Question

**Problem 21-03**

Compressed APV Model with Constant Growth

An unlevered firm has a value of $850 million. An otherwise identical but levered firm has $80 million in debt at a 7% interest rate. Its cost of debt is 7% and 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 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.

$ million

Answer #1

Value of unlevered firm = 850 million

tax benefit of a levered firm = 40% x 80 = 32 million

As free cash flows and tax savings are expected to grow at a constant growth of 4%

so benefit can be calculated as a growing annuity

Benefits = 32 million x 7% x (1+4%)/(7%-4%) = 77.653 million

value of levered firm =adjusted present value = value of unlevered firm + debt tax benefits

= 850 + 77.653 = 927.653

**value of the
levered firm = $ 927.65 million**

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identical but levered firm has $40 million in debt at a 6% interest
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