home / study / math / other math / questions and answers / the following tabulation gives earnings per share ...
Question: The following tabulation gives earnings per share ...
The following tabulation gives earnings per share figures for theFoust Company during the
preceding 10 years. The firm’s common stock, 7.8 millionshares outstanding, is now (1/1/03)
selling for $65 per share, and the expected dividend at the end ofthe current year (2003) is
55 percent of the 2002 EPS. Because investors expect past trends tocontinue, g may be based
on the earnings growth rate. (Note that 9 years of growth arereflected 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. Thefirm’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 commonequity. Calculate the cost of equity
as ks D1/P0 g.
b. Find Foust’s weighted average cost of capital
To calculate Foust's after-tax cost of new debt and common equity, we need to calculate the cost of equity and the cost of debt separately.
a. Cost of Equity (ks):
The cost of equity can be calculated using the Dividend Discount Model (DDM) formula:
ks = (D1 / P0) + g
Where:
D1 = Expected dividend at the end of the current year (2003) = 55% of the 2002 EPS = 0.55 * 7.80 = 4.29
P0 = Current selling price of the common stock = $65
g = Earnings growth rate
To calculate the earnings growth rate (g), we need to find the average growth rate over the 9-year period:
Growth Rate = (Ending EPS / Beginning EPS)^(1 / Number of Years) - 1
Let's calculate the growth rate for the 1993-2002 period:
Growth Rate = (7.80 / 3.90)^(1 / 9) - 1 = 7.36%
Now, let's calculate the cost of equity (ks):
ks = (4.29 / 65) + 0.0736 ≈ 0.0656 + 0.0736 ≈ 0.1392 or 13.92%
b. Cost of Debt:
The cost of debt can be calculated using the formula:
Cost of Debt = Interest Rate * (1 - Tax Rate)
Where:
Interest Rate = Current interest rate on new debt = 9%
Tax Rate = Marginal tax rate = 40%
Let's calculate the cost of debt:
Cost of Debt = 0.09 * (1 - 0.40) = 0.09 * 0.60 = 0.054 or 5.4%
c. Weighted Average Cost of Capital (WACC):
WACC is the weighted average of the after-tax cost of debt and the cost of equity. The weights used are the proportions of debt and equity in the capital structure.
Total Debt = $104,000,000
Total Equity = $156,000,000
WACC = (Debt / Total Capital) * Cost of Debt + (Equity / Total Capital) * Cost of Equity
WACC = (104,000,000 / 260,000,000) * 0.054 + (156,000,000 / 260,000,000) * 0.1392
WACC = 0.4 * 0.054 + 0.6 * 0.1392
WACC ≈ 0.0216 + 0.0835 ≈ 0.1051 or 10.51%
Therefore, Foust's weighted average cost of capital (WACC) is approximately 10.51%.