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Lecture 11

# FINE 2000 Lecture 11: Solutions Chapter 14 (9th ed) Suggested Problems-3 Premium

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School
Department
Finance
Course
FINE 2000
Professor
Greg Chiykowski
Semester
Winter

Description
Solutions to Suggested Problems Chapter 14: Cost of Capital 7. (LO2) a. The pretax cost of debt is the YTM of the company’s bonds, so: P = \$930 = \$35(PVIFA ) + \$1,000(PVIF ) 0 R%,54 R%,54 R = 3.81% YTM = 2 × 3.81% = 7.62% b. The aftertax cost of debt is: R D 0.0762(1 – 0.35) = 0.04953 or 4.953% c. The after-tax rate is more relevant because that is the actual cost to the company. 11. (LO3) Here we have the WACC and need to find the debt-equity ratio of the company. Setting up the WACC equation, we find: WACC = 0.0850 = 0.11(E/V) + 0.061(D/V)(1 – 0.35) Rearranging the equation, we find: 0.085(V/E) = 0.11 + 0.061(0.65)(D/E) Now we must realize that the V/E is just the equity multiplier, which is equal to: V/E = 1 + D/E 0.085(D/E + 1) = 0.11 + 0.03965(D/E) Now we can solve for D/E as: 0.04535(D/E) = 0.025 D/E = 0.5513 12. (LO3) a. The book value of equity is the book value per share times the number of shares, and the book value of debt is the face value of the company’s debt, so: BV E 8,000,000(\$7) = \$56,000,000 BV D \$85,000,000 + 50,000,000 = \$135,000,000 So, the total value of the company is: V = \$56,000,000 + 135,000,000 = \$191,000,000 And the book value weights of equity and debt are: E/V = \$56,000,000/\$191,000,000 = 0.2932 D/V = 1 – E/V = 0.7068 b. The market value of equity is the share price times the number of shares, so: MV =E8,000,000(\$73) = \$584,000,000 Using the relationship that the total market value of debt is the price quote times the par value of the bond, we find the market value of debt is: MV =D0.97(\$85,000,000) + 1.08(\$50,000,000) = \$136,450,000 This makes the total market value of the company: V = \$584,000,000 + 136,450,000 = \$720,450,000 And the market value weights of equity and debt are: E/V = \$584,000,000/\$720,450,000 = 0.8106 D/V = 1 – E/V = 0.1894 c. The market value weights are more relevant because the market values measure management’s success in achieving its goal: maximizing shareholder wealth. 13. (LO3) First, we will find the cost of equity for the company. The information provided allows us to solve for the cost of equity using the dividend growth model, so: R E [\$3.90(1.06)/\$73] + 0.06 = 0.1166 or 11.66% Next, we need to find the YTM on both bond issues. Doing so, we find: P 1 \$970 = \$35(PVIFA R%,42) + \$1,000(PVIF R%,42 R = 3.64% YTM = 3.64% × 2 = 7.28% P 2 \$1,080 = \$40(PVIFA R%,12 + \$1,000(PVIF R%,12 R = 3.187% YTM = 3.187% × 2 = 6.374% To find the weighted average after-tax cost of debt, we need the weight of each bond as a percentage of the total debt. We find: w = 0.97(\$85,000,000)/\$136,450,000 = 0.604 D1 w D2 = 1.08(\$50,000,000)/\$136,450,000= 0.396 Now we can multiply the weighted average cost of debt times one minus the tax rate to find the weighted average after-tax cost of debt. This gives us: R D (1 – 0.35)[(0.604)(0.0728) + (0.396)(0.06374)] = 0.04499 or 4.499% Using these costs we have found and the weight of debt we calculated earlier, the WACC is: WACC = 0.8106 (0.1166) + 0.1894 (0.04499) = 0.1030 or 10.30% 15. (LO3) We will begin by finding the market value of each type of financing. We find: MV = 10,000(\$1,000)(1.08) = \$10,800,000 D MV =E495,000(\$63) = \$31,185,000 MV = 35,000(\$72) = \$2,520,000 P And the total market value of the firm is: V = \$10,800,000 + 31,185,000 + 2,520,000 = \$44,505,000 Now, we can find the cost of equity using the CAPM. The cost of equity is: R E 0.032 + 1.15(0.07) = 0.1125 or 11.25% The cost of debt is the YTM of the bonds, so: P 0 \$1,080 = \$32(PVIFA R%,50) + \$1,000(PVIF R%,50) R =
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