"You are investing $6,000 immediately in a stock that you will keep for 13 years. At the end of 13 years, the stock will be worth $16,813 with a probability of 0.48 and worth $22,785 with a probability of 0.52. When you sell the stock, you will need to pay taxes on the profit earned from selling the stock (i.e., taxes on the difference between the selling and buying prices of the stock). The tax rate will be 8% with a probability of 0.8 or 16% with a probability of 0.2. Your MARR is 4.7% What is the variance of the net present worth from investing in the stock?"

The following example illustrates how inflation raises the tax burden on saving:

Economy A                    Economy B

        Nominal Interest Rate             5%                             10 %

        Inflation Rate                     3%                             (b)

        Real interest rate                 (a)                              4 %

        Reduced interest due to 20% tax

            (0.2 x nominal interest rate)    1%                            2 %

        After-tax nominal interest rate

           (0.8 x nominal interest rate)     4 %                            8%

        After tax real interest rate          (c)                             (d)

        Fill in with appropriate numbers: (a)___________ (b)___________ (c)__________ (d)____________

Problem 15-11
WACC and Optimal Capital Structure

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

F. Pierce uses the CAPM to estimate its cost of common equity, rs and at the time of the analaysis the risk-free rate is 5%, the market risk premium is 5%, and the company's tax rate is 35%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 0.95. Based on this information, what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? Do not round intermediate calculations. Round your answers to two decimal places.

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

* Use the exact value of 2/3 in your calculations.

F. Pierce uses the CAPM to estimate its cost of common equity, r_s and at the time of the analaysis the risk-free rate is 5%, the market risk premium is 4%, and the company's tax rate is 30%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 0.85. Based on this information, what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? Do not round intermediate calculations. Round your answers to two decimal places.

Debt:   %
Equity:   %
WACC:   %

WACC and Optimal Capital Structure

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

* Use the exact value of 2/3 in your calculations.

F. Pierce uses the CAPM to estimate its cost of common equity, r_s and at the time of the analaysis the risk-free rate is 7%, the market risk premium is 6%, and the company's tax rate is 35%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 1.25. Based on this information, what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? Do not round intermediate calculations. Round your answers to two decimal places.

Debt:   %
Equity:   %
WACC:   %

The following data apply to Computational Problems 7‐1 through 7‐4. Assume expected returns and standard deviations as follows:

EG&G Return (%)   25

Standard deviation (%)   30 Covariance   112.5 The correlation coefficient,

ρ, is 0.15. GF 23 25

EG&G wi 1.0 0.8 0.6 0.2 0.0

GF wj = (1 − wi) 0.0 0.2 0.4 0.8 1.0

(1) Portfolio Expected Returns (%) 25.0 24.6 24.2 23.4 23.0

(2) Variance 900 637 478 472 625

(3) Standard Deviation (%) 30.0 25.2 21.9 21.7 25.0

7‐1   Confirm the expected portfolio returns in column 1.

7‐2   Confirm the expected portfolio variances in column 2.

7‐3   Confirm the expected standard deviations in column 3

. 7‐4   On the basis of these data, determine the lowest risk portfolio.

7‐5   Assume that the risk‐free rate is 7 percent, the estimated return on the market is 12 percent, and the standard deviation of the market’s expected return is 21 percent. Calculate the expected return and risk (standard deviation) for the following portfolios:

a. 60 percent of investable wealth in riskless assets, 40 percent in the market portfolio

b.   150 percent of investable wealth in the market portfolio

c.   100 percent of investable wealth in the market portfolio

WACC and Optimal Capital Structure

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

* Use the exact value of 2/3 in your calculations.

F. Pierce uses the CAPM to estimate its cost of common equity, r_s and at the time of the analaysis the risk-free rate is 7%, the market risk premium is 8%, and the company's tax rate is 35%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 1.2. Based on this information, what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? Do not round intermediate calculations. Round your answers to two decimal places.

Debt:   %
Equity:   %
WACC:   %

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

* Use the exact value of 2/3 in your calculations.

F. Pierce uses the CAPM to estimate its cost of common equity, r_s and at the time of the analaysis the risk-free rate is 7%, the market risk premium is 8%, and the company's tax rate is 40%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 1. Based on this information, what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? Do not round intermediate calculations. Round your answers to two decimal places.

Debt:   %
Equity:   %
WACC:   %

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

* Use the exact value of 2/3 in your calculations.

F. Pierce uses the CAPM to estimate its cost of common equity, r_s and at the time of the analaysis the risk-free rate is 7%, the market risk premium is 8%, and the company's tax rate is 40%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 1. Based on this information, what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? Do not round intermediate calculations. Round your answers to two decimal places.

Debt:   %
Equity:   %
WACC:   %

F. Pierce Products Inc. is considering changing its capital structure. F. Pierce currently has no debt and no preferred stock, but it would like to add some debt to take advantage of low interest rates and the tax shield. Its investment banker has indicated that the pre-tax cost of debt under various possible capital structures would be as follows:

* Use the exact value of 2/3 in your calculations.

F. Pierce uses the CAPM to estimate its cost of common equity, r_s and at the time of the analaysis the risk-free rate is 5%, the market risk premium is 6%, and the company's tax rate is 40%. F. Pierce estimates that its beta now (which is "unlevered" because it currently has no debt) is 1.4. Based on this information, what is the firm's optimal capital structure, and what would be the weighted average cost of capital at the optimal capital structure? Do not round intermediate calculations. Round your answers to two decimal places.

Debt:   %
Equity:   %
WACC:   %