Question

Perpetuum Mobile Inc. is an all-equity firm that generates $6m in annual after-tax cash flows that are expected to remain constant forever. It's cost of capital is currently 11%. The firm is planning to borrow $15M and use the proceeds to buy back shares. The cost of debt is 5%. The debt will mature in 10 years after which the firm is expected to maintain zero-leverage capital structure. What is the new value of the firm if the tax rate is 30%?

A. $56.53M
B. $56.28M
C. $56.01M
D. $56.96M
E. $56.76M

Answer 1

The new value of the firm, considering the borrowing, is $55.26 million.

Step-by-step explanation:

To calculate the new value of the firm, we need to determine the present value of the after-tax cash flows and the tax shield from the debt. The after-tax cash flows are $6 million and the cost of capital is 11%. Using the perpetuity formula, the present value of the cash flows is $54.55 million.

The interest expense from the debt is tax-deductible, creating a tax shield. The present value of the tax shield is calculated by multiplying the tax rate (30%) by the interest expense ($15 million * 5% = $0.75 million). The present value of the tax shield is $0.71 million.

The new value of the firm is the sum of the present value of the cash flows and the present value of the tax shield: $54.55 million + $0.71 million = $55.26 million. Therefore, none of the provided options match the correct value.