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Chapter 12: Risk, Return, and Capital Budgeting 12.1 Cost of equity RS = 6 + 1.21 (9) = 16.89%

⎡ ⎤ 1 − (1+ .1689)−5 ⎥ NPV = −1, 200, 000 + 340, 000 ⎢ ⎢ ⎥ = −$109, 466.26 .1689 ⎢ ⎥ ⎣ ⎦ Do not undertake the project.
E( RDouglas ) = (-0.04 + 0.04 + 0.07 + 0.14 + 0.10) / 5 = 0.062

12.2 a.

E( RM ) = (-0.12 + 0.01 + 0.06 + 0.10 + 0.05) / 5 = 0.02 b.
R(d) -0.04 0.04 0.07 0.14 0.1 0.31 0.062R(m) -0.12 0.01 0.06 0.1 0.05 0.1 R-E(Rd) -0.102 -0.022 0.008 0.078 0.038 R-E(Rm) -0.14 -0.01 0.04 0.08 0.03 (R-E(Rm))^2 (R-E(Rd))*(R-E(Rm)) 0.0196 0.01428 0.0001 0.00022 0.0016 0.00032 0.0064 0.00624 0.0009 0.00114 0.0286 0.0222

Sum E(R) VAR (m) COV(Rd,Rm)

0.02 0.0286/4 =0.00715 0.0222/4 =0.00555

12.3 RS RB a. b.

VAR( Rm ) = 6% + 1.15 × 10% = 17.5% = 6% + 0.3 × 10% = 9% Cost of equity= RS = 17.5% D/E = 1/3 D/(D+E) =1/4 E/(D+E) = 3/4 WACC = .75 × 17.5% + 0.25× 9% (1 - 0.35) = 14.59% = (0.004225) 2 = 0.065
1 1

β Douglus =

COV( Rm ,RDouglas )

=

0.00715 = 0.7762 0.00555

12.4 σC

σ M = (0.001467 ) 2 = 0.0383
Beta of Ceramics Craftsman = ρCM σC σ M / σ M 2 = ρCM σC / σ M = (0.415) (0.065) / 0.0383 = 0.7043 12.5 a. To compute the beta of Travis Manufacturing’sstock, you need the product of the deviations of Travis’ returns from their mean and the deviations of the market’s returns from their mean. You also need the squares of the deviations of the market’s

B-82

Answers to End-of-Chapter Problems

returns from their mean. The mechanics of computing the means and the deviations were presented in an earlier chapter.
R(Travis) R(market) 0.018 0.0460.102 0.116 -0.002 -0.04 -0.09 -0.1 0.17 0.142 0 0.024 -0.16 -0.15 0.04 0.1 0.25 0.24 0.22 0.098 -0.2 -0.06 0.08 0.056 0.428 0.472 0.035667 R-E(R) -0.01767 0.066333 -0.03767 -0.12567 0.134333 -0.03567 -0.19567 0.004333 0.214333 0.184333 -0.23567 0.044333 R-E(Rm) 0.006667 0.076667 -0.07933 -0.13933 0.102667 -0.01533 -0.18933 0.060667 0.200667 0.058667 -0.09933 0.016667 (R-E(Rm))^2 (R-E(R))*(R-E(Rm))4.44489E-05 -0.000117786 0.005877829 0.005085552 0.006293725 0.002988236 0.019413685 0.01750956 0.010540513 0.013791566 0.000235101 0.000546882 0.035846985 0.03704622 0.003680485 0.00026287 0.040267245 0.04300956 0.003441817 0.010814264 0.009867045 0.02340951 0.000277789 0.000738898 0.135786667 0.155085333

Sum E(R) VAR(m) COV(T,m) Beta

0.039333 0.135787/11 =0.012344 0.155085/11 =0.0140991.142125

E( RTravis ) = 0.428 /12 = 0.035667 E( RMarket ) = 0.472 /12 = 0.039333 COV ( RTravis , RM ) = E[( RT − E( RT ))( RM − E( RM ))] = 0.01409867 VAR( RM ) = E( RM − E( RM ))2 = 0.01234424 COV ( RTravis , RM ) = 1.142 VAR( RM ) The beta of the average stock is 1. Travis’ beta is higher. This indicates that Travis’s stock is riskier than the average stock.

β Travis =

b.

12.6 a. RMcan have three values, 0.32, 0.36 or 0.40. The probability that RM takes one of these values is the sum of the joint probabilities of the return pair that include the particular value of RM . For example, if RM is 0.32, RJ will be 0.32, 0.36 or 0.44.The probability that RM is 0.32 and RJ is 0.32 is 0.10. The probability that RM is 0.32 and RJ is 0.36 is 0.06. The probability that RM is 0.32 andRJ is 0.44 is 0.04. The probability that RM is 0.32 is, therefore, 0.10 + 0.06 + 0.04 = 0.20. The same procedure is used to calculate the probability that RM is 0.36 and the probability that RM is 0.40. Remember, the sum of the probability must be one.

Answers to End-of-Chapter Problems

B-83

RM 0.32 0.36 0.40 b. i. E( RM )

Probability 0.20 0.60 0.20 = 0.32 (0.20) + 0.36 (0.60) + 0.40(0.20) = 0.36

ii.

σ 2 = (0.32 - 0.36) 2 (0.20) + (0.36 - 0.36) 2 (0.60) M
+ (0.40 - 0.36) 2 (0.20) = 0.00064
1

iii.

σ M = (0.00064)2 = 0.025298
Probability .10 .20 .40 .20 .10

c.

RJ .32 .36 .40 .44 .48

d.

i. E( Rj ) = .32 (.10) + .36 (.20) + .40 (.40) + .44 (.20) + .48(.10) = .40 ii. σj2 = (.32 - .40)2 (.10) + (.36 - .40)2 (.20) + (.40 - .40)2 (.40) + (.44 - .40)2 (.20)...
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