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Percy Motors has a target capital structure of \(40 \%\) debt and \(60 \%\) common equity, with no preferred stock. The yield to maturity on the company's outstanding bonds is \(9 \%\), and its tax rate is \(40 \%\). Percy's CFO estimates that the company's WACC is \(9.96 \%\). What is Percy's cost of common equity?

Short Answer

Expert verified
Percy's cost of common equity is 13%.

Step by step solution

01

Identify the WACC Formula

To find Percy's cost of common equity, we start with the Weighted Average Cost of Capital (WACC) formula: \[ WACC = w_d \times r_d \times (1 - T_c) + w_e \times r_e \]where:- \(w_d\) is the weight of debt,- \(r_d\) is the cost of debt (yield to maturity),- \(T_c\) is the tax rate,- \(w_e\) is the weight of equity,- \(r_e\) is the cost of equity.
02

Substitute Known Values

Now substitute the known values into the WACC formula. We know:- \(WACC = 9.96\% = 0.0996\),- \(w_d = 40\% = 0.4\),- \(r_d = 9\% = 0.09\),- \(T_c = 40\% = 0.4\),- \(w_e = 60\% = 0.6\).Substituting the known values gives us:\[ 0.0996 = 0.4 \times 0.09 \times (1 - 0.4) + 0.6 \times r_e \]
03

Simplify the Equation

Simplify the equation by first calculating the effective cost of debt:\[ 0.4 \times 0.09 \times 0.6 = 0.0216 \]Update the equation with this simplified value:\[ 0.0996 = 0.0216 + 0.6 \times r_e \]
04

Solve for Cost of Equity

Solve for \(r_e\) by isolating it on one side of the equation:1. Subtract the effective cost of debt from both sides: \[ 0.0996 - 0.0216 = 0.6 \times r_e \]2. Simplify this to get: \[ 0.078 = 0.6 \times r_e \]3. Divide both sides by 0.6 to solve for \(r_e\): \[ r_e = \frac{0.078}{0.6} = 0.13 \]Thus, Percy's cost of common equity \(r_e\) is \(13\%\).

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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
The Weighted Average Cost of Capital, commonly known as WACC, is a crucial financial metric used to gauge the average rate a company is expected to pay to finance its assets. It combines the cost of equity and cost of debt, adjusted for the company's capital structure proportions. In addition, it accounts for any tax advantages associated with debt financing. For a company like Percy Motors, whose capital structure includes only debt and equity, WACC is calculated with the following formula:\[WACC = w_d \times r_d \times (1 - T_c) + w_e \times r_e\]Where:- \(w_d\) is the weight of debt in capital structure,- \(r_d\) is the return or yield on debt,- \(T_c\) is the tax rate,- \(w_e\) is the weight of equity in capital structure,- \(r_e\) is the return or cost of equity.Knowing the WACC helps investors and analysts understand the minimum return a company needs to earn on its assets to satisfy investors or creditors. Firm managers aim to have a WACC as low as possible, indicating cheaper overall costs to finance the company.
Capital Structure
Capital structure refers to how a corporation finances its overall operations and growth by using different sources of funds. This typically includes a mix of debt and equity. For Percy Motors, the ideal or target capital structure consists of 40% debt and 60% equity. Having a well-considered capital structure is critical for achieving a low cost of capital. Using debt allows companies to leverage tax shields, effectively reducing the cost of financing due to tax-deductible interest payments. In contrast, equity does not offer such tax advantages, yet it doesn't impose obligatory repayment burdens on the company. Balancing these assets enables Percy Motors to handle its financial risk while optimizing growth potential.
Cost of Debt
The cost of debt represents the effective rate a company pays on its borrowed funds. It reflects the interest payable annually on the bonded debt and is a component of a company's capital expenses. In the scenario of Percy Motors, the yield to maturity on the company's bonds, which determines the effective cost of debt, is 9%.This cost can be reduced by the tax deductibility of interest expenses, allowing the firm to pay less in taxes. The tax-deducted cost of debt is part of the WACC calculation, formulated as:\[Effective \ Cost \ of \ Debt = r_d \times (1 - T_c)\]This incentivizes firms to utilize debt in their capital structures judiciously, thus lowering overall financing costs while managing financial risk.
Tax Rate
The tax rate is a critical element in determining a firm's cost of capital. It directly impacts the effective cost of debt by reducing the pre-tax interest rate to a net of tax rate. In Percy Motors' case, the tax rate is 40%.The role of the tax rate in calculations like WACC helps the company gauge the after-tax cost of debt. Using the formula:\[Effective \ Cost \ of \ Debt = r_d \times (1 - T_c)\]The tax shield from interest payment reductions can significantly lower the overall cost of capital. Companies strive to maximize this benefit by taking advantage of these tax deductions, effectively optimizing their capital structure. Understanding the impact of the tax rate is vital for accurate financial planning and strategy. This assists firms like Percy Motors in making informed decisions regarding financing options and investment planning.

