Question

An unlevered firm has a value of $800 million. An otherwise identical but levered firm has $40 million in debt at a 4% interest rate. Its cost of debt is 4% and its unlevered cost of equity is 12%. 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 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

Interest expense of the levered firm = Value of debt * Interest rate = $40 million * 4% = $1.6 million

Tax savings on account of interest expense = Interest expense of the levered firm * Tax rate

= $1.6 million*40% = $0.64 million

Since the growth rate is expected to be 3% in perpetuity, the adjusted cost of capital is

Adjusted cost of capital = Cost of equity - Growth rate = 12% - 3% = 9%

Present value of tax benefits due to interest expense = Tax savings/(1 + Adjusted cost of capital)

= $0.64 million/1.09 = $0.59 million

Hence,

Value of levered firm = Value of unlevered firm + Present value of tax benefits due to int. expense

  = $800 million + $0.59 million = $800.59 million