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Chapter 16: Problem 19

MM Proposition I with Taxes The Maxwell Company is financed entirely with equity. The company is considering a loan of \(\$ 1.4\) million. The loan will be repaid in equal installments over the next two years, and it has an 8 percent interest rate. The company's tax rate is 35 percent. According to MM Proposition I with taxes, what would be the increase in the value of the company after the loan?

Short Answer

Expert verified
The increase in the value of the company after taking the loan is due to the tax shield created by the loan's interest expense. According to MM Proposition I with taxes, the increase in the company value can be calculated using the formula: \(PV_{Tax Shield} = TC \times \frac{D \times r}{1 + r} - TC \times \frac{D \times r }{(1 + r)^2}\). By substituting the given values, we get \(PV_{Tax Shield} = 0.35 \times \frac{1.4 \times 10^6 \times 0.08}{1 + 0.08} - 0.35 \times \frac{1.4 \times 10^6 \times 0.08 }{(1 + 0.08)^2} = \$31,558.44\), which represents the benefit of debt in the firm's capital structure in terms of the present value of tax shields.

Step by step solution

01

Identify and Define the Variables

The variables needed for the calculations are already given in the exercise, which are: - \(D\) (the total debt/loan value) = $1.4 million - \(r\) (the annual interest rate) = 8% or 0.08 - \(TC\) (The Tax Rate) = 35% or 0.35
02

Calculate the Interest Tax Shield for Each Year

Firstly, we need to calculate the interest tax shield for each year. It is the amount of tax saved by the company due to the tax deductibility of the interest payments. Use the formula \(Tax Shield = TC \times D \times r\).
03

Calculate the Present Value of the Tax Shields

To calculate the present value of the tax shield over the two years, the formula is \(PV_{Tax Shield} = TC \times \frac{D \times r}{1 + r} - TC \times \frac{D \times r }{(1 + r)^2}\). Use this formula to calculate the present value of the tax shield.
04

Interpret the Result

By following these steps, we calculate the increase in the value of the company after taking the loan. This increase is due to the tax shield created by the loan's interest expense, which reduces the overall tax liability of the company. According to MM Proposition I with taxes, this increase represents the benefit of debt in the firm's capital structure in terms of the present value of tax shields.

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Key Concepts

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

Interest Tax Shield
When a company takes on debt, it can benefit from an interest tax shield. This is the tax savings a company enjoys because it can deduct interest payments from its taxable income. In essence, it reduces the net taxable income, resulting in lower taxes dues and increasing cash flows, benefiting the company's work and growth. The calculation for the tax shield is straightforward. It is calculated as the interest payment multiplied by the corporate tax rate (TC).
  • Tax Shield Calculation: \[\text{Tax Shield} = TC \times D \times r\]where:
    • \(TC\) is the corporate tax rate
    • \(D\) is the total debt value
    • \(r\) is the interest rate
With this formula, you can easily measure how much tax the company saves in a specific year by merely having debt. This incentive can be enticing enough for businesses to take loans.
Capital Structure
Capital structure refers to the way a company finances its operations and growth through different sources of funds. Generally, it comprises a mix of debt and equity. Each source of funding comes with characteristics that can influence the firm's balance sheet and operational strategy.
  • Equity: This is funds raised through shareholders who are the owners of the company. While there is no repayment obligation, issuing equity can dilute ownership.
  • Debt: Borrowed money that needs to be repaid with interest. It doesn't dilute ownership, but it requires periodic interest payments.
When considering changes to their capital structure, companies must weigh the benefits of debt鈥攕uch as tax deductibility of interest鈥攁gainst the risks, like financial distress from high leverage. Through MM Proposition I, with taxes, it's shown that using debt strategically enhances the total value of the company due to the interest tax shield.
Present Value of Tax Shield
The present value of the tax shield is the current worth of all future tax savings obtained by the tax shield due to interest deductions. To compute this, we need to account for the time value of money through discounting future tax savings back to their present value.
  • The formula is:\[PV_{Tax Shield} = TC \times \left( \frac{D \times r}{1 + r} - \frac{D \times r }{(1 + r)^2} \right)\]
  • Here, \(PV_{Tax Shield}\) represents the present value of multiple-year tax savings.
This calculation presents an effective way to understand how the tax shield contributes towards the company's overall valuation. The longer the debt term or higher the interest rate, the larger the tax shield might become, making more room for future financial planning.
Corporate Tax Rate
The corporate tax rate plays a pivotal role in determining the size of a company's tax shield. It is the percentage of taxable income that a company is required to pay to the government. As the corporate tax rate increases, the benefit of having a debt in the firm's capital structure (like the tax shield) becomes more substantial due to the larger amount of interest being tax-deductible.
  • A higher corporate tax rate means greater tax savings from the same amount of interest, thus a more valuable tax shield.
  • Conversely, a lower tax rate diminishes these savings, reducing the advantage of leveraging through debt.
Understanding the corporate tax rate is crucial for financial decision-making, especially when planning for optimal capital structures and maximizing corporate value. The greater the tax rate, the greater the incentive for efficient debt management.

