Final answer:
The value of the levered firm using the compressed APV model is $837.875 million, which is calculated by adding the value of the unlevered firm ($800 million) and the present value of the tax shield ($37.875 million) obtained from the debt structure.
Step-by-step explanation:
To determine the value of the levered firm using the compressed adjusted present value (APV) model, we first calculate the present value of the unlevered firm and then add the present value of the tax shield due to debt. Given that the unlevered firm has a value of $800 million, we maintain this as a starting point. The levered firm has $60 million in debt at a 5% interest rate, which amounts to an annual interest expense of $3 million. The corporate tax rate is 25%, so the annual tax saving from the interest expense is 0.25 × $3 million = $0.75 million. Using the perpetual growth formula for the tax shield, PV(Tax Shield) = Tax Saving × (1 + g) / (r - g), where g is the constant growth rate of 3% and r is the cost of debt of 5%, we get PV(Tax Shield) = $0.75 million × (1 + 0.03) / (0.05 - 0.03) = $37.875 million. Thus, the value of the levered firm is $800 million (value of the unlevered firm) + $37.875 million (value of the tax shield) = $837.875 million.