Question

Suppose the corporate tax rate is 35%. Consider a firm that earns $10,000 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 5.0%.
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 $1,500 per year. What is the value of the equity? What is the value of the 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?

Answer 1

Answer:

a) $130,000

b)Equity = $110,500

Value of debt = $30,000

c) $10,500

d) 35%

Explanation:

Given:

Tax rate = 35%

Earnings before tax & interests = $10,000

Risk free interest rate = 5.0%

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?

First find net income.

Net income = $10,000(1 - 0.35)

= $(10,000 - 0.65)

= $6,500

Since net income is $6,500 it means equity shareholders receive dividends of $6,500 annually without risk.

Therefore,

equity = Net income / risk free rate

= 6500/0.05

= $130,000

Equity = $130,000

b) First find net income:

($10,000 - $1,500)(1 - 0.35)

($8,500)(0.65) = $5,525

Net income = $5,525

Find equity:

Equity = Net income / risk free rate

= $5,525 / 0.05

= $110,500

Equity = $110,500

Value of debt:

Use the formula below to find value of debt:

Debt = Interest / risk free rate

= $1,500 / 0.05

= $30,000

Value of debt = $30,000

c) Find the total value of the firm with leverage:

$110,500 + $30,000

= $140,500

The total value of the firm without leverage: $130,000

Now, the difference between the total value of the firm with leverage and without leverage:

$140,500 - $130,000

= $10,500

Difference = $10,500

d) Find the percentage difference:

% difference = difference/debt * 100

$= \frac{10500}{30000} * 100$

$0.35 * 100 = 35 percent$