Question

Suppose the corporate tax rate is 40 %. Consider a firm that earns $ 3 comma 000 in earnings before interest and taxes each year with no risk. The firm's capital expenditures equal its depreciation expenses each year, and it will have no changes to its net working capital. The risk-free interest rate is 8 %. a. Suppose the firm has no debt and pays out its net income as a dividend each year. What is the value of the firm's equity? b. Suppose instead the firm makes interest payments of $ 500 per year. What is the value of equity? What is the value of debt? c. What is the difference between the total value of the firm with leverage and without leverage? d. To what percentage of the value of the debt is the difference in part (c) equal?

Answer #1

a. Suppose the firm has no debt and pays out its net income as a dividend each year. What is the value of the firm's equity?

Net income = 3000 * (1 - 40%)

= $1800.

Thus, equity holders receive dividends of $1800 per year with no risk.

E = 1800 / 0.08 = 22500

b. Suppose instead the firm makes interest payments of $ 500 per year. What is the value of equity? What is the value of debt?

Answer = Net Income = (3000 - 500) * (1 - 40)

= 1500

E = 1500 / 0.08= 18750

Debt holders receive interest of $500 per year

D = 6250

c. What is the difference between the total value of the firm with leverage and without leverage?

With leverage = 18,750 + 6,250 = $25,000

Without leverage = $22,500

Difference = 25,000 – 22,500

= $2500

d. To what percentage of the value of the debt is the difference in part (c) equal?

Corporate tax rate = 2500 / 6250

= 40 %

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