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Chapter 10: Problem 11

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?

Short Answer

Expert verified
20% of the company's capital structure consists of debt.

Step by step solution

01

Calculate Cost of Equity

To find the cost of equity, we use the Gordon Growth Model (Dividend Discount Model for Constant Growth): \[ r_e = \frac{D_1}{P_0} + g \] where \( D_1 \) is the expected dividend next year, \( P_0 \) is the current stock price, and \( g \) is the growth rate. First, calculate \( D_1 \): \[ D_1 = D_0 \times (1 + g) = 2.00 \times (1 + 0.07) = 2.14 \] Now, calculate the cost of equity \( r_e \): \[ r_e = \frac{2.14}{24.75} + 0.07 = 0.0865 + 0.07 = 0.1565 \, (15.65\%) \]
02

Calculate After-Tax Cost of Debt

The after-tax cost of debt \( r_d (1-T) \) is calculated as: \[ r_d (1-T) = r_d \times (1-T_C) \] where \( r_d = 0.11 \) (11\%) is the cost of debt and \( T_C = 0.35 \) (35\%) is the tax rate. So, \[ r_d (1-T) = 0.11 \times (1 - 0.35) = 0.11 \times 0.65 = 0.0715 \, (7.15\%) \]
03

Use WACC Formula

The formula for Weighted Average Cost of Capital (WACC) is: \[ WACC = (E/V) \times r_e + (D/V) \times r_d (1-T) \] Given \( WACC = 0.1395 \) (13.95\%), cost of equity \( r_e = 0.1565 \) (15.65\%), and after-tax cost of debt \( r_d (1-T) = 0.0715 \) (7.15\%). We have two unknowns: \( E/V \) and \( D/V \) such that \( E/V + D/V = 1 \). Thus, \( D/V = 1 - E/V \).
04

Solve for Debt Percentage

Plug values into the WACC formula: \[ 0.1395 = (E/V) \times 0.1565 + (1-E/V) \times 0.0715 \] Distribute and simplify: \[ 0.1395 = 0.1565(E/V) + 0.0715(1-E/V) \] \[ 0.1395 = 0.1565(E/V) + 0.0715 - 0.0715(E/V) \] Combine like terms: \[ 0.1395 = 0.085(E/V) + 0.0715 \] Subtract 0.0715 from both sides: \[ 0.068 = 0.085(E/V) \] Solve for \( E/V \): \[ E/V = \frac{0.068}{0.085} \approx 0.8 \] Thus, \( D/V = 1 - E/V \approx 0.2 \).
05

Convert to Percentage

Finally, convert the decimal \( D/V \) to a percentage: \[ D/V = 0.2 \times 100\% = 20\% \] Therefore, 20\% of the company's capital structure consists of debt.

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Key Concepts

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

Capital Structure
When discussing capital structure, we are referring to the way in which a company finances its overall operations and growth. It is typically composed of two main components: debt and equity.
The capital structure essentially determines how much of a company's funding comes from borrowing (debt) compared to owners' contributions (equity). Companies strive to find an ideal balance that minimizes costs while maximizing value.
  • Debt: This includes any borrowed funds that the company must pay back with interest. Debt can be a cheaper source of financing due to tax benefits, as interest is tax-deductible.
  • Equity: Represents ownership stakes, typically in the form of stock. Unlike debt, equity does not require repayment but usually requires the distribution of dividends.
Finding the perfect mix between these components is crucial as it affects a firm鈥檚 Weighted Average Cost of Capital (WACC), which in turn impacts its valuation and financial strategy.
Cost of Equity
The cost of equity represents the return a company must earn on its equity investments to satisfy its shareholders. In other words, it is the "price" of equity financing. The Gordon Growth Model is a popular method used to determine the cost of equity by evaluating expected future dividends and the growth rate.
The formula used in the model is:
\[ r_e = \frac{D_1}{P_0} + g \]
  • \(D_1\): The expected dividend in the next period, calculated as the current dividend times one plus the growth rate.
  • \(P_0\): The current price of the stock.
  • \(g\): The dividend growth rate, assumed to be constant in this model.
By using this method, firms can determine how costly their equity is, compared to other forms of financing like debt.
Cost of Debt
Understanding the cost of debt is crucial for businesses as it is a major component of the capital structure. The cost of debt refers to the effective rate that a company pays on its borrowed funds. It is calculated after considering tax implications, since interest is tax-deductible.
The after-tax cost of debt can be calculated using the formula:
\[ r_d (1-T) = r_d \times (1-T_C) \]
  • \(r_d\): The interest rate paid on the company's debt.
  • \(T_C\): The corporate tax rate.
This calculation provides the effective cost of debt after tax savings, thereby helping companies evaluate their financing choices effectively.
Gordon Growth Model
The Gordon Growth Model, also known as the Dividend Discount Model, is an essential tool for calculating the cost of equity. This model assumes that dividends will increase at a constant rate indefinitely.
It helps in assessing the required rate of return for equity holders, providing insight into the valuation of a company鈥檚 stock.
The basic equation used is:
\[ r_e = \frac{D_1}{P_0} + g \]
Here is how each element is used:
  • \(D_1\): The forecasted dividend for the next year, extrapolated from a current known dividend.
  • \(P_0\): The market price per share of the stock today.
  • \(g\): The expected annual dividend growth rate.
This model is particularly useful for stable companies with a predictable dividend pattern. It helps investors understand the return they should expect from their investment given the anticipated growth in dividends.

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Most popular questions from this chapter

cost of COMMON EQUITY The Bouchard Company's EPS was \(\$ 6.50\) in \(2008,\) up from \(\$ 4.42\) in \(2003 .\) The company pays out \(40 \%\) of its earnings as dividends, and its common stock sells for \(\$ 36.00\) a. Calculate the past growth rate in earnings. (Hint: This is a 5-year growth period.) b. The last dividend was \(D_{0}=0.4(\$ 6.50)-\$ 2.60 .\) Calculate the next expected dividend, \(D_{1},\) assuming that the past growth rate continues. c. What is Bouchard's cost of retained earnings, \(r_{s} ?\)

WACC 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 \(45 \%\) debt and \(55 \%\) common equity. Its last dividend was \(\$ 2,\) its expected constant growth rate is \(4 \%,\) and its common stock sells for \(\$ 20 .\) MEC's tax rate is \(40 \%\). Two projects are available: Project \(A\) has a rate of return of \(13 \%\), while Project B's return is \(10 \%\). These two projects are equally risky and 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?

The future earnings, dividends, and common stock price of Carpetto Technologies Inc. are expected to grow \(7 \%\) per year. Carpetto's common stock currently sells for \(\$ 23.00\) per share; its last dividend was \(\$ 2.00 ;\) and it will pay a \(\$ 2.14\) dividend at the end of the current year. a. Using the DCF approach, what is its cost of common equity? b. If the firm's beta is \(1.6,\) the risk-free rate is \(9 \%\), and the average return on the market is \(13 \%,\) what will be the firm's cost of common equity using the CAPM approach? c. If the firm's bonds earn a return of \(12 \%\), based on the bond-yield-plus- risk-premium approach, what will be \(\mathrm{r}_{\mathrm{s}}\) ? Use the midpoint of the risk premium range discussed in Section \(10-5\) in your calculations. d. If you have equal confidence in the inputs used for the three approaches, what is your estimate of Carpetto's cost of common equity?

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, \(r_{p}\) ?

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?
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