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%

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