Question

Suppose the corporate tax rate is 40%. Consider a firm that earns $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 4%.

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 $1,000 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.

EBIT = $2,500
Tax Rate = 40%

Net Income = EBIT * (1 - Tax Rate)
Net Income = $2,500 * (1 - 0.40)
Net Income = $1,500

Value of Equity = Net Income / Risk-free Interest Rate
Value of Equity = $1,500 / 0.04
Value of Equity = $37,500

Answer b.

EBIT = $2,500
Interest Expense = $1,000
Tax Rate = 40%

Net Income = (EBIT - Interest Expense) * (1 - Tax Rate)
Net Income = ($2,500 - $1,000) * (1 - 0.40)
Net Income = $900

Value of Equity = Net Income / Risk-free Interest Rate
Value of Equity = $900 / 0.04
Value of Equity = $22,500

Value of Debt = Interest Expense / Risk-free Interest Rate
Value of Debt = $1,000 / 0.04
Value of Debt = $25,000

Answer c.

Value of Levered Firm = Value of Debt + Value of Equity
Value of Levered Firm = $25,000 + $22,500
Value of Levered Firm = $47,500

Value of Unlevered Firm = Value of Equity
Value of Unlevered Firm = $37,500

Difference = Value of Levered Firm - Value of Unlevered Firm
Difference = $47,500 - $37,500
Difference = $10,000

Answer d.

Corporate Tax Rate = Difference / Value of Debt
Corporate Tax Rate = $10,000 / $25,000
Corporate Tax Rate = 40%