Question

Compressed APV Model with Constant Growth

An unlevered firm has a value of $700 million. An otherwise identical but levered firm has $70 million in debt at a 6% interest rate. Its cost of debt is 6% 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 2%. Assuming the corporate tax rate is 35%, 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.

$ ？ million

Answer 1

Interest expense of the levered firm = Value of debt*Interest rate

Interest expense of the levered firm = $70 million*6% = $4.2 million

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

  = $4.2 million * 35% = $1.47 million

Since the growth rate is expected to be 2% in perpetuity, the adjusted cost of capital is

Adjusted cost of capital = Cost of equity - Growth rate

= 12% - 2% = 10%

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

= $1.47 million / 1.10 = 1.34 million

Hence,

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

Value of levered firm = $700 million + $1.34 million = $701.34 million