The cost of capital wacc 
Solutions to Chapter 12
The Cost of Capital
1. The yield to maturity for the bonds (since maturity is now 19 years) is the interest rate (r) that is the solution to the following equation:
[$80 annuity factor(r, 19 years)] + [$1,000/(1 + r)19] = $1,050 Using a financial calculator, enter: n = 19, FV = 1000, PV = (-)1050, PMT = 90, and then compute i = 7.50%
Therefore, the after-tax cost of debt is: 7.50% (1 – 0.35) = 4.88%
2. r = DIV/P0 = $4/$40 = 0.10 = 10%
3. = [0.3 7.50% (1 – 0.35)] + [0.2 10%] + [0.5 12.0%] = 9.46%
4.
5. The total value of the firm is $80 million. The weights for each security class are as follows:
Debt: D/V = 20/80 = 0.250 Preferred: P/V = 10/80 = 0.125 Common: E/V = 50/80 = 0.625 = [0.250 6% (1 – 0.35)] + [0.125 8%] + [0.625 12.0%] = 9.475%
6. Executive Fruit should use the WACC of Geothermal, not its own WACC, when evaluating an investment in geothermal power production. The risk of the project determines the discount rate, and in this case, Geothermal’s WACC is more reflective of the risk of the project in question. The proper discount rate, therefore, is not 12.3%. It is more likely to be 11.4%.
7. The flotation costs reduce the NPV of the project by $1.2 million. Even so, project NPV is still positive, so the project should be undertaken.
8. The rate on Buildwell’s debt is 5 percent. The cost of equity capital is the required rate of return on equity, which can be calculated from the CAPM as follows: 4% + (0.90 8%) = 11.2% The weighted average cost of capital, with a tax rate of zero, is: = [0.30 5% (1 – 0)] + [0.70 11.2%] = 9.34%
9. The internal rate of return, which is 12%, exceeds the cost of capital. Therefore, BCCI should accept the project. The present value of the project cash flows is: $100,000 annuity factor(9.34%, 8 years) = $546,556.08 This is the most BCCI should pay for the project.
10.
Security
Market Value
Explanation
Debt $ 5.5 million
The Cost of Capital
1. The yield to maturity for the bonds (since maturity is now 19 years) is the interest rate (r) that is the solution to the following equation:
[$80 annuity factor(r, 19 years)] + [$1,000/(1 + r)19] = $1,050 Using a financial calculator, enter: n = 19, FV = 1000, PV = (-)1050, PMT = 90, and then compute i = 7.50%
Therefore, the after-tax cost of debt is: 7.50% (1 – 0.35) = 4.88%
2. r = DIV/P0 = $4/$40 = 0.10 = 10%
3. = [0.3 7.50% (1 – 0.35)] + [0.2 10%] + [0.5 12.0%] = 9.46%
4.
5. The total value of the firm is $80 million. The weights for each security class are as follows:
Debt: D/V = 20/80 = 0.250 Preferred: P/V = 10/80 = 0.125 Common: E/V = 50/80 = 0.625 = [0.250 6% (1 – 0.35)] + [0.125 8%] + [0.625 12.0%] = 9.475%
6. Executive Fruit should use the WACC of Geothermal, not its own WACC, when evaluating an investment in geothermal power production. The risk of the project determines the discount rate, and in this case, Geothermal’s WACC is more reflective of the risk of the project in question. The proper discount rate, therefore, is not 12.3%. It is more likely to be 11.4%.
7. The flotation costs reduce the NPV of the project by $1.2 million. Even so, project NPV is still positive, so the project should be undertaken.
8. The rate on Buildwell’s debt is 5 percent. The cost of equity capital is the required rate of return on equity, which can be calculated from the CAPM as follows: 4% + (0.90 8%) = 11.2% The weighted average cost of capital, with a tax rate of zero, is: = [0.30 5% (1 – 0)] + [0.70 11.2%] = 9.34%
9. The internal rate of return, which is 12%, exceeds the cost of capital. Therefore, BCCI should accept the project. The present value of the project cash flows is: $100,000 annuity factor(9.34%, 8 years) = $546,556.08 This is the most BCCI should pay for the project.
10.
Security
Market Value
Explanation
Debt $ 5.5 million