The following tabulation gives earnings per share figures for the Foust Company during the
preceding 10 years. The firm’s common stock, 7.8 million shares outstanding, is now (1/1/03)
selling for $65 per share, and the expected dividend at the end of the current year (2003) is
55 percent of the 2002 EPS. Because investors expect past trends to continue, g may be based
on the earnings growth rate. (Note that 9 years of growth are reflected in the data.)
YEAR EPS YEAR EPS
1993 $3.90 1998 $5.73
1994 4.21 1999 6.19
1995 4.55 2000 6.68
1996 4.91 2001 7.22
1997 5.31 2002 7.80
The current interest rate on new debt is 9 percent. The firm’s marginal tax rate is 40 percent.
Its capital structure, considered to be optimal, is as follows:
Debt $104,000,000
Common equity 156,000,000
Total liabilities and equity $260,000,000
a. Calculate Foust’s after-tax cost of new debt and common equity. Calculate the cost of equity
as ks D1/P0 g.
b. Find Foust’s weighted average cost of capital. 9(1-0.40)x104/260 + 37x156/260==24.36%
The answer to question A. is $189,500
To calculate Foust's after-tax cost of new debt, we need to use the formula:
After-tax cost of debt = Pre-tax cost of debt x (1 - Marginal tax rate)
Given that the current interest rate on new debt is 9% and the marginal tax rate is 40%, we can calculate the after-tax cost of debt as follows:
After-tax cost of debt = 9% x (1 - 40%) = 9% x 0.6 = 5.4%
Now, let's calculate Foust's cost of common equity using the formula:
Cost of equity (ks) = Dividends per share (D1) / Price per share (P0) + Growth rate (g)
The given information states that the expected dividend at the end of the current year (2003) is 55% of the 2002 EPS. Therefore, the dividends per share (D1) can be calculated as:
D1 = 55% x 7.8 million shares x 7.80 (2002 EPS) = 30.51 million
The price per share (P0) is given as $65 per share.
The growth rate (g) can be approximated using the earnings growth rate over the 9-year period. We can calculate this as:
(6.68/3.90)^(1/9) - 1 = 7.2%
Now, we can calculate the cost of common equity (ks) as follows:
Cost of equity (ks) = 30.51 million / (7.8 million shares x $65) + 7.2% = 0.6075 + 7.2% = 7.8075%
Therefore, Foust's cost of common equity is 7.8075%.
b. To find Foust's weighted average cost of capital (WACC), we will use the formula:
WACC = (Weight of debt x After-tax cost of debt) + (Weight of equity x Cost of equity)
Given that the weight of debt is $104 million and the weight of equity is $156 million, and we have already calculated the after-tax cost of debt as 5.4% and the cost of equity as 7.8075%, we can substitute these values into the formula:
WACC = (104/260) x 5.4% + (156/260) x 7.8075% = 2.16% + 4.7095% = 6.8695%
Therefore, Foust's weighted average cost of capital (WACC) is 6.8695%.
To calculate Foust's after-tax cost of new debt and common equity, you need to follow these steps:
a. Calculate the after-tax cost of new debt:
1. Determine the interest rate on the new debt given in the problem. In this case, the interest rate is 9 percent.
2. Determine the marginal tax rate of the company. In this case, the marginal tax rate is 40 percent.
3. Multiply the interest rate by (1 - marginal tax rate) to get the after-tax cost of debt.
After-tax cost of debt = Interest rate on debt x (1 - Marginal tax rate)
b. Calculate the cost of common equity:
1. Use the dividend discount model to calculate the cost of common equity.
Cost of equity (ks) = (Dividend per share (D1) / Price per share (P0)) + Dividend growth rate (g)
2. Determine the dividend per share (D1). In this case, it is given that the expected dividend at the end of the current year (2003) is 55 percent of the 2002 EPS (Earnings per share).
D1 = 55% x 2002 EPS
3. Determine the price per share (P0). In this case, it is given that the common stock is selling for $65 per share.
P0 = $65 per share
4. Determine the dividend growth rate (g). Since the problem states that investors expect past trends to continue, you can use the earnings growth rate as the dividend growth rate. Calculate the average growth rate in earnings over the past 9 years using the given data.
g = (Current year EPS / Earliest year EPS)^(1 / Number of years) - 1
g = (2002 EPS / 1993 EPS)^(1/9) - 1
To find Foust's weighted average cost of capital (WACC), you can use the formula:
WACC = (Weight of debt x After-tax cost of debt) + (Weight of equity x Cost of equity)
In this case, the weight of debt is the total debt divided by the total liabilities and equity, and the weight of equity is the total common equity divided by the total liabilities and equity.
Note: The calculation of WACC may vary depending on the specific assumptions and formula used. The given formula in the question seems to be using the weights of debt and equity directly instead of calculating the weights based on the market values of debt and equity.