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Chapter 10: Problem 1

Percy Motors has a target capital structure of 40 percent debt and 60 percent equity. The yield to maturity on the company's outstanding bonds is 9 percent, and the company's tax rate is 40 percent. Percy's CFO has calculated the company's WACC as 9.96 percent. What is the company's cost of common equity?

Short Answer

Expert verified
The cost of common equity is 13%.

Step by step solution

01

Understand the WACC Formula

The Weighted Average Cost of Capital (WACC) is the average rate of return a company expects to compensate all its security holders. The formula is: \( WACC = (E/V) \, \cdot \, r_e + (D/V) \, \cdot \, r_d \, \cdot \, (1 - T) \) where \( E \) is the market value of equity, \( D \) is the market value of debt, \( V = E + D \) is the total market value of the company's financing, \( r_e \) is the cost of equity, \( r_d \) is the cost of debt, and \( T \) is the corporate tax rate.
02

Identify the Given Values

From the problem, we have: the target capital structure is 40% debt (\( D/V = 0.4 \)) and 60% equity (\( E/V = 0.6 \)). The yield to maturity on the bonds, \( r_d \), is 9%, and the corporate tax rate, \( T \), is 40% (0.4). The WACC is given as 9.96%.
03

Substitute Known Values into WACC Formula

Substitute the known values into the WACC formula to find the cost of equity \( r_e \): \( 0.0996 = (0.6) \, \cdot \, r_e + (0.4) \, \cdot \, 0.09 \, \cdot \, (1 - 0.4) \).
04

Simplify the Equation

Simplify the second part of the equation to find the effective cost of debt: \( (0.4) \, \cdot \, 0.09 \, \cdot \, (1 - 0.4) = 0.0216 \). Therefore, the equation becomes \( 0.0996 = 0.6r_e + 0.0216 \).
05

Solve for the Cost of Equity \( r_e \)

Subtract 0.0216 from both sides of the equation: \( 0.0996 - 0.0216 = 0.6r_e \). This simplifies to \( 0.078 = 0.6r_e \). Divide both sides by 0.6 to solve for \( r_e \): \( r_e = \frac{0.078}{0.6} = 0.13 \).
06

Conclusion

The cost of common equity for Percy Motors, \( r_e \), is 13%.

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Key Concepts

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

Cost of Equity
The cost of equity represents the return required by a company鈥檚 shareholders for investing in equity. Think of it as the reward they expect for the risk they are taking. It is a critical component in finance because it helps companies determine the minimum rate of return needed to satisfy investors. Here's how it fits into the broader financial picture:

  • Shareholders expect a certain return for the risk they take in investing.
  • Companies use cost of equity to assess whether projects or investments will be profitable enough.
  • An accurate estimate ensures that the company maintains a competitive edge in attracting investment.
Cost of equity is an essential part of calculating the Weighted Average Cost of Capital (WACC), which helps a company decide on long-term strategies regarding financing and investments.
Target Capital Structure
A target capital structure is the ideal mix of debt and equity financing that a company aims to maintain. This mix influences the firm's overall cost of capital and risk. Here's why it matters:

  • It's a strategic choice made by the company's management to balance risk and return.
  • Companies with different risk profiles and business models will have different target capital structures.
  • A well-chosen capital structure can lower costs, reduce risk, and increase a company's value.
In our exercise, Percy Motors has a target capital structure of 60% equity and 40% debt. This indicates a balance where the company relies moderately on debt while leveraging equity to fund its operations. Having too much debt could increase financial risk, while too little might not take full advantage of leverage opportunities.
Yield to Maturity
Yield to Maturity (YTM) measures the total return anticipated on a bond if the bond is held until maturity. It is expressed as an annual rate. Here are some important aspects:

  • YTM helps investors compare the profitability of bonds having different maturities and coupon rates.
  • Investors use YTM to gauge the potential long-term yield of a bond apart from other considerations like market fluctuations.
  • The YTM is often used as a benchmark for estimating the cost of debt.
For Percy Motors, their bonds have a yield to maturity of 9%. This rate is crucial for calculating the cost of debt in the company's WACC equation, as it reflects the interest that Percy Motors needs to pay to its debt holders over time.
Corporate Tax Rate
The corporate tax rate is the percentage of a company's profits that is taken as tax by the government. It plays a key role in financial planning and decision-making. Here's why it matters:

  • Tax rates directly influence the company's net income and profitability.
  • A higher corporate tax rate can reduce the after-tax return on investments.
  • Companies account for taxes when calculating WACC because interest payments on debt are tax-deductible, thereby reducing the cost of debt through a tax shield.
In the case of Percy Motors, the corporate tax rate is 40%. This rate is applied in adjusting the cost of debt in the WACC formula, making debt cheaper and thus impacting the overall WACC calculation.

