Problem 21-4 APV Model with Constant Growth An unlevered firm has a value of $85

Question

Problem 21-4
APV Model with Constant Growth

An unlevered firm has a value of $850 million. An otherwise identical but levered firm has $40 million in debt at a 5% interest rate. Its cost of debt is 5% 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 3%. Assuming the corporate tax rate is 30%, 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

Explanation / Answer

Value of the unlevered firm = $850 mn

A levered firm can have a tax benefit from its debt which is equal to Tax * Debt

So tax benefit from debt = 30% * 40 = $12 Mn

But this is in the case of cash flows are same to perpetuity. In our case, cash flows are increasing at a rate of 3%, so debt benefit = 40 * 30% * 5% *(1+3%) / (5%-3%)

Debt Benefit = $30.9Mn

So value of a levered firm = Value of the unlevered firm + Debt Tax benefit

So value of a levered firm = 850 + 30.9 = $880.9 Mn

Answer is 880.90

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