Question

An unlevered firm has a value of $900 million. An otherwise identical but levered firm has $70 million in debt at a 4% interest rate, which is its pre-tax cost of debt. Its unlevered cost of equity is 11%. After Year 1, free cash flows and tax savings are expected to grow at a constant rate of 3%. Assuming the corporate tax rate is 25%, 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 $10,550,000 should be entered as 10.55. Do not round intermediate calculations. Round your answer to two decimal places.

$    million

Answer 1

Solution:-

Given,

Corporate tax rate = 25%

Growth rate = 3%

Required rate on return on equity = 11%

Value of Unlevered firm = $900 million --------> 1

Value of Levered firm debt = $70 million

Interest expense of the levered firm = $70 million * 4%

= $2.8 million

Tax saving on account of interest expense = $2.8 million * 25%

= $0.7 million

Value of the Levered firm = Value of Unlevered firm + Present value of tax saving on account of interest expense

Adjusted Cost of capital = Cost of equity - Growth rate

= 11% - 3%

= 8%

Present value of tax savings due to interest expense in perpetuity = $0.7 / 0.08

= $8.75 million ------> 2

Hence Value of Levered firm = (1) + (2)

= $900 million + $8.75 million

= $908.75 million.

Therefore the value of Lrevered firm is $908.75 millions.