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Most popular questions from this chapter

Calculate the after-tax cost of debt under each of the following conditions: a. Interest rate, 13 percent; tax rate, 0 percent. b. Interest rate, 13 percent; tax rate, 20 percent. c. Interest rate, 13 percent; tax rate, 35 percent.

Here is the condensed balance sheet for Skye Computer Company (in thousands of dollars): Skye Computer's earnings per share last year were \(\$ 3.20 ;\) the stock sells for \(\$ 55,\) and last year's dividend was \(\$ 2.10 .\) A flotation cost of 10 percent would be required to issue new common stock. Skye's preferred stock pays a dividend of \(\$ 3.30\) per share, and new preferred could be sold at a price to net the company \(\$ 30\) per share. Security analysts are projecting that the common dividend will grow at a rate of 9 percent per year. The firm can issue additional long-term debt at an interest rate (or before-tax cost) of 10 percent, and its marginal tax rate is 35 percent. The market risk premium is 5 percent, the risk-free rate is 6 percent, and Skye's beta is \(1.516 .\) In its cost of capital calculations, the company considers only long-term capital, hence it disregards current liabilities for this purpose. a. Calculate the cost of each capital component, that is, the after-tax cost of debt, the cost of preferred stock, the cost of equity from retained earnings, and the cost of newly issued common stock. Use the DCF method to find the cost of common equity. b. Now calculate the cost of common equity from retained earnings using the CAPM method. c. What is the cost of new common stock, based on the CAPM? (Hint: Find the difference between \(k_{c}\) and \(k_{s}\) as determined by the \(D C F\) method, and add that differential to the CAPM value for \(\left.k_{s} .\right)\) d. If Skye Computer continues to use the same capital structure, what is the firm's WACC assuming (1) that it uses only retained earnings for equity and (2) that it expands so rapidly that it must issue new common stock? e. Suppose Skye is evaluating three projects with the following characteristics: Each project has a cost of \(\$ 1\) million. They will all be financed using the target mix of long-term debt, preferred stock, and common equity. The cost of the common equity for each project should be based on the beta estimated for the project. All equity will come from retained earnings. Equity invested in Project A would have a beta of 0.5 and an expected return of 9.0 percent. Equity invested in Project \(\mathrm{B}\) would have a beta of 1.0 and an expected return of 10.0 percent. Equity invested in Project \(C\) would have a beta of 2.0 and an expected return of 11.0 percent. Analyze the company's situation and explain why each project should be accepted or rejected.

Goodtread Rubber Company has two divisions: the tire division, which manufactures tires for new autos, and the recap division, which manufactures recapping materials that are sold to independent tire recapping shops throughout the United States. since auto manufacturing fluctuates with the general economy, the tire division's earnings contribution to Goodtread's stock price is highly correlated with returns on most other stocks. If the tire division were operated as a separate company, its beta coefficient would be about \(1.50 .\) The sales and profits of the recap division, on the other hand, tend to be countercyclical, because recap sales boom when people cannot afford to buy new tires. The recap division's beta is estimated to be 0.5. Approximately 75 percent of Goodtread's corporate assets are invested in the tire division and 25 percent are invested in the recap division. Currently, the rate of interest on Treasury securities is 9 percent, and the expected rate of return on an average share of stock is 13 percent. Goodtread uses only common equity capital, so it has no debt outstanding. a. What is the new corporate beta? b. What is the required rate of return on Goodtread's stock? c. What is the cost of capital for projects in each division?

Midwest Electric Company (MEC) uses only debt and equity, It can borrow unlimited amounts at an interest rate of 10 percent 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 stock sells at a price of \(\$ 20 .\) MEC's tax rate is 40 percent. Two projects are available: Project A has a rate of return of 13 percent, while Project \(\mathrm{B}\) has a rate of return of 10 percent. All of the company's potential projects are equally risky and as risky as the firm's other assets. a. What is MEC's cost of common equity? b. What is MEC's WACC? c. Which projects should MEC select?

The earnings, dividends, and stock price of Carpetto Technologies Inc. are expected to grow at 7 percent per year in the future. Carpetto's common stock sells for \(\$ 23\) per share, its last dividend was \(\$ 2.00\), and the company will pay a dividend of \(\$ 2.14\) at the end of the current year. a. Using the discounted cash flow approach, what is its cost of common equity? b. If the firm's beta is \(1.6,\) the risk-free rate is 9 percent, and the average return on the market is 13 percent, what will be the firm's cost of common equity using the CAPM approach? c. If the firm's bonds earn a return of 12 percent, what will \(\mathrm{k}_{\mathrm{s}}\) be using the bond-yieldplus-risk-premium approach? (Hint: Use the midpoint of the risk premium range.) d. On the basis of the results obtained in parts a through \(c,\) what would you estimate Carpetto's cost of common equity to be?
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