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Chapter 10: Problem 5

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.

Short Answer

Expert verified
a. 13%, b. 10.4%, c. 8.45%

Step by step solution

01

Understanding the Formula

The after-tax cost of debt can be calculated using the formula: \[ ext{After-tax Cost of Debt} = ext{Interest Rate} imes (1 - ext{Tax Rate})\]This formula accounts for the reduction in interest costs due to tax savings since interest payments are typically tax-deductible.
02

Calculate Cost for 0% Tax Rate

Substitute the given values into the formula: Interest rate = 13%, Tax rate = 0%:\[ ext{After-tax Cost of Debt} = 0.13 imes (1 - 0) = 0.13 ext{ or } 13 ext{%}\]At a 0% tax rate, the after-tax cost remains the same as the interest rate.
03

Calculate Cost for 20% Tax Rate

Substitute the values into the formula: Interest rate = 13%, Tax rate = 20%:\[ ext{After-tax Cost of Debt} = 0.13 imes (1 - 0.20) = 0.13 imes 0.80 = 0.104 ext{ or } 10.4 ext{%}\]The after-tax cost decreases due to the 20% tax deduction on interest payments.
04

Calculate Cost for 35% Tax Rate

Substitute these values back into the formula:Interest rate = 13%, Tax rate = 35%:\[ ext{After-tax Cost of Debt} = 0.13 imes (1 - 0.35) = 0.13 imes 0.65 = 0.0845 ext{ or } 8.45 ext{%}\]The tax savings are greater at a 35% tax rate, further reducing the after-tax cost.

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Key Concepts

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

Understanding Interest Rate
The interest rate is the percentage charged on the total borrowed amount. It represents the cost of borrowing money over a certain period. When you take a loan, the lender expects you to pay back the principal amount of the loan along with interest. The interest rate determines how much money you will pay in interest over time. A higher interest rate means you pay more for borrowing the same amount of money. In the context of the after-tax cost of debt, the interest rate is the starting point for our calculations. It is applied before accounting for tax savings, so understanding it is crucial in determining the expense associated with a loan.
Explaining Tax Rate
The tax rate refers to the percentage of income or profit that is taken by the government as tax. Businesses and individuals alike must pay taxes on their earnings, and this rate can influence financial decisions, such as taking on debt. In calculating the after-tax cost of debt, the tax rate plays a significant role because:
  • The higher the tax rate, the more tax savings you achieve on your interest payments.
  • It directly affects the net interest cost of a loan after accounting for tax savings.
Thus, understanding how tax rates impact financial strategies can help in effective debt management. In this exercise, reducing tax burden via deductible interest payments decreases the overall cost of debt.
Concept of Tax-Deductible Interest
Tax-deductible interest is a significant advantage that reduces the effective interest expense of a loan. Certain types of interest payments, such as those on a mortgage or certain business loans, can be deducted from taxable income. This deduction reduces the amount of income tax owed, effectively lowering the net cost of borrowing. For example, if a business pays 13% in interest but can deduct 35% of that interest from taxable income, the real cost becomes lower. The formula for the after-tax cost of debt, which is \[ \text{After-tax Cost of Debt} = \text{Interest Rate} \times (1 - \text{Tax Rate}) \],reflects these savings: the greater the tax rate, the greater the reduction multiplied against the interest rate.In our exercise, tax-deductible interest is the key reason why the after-tax cost of debt at a 35% tax rate (8.45%) is lower than at a 20% or 0% tax rate. These deductions provide more cash flow flexibility and highlight the importance of understanding tax implications in financial planning.

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Most popular questions from this chapter

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.

Patton Paints Corporation has a target capital structure of 40 percent debt and 60 percent common equity. The company's before-tax cost of debt is 12 percent and its marginal tax rate is 40 percent. The current stock price is \(\mathrm{P}_{0}=\$ 22.50 ;\) the last dividend was \(\mathrm{D}_{0}=\$ 2.00 ;\) and the dividend is expected to grow at a constant rate of 7 percent. What will be the firm's cost of common equity and its WACC?

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.

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 Water Works estimates that its WACC is 10.5 percent. The company is considering the following seven investment projects: $$\begin{array}{ccc}\text { ?R0JECT } & \text { SIZE } & \text { RATE OF RETURN } \\ \hline \mathrm{A} & \mathrm{} 1 \mathrm{million} & 12.0 \% \\\\\mathrm{B} & 2 \text { million } & 11.5 \\ \mathrm{C} & 2 \text { million } & 11.2 \\\\\mathrm{D} & 2 \text { million } & 11.0 \\\\\mathrm{E} & 1 \text { million } & 10.7 \\ \mathrm{F} & 1 \text { million } & 10.3 \\\\\mathrm{G} & 1 \text { million } & 10.2\end{array}$$ Assume that each of these projects is just as risky as the firm's existing assets, and the firm may accept all the projects or only some of them. Which set of projects should be accepted?
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