# Cost of Capital End of Book Solutions

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CHAPTER

3

COST OF CAPITAL
SOLUTIONS
1. B is correct. The cost of equity is deﬁned as the rate of return required by stockholders.
2. B is correct. Debt is generally less costly than preferred or common stock. The cost of debt is further reduced if interest expense is tax deductible.
3. C is correct. First calculate the growth rate using the sustainable growth calculation, and then calculate the cost of equity using the rearranged dividend discount model: g ¼ ð1 À Dividend payout ratioÞðReturn on equityÞ ¼ ð1 À 0:30Þð15%Þ ¼ 10:5% re ¼ ðD1 =P0 Þ þ g ¼ ð\$2:30=\$45Þ þ 10:50% ¼ 15:61%
4. C is correct. FV ¼ \$1,000; PMT ¼ \$40; N ¼ 10; PV ¼ \$900
Solve for i. The six-month yield, i, is 5.3149%.
YTM ¼ 5:3149% 3 2 ¼ 10:62985% rd ð1 À
B is correct.
Asset betas: βequity/[1 þ (1 À t)(D/E)]
Relevant ¼ 1:702=½1 þ ð0:77Þð0Þ ¼ 1:702
ABJ ¼ 2:8=½1 þ ð0:77Þð0:003Þ ¼ 2:7918
Opus ¼ 3:4=1 þ ½ð0:77Þð0:013Þ ¼ 3:3663
20. C is correct. Weights are determined based on relative market values:

Pure-Play

Market Value of
Equity in Billions

Proportion of Total

Relevant

\$3.800

0.5490

ABJ

2.150

0.3106

Opus

0.972

0.1404

Total

\$6.922

1.0000

Weighted average beta ¼ ð0:5490Þð1:702Þ þ ð0:3106Þð2:7918Þ þ ð0:1404Þð3:3572Þ ¼ 2:27
21. B is correct.
Asset beta ¼ 2:27
Levered beta ¼ 2:27f1 þ ½ð1 À 0:23Þð0:01Þg ¼ 2:2875
Cost of equity capital ¼ 0:0525 þ ð2:2875Þð0:07Þ ¼ 0:2126 or 21:26%
22. C is correct.
For debt: FV ¼ 2,400,000; PV ¼ 2,156,000; n ¼ 10; PMT ¼ 150,000
Solve for i. i ¼ 0.07748. YTM ¼ 15.5%
Before-tax cost of debt ¼ 15.5%
Market value of equity ¼ 1 million shares outstanding plus 1 million newly issued shares ¼ 2 million shares at \$8 ¼ \$16 million

part-ii-03

13 January 2012; 10:25:56

102

Solutions

Total market capitalization ¼ \$2.156 million þ \$16 million ¼ \$18.156 million
Levered beta ¼ 2.27{1 þ [(1 À 0.23)(2.156/16)]} ¼ 2.27 (1.1038) ¼ 2.5055
Cost of equity ¼ 0.0525 þ 2.5055(0.07) ¼ 0.2279 or 22.79%
Debt weight ¼ \$2.156/\$18.156 ¼ 0.1187
Equity weight ¼ \$16/\$18.156 ¼ 0.8813
TagOn’s MCC ¼ ½ð0:1187Þð0:155Þð1 À 0:23Þ þ ½ð0:8813Þð0:2279Þ
¼ 0:01417 þ 0:20083
¼ 0:2150 or 21:50%
23. A is correct. The