Question

Suppose the corporate tax rate is 35 %. Consider a firm that earns $ 4 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 7 %.

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?

If the firm has no debt and pays out its net income as a dividend each​ year, the value of the​ firm's equity is ​$_____. ​(Round to the nearest​ dollar.)

b. Suppose instead the firm makes interest payments of $ 2, 700 per year. What is the value of​ equity? What is the value of​ debt?

The value of the firm with leverage is ​$______.

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

The difference between the total value of the firm with leverage and without leverage is ​$______.

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

The percentage of the value of debt to the difference in ​(c​) is ___%.

Answer 1

Solution;

a)Calculation of value of the​ firm's equity

Value of the​ firm's equity=Dividend/Risk free rate

=EBIT(1-tax rate)/7%

=$4000(1-0.35)/7%

=$37,142.86

b)Net Income=(EBIT-Interest)(1-tax rate)

=($4000-$2700)(1-0.35)

=$845

Value of equity=$845/7%=$12071.43

Value of debt=Interest/Risk free rate

=$2700/0.07=$38,571.43

c)Total value of  firm with leverage=Value of debt+Value of equity

=$38,571.43+$12,071.43

=$50,642.86

Value of firm without leverage=value of equity=$37,142.86

Difference in value=$50,642.86-$37,142.86

=$13,500

d)Percentage of the value of debt to the difference in ​(c​) is;

=($13,500/$38,571.43)*40

=35%