Question

Suppose the corporate tax rate is 30 %. Consider a firm that earns $ 1 comma 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 $ 400 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

a) Here EBIT = 1500$ , tax rate =30%

Since there is no debt = EBIT = EBT

PAT = EBT(1-tax rate)

=1500(1-0.3)

=1500(0.7)

=1050$

Value of equity = PAT/Risk free interest rate

=1050/5%

=21000$

b) Here EBIT = 1500$ , tax rate =30% , interest payments = 400$

EBT = EBIT - Interest

=1500-400

=1100$

PAT = EBT(1-tax rate)

=1100(1-0.3)

=1100(0.7)

=770$

Thus value of equity = PAT/Risk free rate of interest

=770/5%

=15400$

Value of debt = Interest payments/ Risk free rate of interest

=400/5%

=8000$

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

=15400+8000

=23400$

Total value of firm without leverage = 21000$

Difference = 23400-21000

=2400$

d) Difference as % of debt = 2400/8000

=30%