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Most popular questions from this chapter

Calculating WACC Weston Industries has a debt-equity ratio of 1.5. Its WACC is 12 percent, and its cost of debt is 9 percent. The corporate tax rate is 35 percent. 1\. What is Weston's cost of equity capital? 2\. What is Weston's unlevered cost of equity capital? 3\. What would the cost of equity be if the debt-equity ratio were 2 ? What if it were 1.0 ? What if it were zero?

Homemade Leverage and WACC ABC Co. and XYZ Co. are identical firms in all respects except for their capital structure. ABC is all equity financed with \(\$ \mathbf{8 0 0 , 0 0 0}\) in stock. XYZ uses both stock and perpetual debt; its stock is worth \(\$ 400,000\) and the interest rate on its debt is 10 percent. Both firms expect EBIT to be \(\$ 95,000\). Ignore taxes. 1\. Richard owns \(\mathbf{\$} \mathbf{3 0 , 0 0 0}\) worth of XYZ's stock. What rate of return is he expecting? 2\. Show how Richard could generate exactly the same cash flows and rate of return by investing in \(\mathrm{ABC}\) and using homemade leverage. 3\. What is the cost of equity for \(A B C\) ? What is it for \(X Y Z\) ? 4\. What is the WACC for \(A B C\) ? For \(X Y Z\) ? What principle have you illustrated?

Stock Value and Leverage Green Manufacturing, Inc., plans to announce that it will issue \(\$ 3\) million of perpetual debt and use the proceeds to repurchase common stock. The bonds will sell at par with a 6 percent annual coupon rate. Green is currently an all-equity firm worth \(\$ 9.5\) million with 600,000 shares of common stock outstanding. After the sale of the bonds, Green will maintain the new capital structure indefinitely. Green currently generates annual pretax earnings of \(\$ 1.8\) million. This level of earnings is expected to remain constant in perpetuity. Green is subject to a corporate tax rate of \(\mathbf{4 0}\) percent. 1\. What is the expected return on Green's equity before the announcement of the debt issue? 2\. Construct Green's market value balance sheet before the announcement of the debt issue. What is the price per share of the firm's equity? 3\. Construct Green's market value balance sheet immediately after the announcement of the debt issue. 4\. What is Green's stock price per share immediately after the repurchase announcement? 5\. How many shares will Green repurchase as a result of the debt issue? How many shares of common stock will remain after the repurchase? 6\. Construct the market value balance sheet after the restructuring. 7\. What is the required return on Green's equity after the restructuring?

Cost of Capital Acetate, Inc., has equity with a market value of \(\$ 35\) million and debt with a market value of \(\$ 14\) million. Treasury bills that mature in one year yield 6 percent per year, and the expected return on the market portfolio is 13 percent. The beta of Acetate's equity is 1.15. The firm pays no taxes. 1\. What is Acetate's debt-equity ratio? 2\. What is the firm's weighted average cost of capital? 3\. What is the cost of capital for an otherwise identical all-equity firm?

MM with Taxes Williamson, Inc., has a debt-equity ratio of 2.5 . The firm's weighted average cost of capital is 15 percent, and its pretax cost of debt is 10 percent. Williamson is subject to a corporate tax rate of 35 percent. 1\. What is Williamson's cost of equity capital? 2\. What is Williamson's unlevered cost of equity capital? 3\. What would Williamson's weighted average cost of capital be if the firm's debt-equity ratio were .75? What if it were 1.5 ?
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