The following tabulation gives earnings per share figures for the Foust’s 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 expected past trends to continue, g may be based on the earning growth rate. (Note that 9 years of growth are reflected in the data.)
YEAR ESP YEAR ESP
1993 $3.90 1998 $5.37
1994 4.21 1999 6.19
1995 4.55 2000 6.68
1996 4.91 2001 7.22
1997 5.31 2002 7.80
(A) Calculate Foust’s after-tax cost of new debt and common equity. Calculate the cost of equity as Ks=D1/P0+g. Thse are exponents however it would not allow me to paste them correctly.
(B) Find Foust’s weighted average cost of capital.
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YEAR ESP YEAR ESP
1993 $3.90 1998 $5.37
1994 4.21
1999 6.19
1995 4.55 2000 6.68
1996 4.91 2001 7.22
1997 5.31 2002 7.80
(A) Calculate Foust’s after-tax cost of new debt and common equity. Calculate the cost of equity as D1/P0+g. 1 and 0 are exponents.
(B) Find Foust’s weighted average cost of capital.
Sure, I can help you with that. Let's break down each part of the question step by step.
(A) 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.
To calculate the cost of equity (Ke), we can use the dividend discount model (DDM) as mentioned in the question. The formula for the cost of equity is Ke = D1 / P0 + g, where D1 is the expected dividend at the end of the current year, P0 is the current stock price, and g is the expected growth rate.
In this case, D1 is given as 55% of the 2002 EPS. We can calculate D1 by multiplying the 2002 EPS ($7.80) by 55%: D1 = $7.80 * 0.55.
The current stock price (P0) is given as $65 per share.
The growth rate (g) can be calculated using the earnings growth rate over the 9-year period. We can calculate g by taking the geometric mean of the growth rates using the formula:
g = (EPSn / EPS0)^(1/n) - 1,
where EPSn is the EPS in the current year (2002) and EPS0 is the EPS in the first year (1993), and n is the number of years.
Using the formula, g = ($7.80 / $3.90)^(1/9) - 1.
Once you have all the values for D1, P0, and g, you can calculate the cost of equity (Ke) using the formula mentioned earlier.
To calculate the cost of debt, we need to know the after-tax cost of debt. If the question provides the tax rate, you can calculate the after-tax cost of debt by multiplying the before-tax cost of debt by (1 - tax rate). If the tax rate is not provided, you may need to assume a tax rate or ask for clarification.
(B) To find Foust's weighted average cost of capital (WACC), you need to calculate the weight of equity (We), the weight of debt (Wd), and their respective costs of capital (Ke and Kd).
The weight of equity (We) can be calculated as the market value of equity divided by the total market value of the firm (equity + debt). In this case, the market value of equity is the number of shares outstanding (7.8 million) multiplied by the stock price ($65 per share). The total market value of the firm includes the market value of equity and the market value of debt.
The weight of debt (Wd) can be calculated as the market value of debt divided by the total market value of the firm. The market value of debt can be estimated using the book value of debt or the market value of debt if provided.
Finally, the WACC can be calculated using the formula: WACC = We * Ke + Wd * Kd.
Once you have all the values, plug them into the formula to calculate Foust's weighted average cost of capital (WACC).
Remember to check if any additional information is provided in the question that might be needed to accurately calculate the cost of debt or the WACC.
I hope this explanation helps you solve the problem. Let me know if you have any further questions!