Question

Tool Manufacturing has an expected EBIT of $91,000 in perpetuity and a tax rate of 24 percent. The firm has $255,000 in outstanding debt at an interest rate of 5.6 percent, and its unlevered cost of capital is 11.5 percent. What is the value of the firm according to M&M Proposition I with taxes? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

To find the value of the firm using M&M Proposition I with taxes, the after-tax EBIT is divided by the unlevered cost of capital and the tax shield from debt is added. For the given EBIT of $91,000, a tax rate of 24%, $255,000 of debt, and an 11.5% unlevered cost of capital, the firm's value is approximately $662,591.30.

Step-by-step explanation:

The student's question relates to calculating the value of a firm based on Modigliani and Miller Proposition I with taxes. To find the value of the firm, we use the formula:

V = EBIT(1 - T) / Ru + (T * D)

where:
V = value of the firm
EBIT = earnings before interest and taxes
T = tax rate
Ru = unlevered cost of capital
D = value of debt

Plugging in the values provided by the student, we have:

V = $91,000(1 - 0.24) / 0.115 + (0.24 * $255,000)

First, calculate the after-tax EBIT:

After-tax EBIT = $91,000 * (1 - 0.24) = $69,160

Then, calculate the value of the unlevered firm (Vu):

Vu = After-tax EBIT / Ru = $69,160 / 0.115 ≈ $601,391.30

Lastly, add the tax shield benefit from the debt:

Tax Shield = T * D = 0.24 * $255,000 = $61,200

Therefore, the total value of the firm including the tax shield is:

V = Vu + Tax Shield ≈ $601,391.30 + $61,200 = $662,591.30

So, the value of the firm according to M&M Proposition I with taxes is approximately $662,591.30.