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 %