Final answer:
To calculate the value of a levered firm using APV, value the firm as if it were unlevered and then add the present discounted value of the tax shield from debt. For perpetual debt's tax shield, the appropriate discount rate is the risk-free rate due to the certainty of the tax savings.
Step-by-step explanation:
To value a levered firm using the Adjusted Present Value (APV) approach, one would begin by valuing the firm as if it had no debt, using the unlevered cost of equity as the discount rate. The interest tax shields that debt provides are then valued separately and added to the firm's value. The right discount rate for the tax shields, particularly in the case of perpetual debt, is typically the risk-free rate because the tax savings on interest payments are relatively certain if the firm's income remains sufficient to pay the debt interest.
Under APV, the firm's value is the sum of the present discounted value (PDV) of its expected free cash flows as an unlevered firm, plus the PDV of the interest tax shields minus any costs of financial distress. When applying APV to a stock, an investor considers the expected future profits and discounts them at an appropriate interest rate to determine the PDV of the stock. It is important to take into consideration the expected capital gains and dividends when deciding this rate.
For Babble, Inc., assuming an interest rate of 15%, one would discount the expected profits for each year separately, add up all the present values, and divide by the number of shares. In this hypothetical case, the price per share is calculated to be approximately $256,500 per share.