An unlevered firm has a value of $750 million. An otherwise identical but levere

Question

An unlevered firm has a value of $750 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 12%. 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

Explanation / Answer

Tax Saving which grows at the rate of 4 % per annum is the annual value of interest tax shields. Hence, the interest tax shields grow at a rate of 4 % per annum.

Year 1: Debt = $ 40 million, Interest Rate = 5 %, Tax Rate = 40 %

Year 1 Interest Tax Shield = 0.05 x 40 x 0.4 = $ 0.8 million

As the interest tax shields grow to perpetuity at a constant rate of g = 4 %, the tax savings grow at the same rate as the unlevered cash flow (free cash flow) and the tax savings have risk equal to that of the unlevered firm, the perpetually growing tax savings should be discounted at the unlevered cost of equity.

Unlevered Cost of Equity = 12 %

Present Value of Interest Tax Shield = 0.8 / (0.12 - 0.04) = $ 10 million

Total Firm Value = Unlevered Firm Value + PV of Interest Tax Shield = 750 + 10 = $ 760 million or $ 760000000

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