1.((8. The di4idend is e3pected to growat a constant rate of a 5ear. "hat stock price is e3pected 1 5ear from now%

"hat is the required rate of return%


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12. 0mith Technologies is e3pected to generate >1( million in free cash flowne3t 5ear and D'D is e3pected to grow at a constant rate of per 5earindefinitel5. 0mith has no de$t or preferred stock and its "A'' is 1(. ,f smithhas ( million shares of stock outstanding what is the stock#s 4alue per share%

The firm#s free cash flow is e3pected to grow at a constant rate hence we canappl5 a constant growth formula to determine the total 4alue of the firm.Dirm 4alue < D'D1E"A'' F g8< >1(((((((E(.1( F (.(8< >/(((((((((.To find the 4alue of an equit5 claim upon the compan5 share of stock8 we mustsu$tract out the market 4alue of de$t and preferred stock. This firm happens to $eentirel5 equit5 funded and this step is unnecessar5. Cence to find the 4alue of ashare of stock we di4ide equit5 4alue or in this case firm 4alue8 $5 the num$er of shares outstanding.Gquit5 4alue per share < Gquit5 4alueE0hares outstanding< >/(((((((((E(((((((< >(.

1/. Dee Dounders has perpetual preferred stock outstanding that sells for >( per share and pa5s a di4idend of > at the end of each 5ear. "hat is the requiredrate of return%

1!. The real risk-free rate is / percent. ,nflation is e3pected to $e / percentthis 5ear ! percent ne3t 5ear and then /. percent thereafter. The maturit5 risk

premium is estimated to $e (.( 9 t-18 where t < num$er of 5ears to maturit5."hat is the 5ield on a 7-5ear Treasur5 note%r < r) ,B HB *B IB.r) < (.(/.,B < J(.(/ (.(! 8(.(/8KE7 < (.(/.HB < (.(((8 < (.((/.*B < (.IB < (.

r T7 < (.(/ (.(/ (.((/ < (.(6 < .6.

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FIN 301 B Porter Rachna Exam III - Review II Soln