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Most popular questions from this chapter

Tunney Industries can issue perpetual preferred stock at a price of \(\$ 47.50\) a share. The stock would pay a constant annual dividend of \(\$ 3.80\) a share. What is the company's cost of preferred stock, \(r_{p}\) ?

Klose Outfitters Inc. believes that its optimal capital structure consists of \(60 \%\) common equity and \(40 \%\) debt, and its tax rate is \(40 \%\). Klose must raise additional capital to fund its upcoming expansion. The firm will have \(\$ 2\) million of new retained earnings with a cost of \(\mathrm{r}_{\mathrm{s}}=12 \%\). New common stock in an amount up to \(\$ 6\) million would have a cost of \(\mathrm{r}_{\mathrm{c}}\) \(=15 \%\), Furthermore, Klose can raise up to \(\$ 3\) million of debt at an interest rate of \(r_{d}=10 \%\) and an additional \(\$ 4\) million of debt at \(r_{d}=12 \%\). The CFO estimates that a proposed expansion would require an investment of \(\$ 5.9\) million. What is the WACC for the last dollar raised to complete the expansion?

CALCULATING THE WACC Here is the condensed 2008 balance sheet for Skye Computer Company (in thousands of dollars): Skye's earnings per share last year were \(\$ 3.20\), the common stock sells for \(\$ 55.00\), last year's dividend was \(\$ 2.10,\) and a flotation cost of \(10 \%\) would be required to sell new common stock. Security analysts are projecting that the common dividend will grow at a rate of \(9 \%\) per year. 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 \(\$ 30.00\) per share. The firm can issue long-term debt at an interest rate (or before-tax cost) of \(10 \%\), and its marginal tax rate is \(35 \%\). The market risk premium is \(5 \%\), the risk-free rate is \(6 \%\), 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. 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 \(r_{e}\) and \(r_{s}\) as determined by the DCF method and add that differential to the CAPM value for \(r_{s^{2}}\) d. If Skye continues to use the same capital structure, what is the firm's WACC assuming that (1) it uses only retained earnings for equity? (2) If it expands so rapidly that it must issue new common stock?

cost of PREFERRED STOCK INCLUDING FLOTATION Trivoli Industries plans to issue perpetual preferred stock with an \(\$ 11.00\) dividend. The stock is currently selling for \(\$ 97.00 ;\) but flotation costs will be \(5 \%\) of the market price, so the net price will be \(\$ 92.15\) per share. What is the cost of the preferred stock, including flotation?

WACC AND PERCENTAGE OF DEBT FINANCING Hook Industries' capital structure consists solely of debt and common equity. It can issue debt at \(\mathrm{r}_{\mathrm{d}}=11 \%,\) and its common stock currently pays a \(\$ 2.00\) dividend per share \(\left(\mathrm{D}_{0}=\$ 2.00\right) .\) The stock's price is currently \(\$ 24.75\) its dividend is expected to grow at a constant rate of \(7 \%\) per year, its tax rate is \(35 \%\), and its WACC is \(13.95 \%\). What percentage of the company's capital structure consists of debt?

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