91Ó°ÊÓ

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 \((1 / 1 / 02)\) selling for \(\$ 65\) per share, and the expected dividend at the end of the current year (2002) is 55 percent of the 2001 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.) $$\begin{array}{lccc}\text { YEAR } & \text { EPS } & \text { YEAR } & \text { EPS } \\ \hline 1992 & \$ 3.90 & 1997 & \$ 5.73 \\ 1993 & 4.21 & 1998 & 6.19 \\\1994 & 4.55 & 1999 & 6.68 \\ 1995 & 4.91 & 2000 & 7.22 \\\1996 & 5.31 & 2001 & 7.80\end{array}$$ 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: a. Calculate Foust's after-tax cost of new debt and common equity. Calculate the cost of cquity as \(k_{s}=D_{1} / P_{0}+g\) b. Find Foust's weighted average cost of capital.

Step by step solution

01

Calculate the after-tax cost of new debt

The after-tax cost of new debt can be calculated using the formula:\[\text{After-tax Cost of New Debt} = r_d (1 - T)\]where:- \(r_d\) is the interest rate on new debt, 9% or 0.09.- \(T\) is the tax rate, 40% or 0.40.Plug in the values:\[0.09 (1 - 0.40) = 0.09 \times 0.60 = 0.054\]So, the after-tax cost of new debt is 5.4%.

02

Determine the growth rate of EPS

The growth rate, \(g\), needs to be calculated using the formula for compound annual growth rate (CAGR):\[g = \left(\frac{\text{EPS}_{\text{final}}}{\text{EPS}_{\text{initial}}}\right)^{\frac{1}{n}} - 1\]where:- \(\text{EPS}_{\text{final}}\) is the EPS in 2001: \\(7.80- \(\text{EPS}_{\text{initial}}\) is the EPS in 1992: \\)3.90- \(n\) is the number of years, 9.Plug in the values:\[g = \left(\frac{7.80}{3.90}\right)^{\frac{1}{9}} - 1 = 2^{\frac{1}{9}} - 1 \approx 0.0808\]Thus, the growth rate, \(g\), is approximately 8.08%.

03

Calculate the cost of equity

The cost of equity can be calculated using the Gordon Growth Model, \(k_s\):\[k_s = \frac{D_1}{P_0} + g\]where:- \(D_1\) is the expected dividend: 55% of the 2001 EPS, \(0.55 \times 7.80 = 4.29\).- \(P_0\) is the price per share: \$65.- \(g\) is the growth rate calculated previously: 0.0808.Plug in the values:\[k_s = \frac{4.29}{65} + 0.0808 \approx 0.1467\]So, the cost of equity is approximately 14.67%.

04

Calculate Foust's WACC

Foust's Weighted Average Cost of Capital (WACC) is calculated using:\[\text{WACC} = w_d \times r_{d\text{(after-tax)}} + w_e \times k_s\]where:- \(w_d\) is the weight of debt: 50% or 0.50.- \(r_{d\text{(after-tax)}}\) is the after-tax cost of new debt: 5.4% or 0.054.- \(w_e\) is the weight of equity: 50% or 0.50.- \(k_s\) is the cost of equity: 14.67% or 0.1467.Substitute the values:\[\text{WACC} = 0.50 \times 0.054 + 0.50 \times 0.1467 = 0.10135\]Therefore, the WACC is 10.135%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Earnings Per Share

Earnings Per Share (EPS) is a key financial metric used by investors to assess the profitability of a company. EPS is calculated by dividing the net income of the company by the number of outstanding common shares. In the context of Foust Company, the EPS figures over the past ten years give investors insight into the company's financial performance and growth trends.

• EPS provides a snapshot of a company's profitability on a per-share basis, making it easier to compare with other companies.
• Investors often look at trends in EPS over several years to see how well the company has been growing.
• High and increasing EPS values typically indicate a company is doing well financially, attracting more investors.

In the exercise, the historical EPS data is used to calculate the growth rate, which helps forecast future dividends and understand potential returns from investing in Foust Company. Understanding EPS is crucial for any potential investor as it directly influences stock valuation and dividend expectations.

Cost of Equity

The cost of equity is essentially the return required by equity investors for investing in a company. This concept can be tricky because it involves both current stock prices and future dividend growth expectations.
The Gordon Growth Model is often used to calculate it, as it considers expected dividends and growth:

• The expected dividend (\(D_1\)) is the payout anticipated for the coming year, which, in Foust Company's case, is 55% of the last year's EPS.
• The current stock price (\(P_0\)) is what an investor would pay today to purchase the stock, providing a crucial point of reference.
• The growth rate (\(g\)) is an estimate based on the company's earnings history, reflecting expected future performance.

Investors use the cost of equity to evaluate whether the returns expected from investing in a stock align with their financial goals. A higher cost of equity indicates that investors need a higher return due to greater perceived risk.

Weighted Average Cost of Capital

Weighted Average Cost of Capital (WACC) is a calculation of a company's cost of capital, whereby each category of capital is proportionately weighted. It serves as a critical metric for investment decision-making, especially in determining the risk and potential return of an investment in a company.
WACC is calculated using both the cost of equity and after-tax cost of debt:

• The weight of debt (\(w_d\)) reflects the proportion of the company's capital structure that is comprised of debt.
• The weight of equity (\(w_e\)) represents the proportion consisting of equity.
• The after-tax cost of debt is lowered by tax savings due to interest expenses.

A company's WACC is an essential indicator for investors. It shows the minimum average return a company must earn on its existing asset base to satisfy its creditors, owners, and other capital providers. A lower WACC suggests lower risk and potential for higher profits, making the company more attractive to investors.