91Ó°ÊÓ

Midwest Electric Company (MEC) uses only debt and common equity. It can borrow unlimited amounts at an interest rate of \(\mathrm{r}_{\mathrm{d}}=10 \%\) as long as it finances at its target capital structure, which calls for 45 percent debt and 55 percent common equity. Its last dividend was \(\$ 2,\) its expected constant growth rate is 4 percent, and its common stock sells for \(\$ 20 .\) MEC's tax rate is 40 percent. Two projects are available: Project A has a rate of return of 13 percent, while Project \(\mathrm{B}^{\prime}\) s return is 10 percent. These two projects are equally risky and also about as risky as the firm's existing assets. a. What is its cost of common equity? b. What is the WACC? c. Which projects should Midwest accept?

Step by step solution

01

Calculate the Cost of Common Equity

To find the cost of common equity, we use the Gordon Growth Model formula:\[R_e = \frac{D_1}{P_0} + g\]where:- \(D_1\) is the expected dividend next year.- \(P_0\) is the current stock price.- \(g\) is the growth rate of dividends.First, calculate the expected dividend:\[D_1 = D_0 (1 + g) = 2 \times (1 + 0.04) = 2.08\]Now substitute in the formula:\[R_e = \frac{2.08}{20} + 0.04 = 0.144 = 14.4\%\]

02

Calculate the Weighted Average Cost of Capital (WACC)

The WACC can be calculated using the following formula:\[\text{WACC} = w_d \times r_d \times (1 - T) + w_e \times R_e\]where:- \(w_d = 0.45\) is the weight of debt.- \(r_d = 0.10\) is the cost of debt.- \(T = 0.4\) is the tax rate.- \(w_e = 0.55\) is the weight of equity.- \(R_e = 0.144\) is the cost of equity.Substitute the values:\[\text{WACC} = 0.45 \times 0.10 \times (1 - 0.4) + 0.55 \times 0.144\]\[\text{WACC} = 0.027 + 0.0792 = 0.1062 = 10.62\%\]

03

Evaluate Which Projects to Accept

To decide which projects to accept, compare their rates of return to the WACC: - Project A: 13% - Project B: 10% The decision rule is to accept projects with a return higher than the WACC (10.62%): - Project A's return (13%) is higher than the WACC, so it should be accepted. - Project B's return (10%) is lower than the WACC, so it should not be accepted.

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Key Concepts

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

Weighted Average Cost of Capital (WACC)

Calculating the Weighted Average Cost of Capital, or WACC, is crucial for evaluating investment decisions. It's like finding the average rate of return required by all of a company's investors, both those who hold debt and those who hold equity. The WACC formula accounts for the proportions of debt and equity in a company's capital structure and the cost of each:

• To compute the WACC, you multiply the cost of debt by the proportion of debt, adjust for taxes since interest is tax-deductible.
• Then, you add the product of the cost of equity and its related proportion.

Understanding WACC helps determine the minimum acceptable return for new projects. If a project's expected return exceeds the WACC, it should ideally be adopted as it will add value to the company.

Gordon Growth Model

The Gordon Growth Model is one of the simplest methods to estimate the cost of equity capital. It assumes that dividends will continue to grow at a constant rate indefinitely. With this model, calculating the cost of equity is straightforward:

• You need the expected dividend amount for the next year. This can be estimated using the latest dividend and growth rate.
• Then, you divide this value by the current share price and add the growth rate.

This method is particularly suited for companies with a stable growth pattern. It provides insight into the expected return that equity investors demand, which is crucial for both managing the company's financial strategy and evaluating investment opportunities.

Capital Structure

Capital structure refers to the mix of different types of capital a company uses. Typically, this means a combination of equity and debt. Each component of a company's capital structure comes with its own cost and risk. Here are the two main components:

• Debt: This is typically cheaper due to tax advantages, as interest payments are deductible. However, too much debt increases financial risk.
• Equity: More expensive as equity investors require a higher return rate for their money due to higher risk.

A strategic focus on achieving an optimal capital structure can significantly enhance a company’s financial performance. Balancing the right mix of debt and equity is key to minimizing the overall cost of capital, which in turn maximizes shareholder value.