Suppose the corporate tax rate is 35%. Consider a firm that earns $2,000 in earnings before...

Suppose the corporate tax rate is 35%. Consider a firm that earns $2,000 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?

b. Suppose instead the firm makes interest payments of $ 1,400 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. To what percentage of the value of the debt is the difference in part (c) equal?

Expert Solution

A.cashflow to Equity = EBIT*(1-tax rate)
2000*(1-0.35)
1300
Risk free rate=   7%

value of firm = cash flow to Equity/Risk free rate
1300/7%
18571.42857
So value of Equity =   18571.42857

B
If interest paid=   $1,400
Cash flow to Equity = (EBIT- Interest)*(1-tax rate)
(2000-1400)*(1-0.35)
=$ 390

Value of Equity = 390/7%
5571.428571

Value of Equity is $5571.43

Value of debt = Cash flow to debt/Risk free rate
= 1400/7%=
20000

Value of debt is$20000

C.
Total value of Firm = Value of debt = Value of Equity
20000+5571.43
$25,571.43
"Difference in Total value of Levergae and unleveraged value of Firm
"
25571.43-18571.43
$7,000.00

Difference in % of Debt= 7000/20000
0.35   or 35%

So 35 percentage of the value of the debt is the difference in part (c) equal.

jeff jeffy answered 5 months ago

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