Question

An unlevered firm has a value of $700 million. An otherwise identical but levered firm has $40 million in debt at a 6% interest rate. Its cost of debt is 6% 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 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.

Answer #1

Step 1:

Calculate the adjusted cost of capital as follows:

Adjusted cost of capital = cost of capital - growth rate

= 10%- 2%

= 8%

----------------------------------------------------------------------------

Step 2:

Calculate the present value of tax savings on interest as follows:

Present value of tax savings = (Debt * Interest rate * Tax rate) / (adjusted cost of capital)

= ($40 million * 6% * 35%) / 8%

= $0.84 million / 8%

= $10.50 million

------------------------------------------------------------------------------------------------------

Step 3:

Calculate the value of levered firm as follows:

Levered firm = Value of unlevered firm + Present value of tax savings

= $700 million + $10.50 million

= $710.50 million

Therefore, the value of levered firm is **$710.50
million**.

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