Question

Suppose the corporate tax rate is 40 %40%. Consider a firm that earns $ 2 comma 500$2,500 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 5 % 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 $ 700$700 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. The difference in ​(c​) is equal to what percentage of the value of the​ debt?

Answer 1

Answer: a. $30,000

b. $21,600; $14,000

c. $5,600

d. 40%

Explanation;

a. When the company is assumed to have no debt and pays its net income entirely as dividends then the Value of the firm's equity is;

= Earnings after taxes / Cost of Equity

Risk free interest rate will be used. The Earnings after taxes are used because taxes have to be taken out to find out the amount due to shareholders for the year.

= 2,500 ( 1 - 40%) / 5%

= 1,500/ 5%

= $30,000

b. If interest is paid then the Value of equity will be;

= Earnings after interest and taxes / Cost of Equity

= (2,500 - interest * ( 1 - tax) ) / Cost of Equity

= (2,500 - 700 * ( 1 - 40%) ) / 5%

= $21,600

Value of debt = Interest/cost of debt

=700/5%

= $14,000

c. The total value of the firm without Leverage has been shown to be $30,000.

The total value of the firm with leverage would be;

= Value of Equity assuming debt + Value of Debt

= 21,600 + 14,00

= $35,600

Difference;

= 35,600 - 30,000

=$5,600

d. Value of debt is $14,000

= (5,600/14,000) * 100%

= 40%