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 levered firm = value of the Unlevered firm + present Value of Interest Tax shield discounted by Cost of Debt Financing

Value of the Unlevered firm = 850 million

Next Year Interest tax shield = $40 Million×5%×30% = $0.60 Million

Present Value of Interest Tax shield = Next Year Interest tax shield /(Cost of Debt-Growth rate)

Present Value of Interest Tax shield = $0.60 Million/(5%-3%)

Present Value of Interest Tax shield = $30

Value of the levered firm = $850 Million + $30 Million

Value of the levered firm = $ 880 Million

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