Question

An unlevered firm has a value of $700 million. An otherwise identical but levered firm has $50 million in debt at a 3% interest rate. Its cost of debt is 3% and its unlevered cost of equity is 10%. After Year 1, free cash flows and tax savings are expected to grow at a constant rate of 4%. Assuming the corporate tax rate is 40%, use the compressed adjusted present value model to determine the value of the levered firm. (Hint: The interest expense at Year 1 is based on the current level of debt.) Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Do not round intermediate calculations. Round your answer to two decimal places

Answer 1

value of the levered firm: 728.62

Step-by-step explanation:

the modigliani miller proposition suggest that a leverege firm has a higher value than an unlevered firm if there is income taxes.

This is because the returns on the bedt provides a tax shield while the dividends, don't.

Vl = Vu + tc x D

Vl = 700,000,000 +50,000,000 x 3% x 40%

Vl = 700,000,000 + 600,000 = 700.6 millions

now we multiply by the grow rate to know the value in one year.

700.6 x (1 +g ) = 700.6 x 1.04 = 728,624

value of the levered firm after a year: 728.62