In year 1, AMC will earn $1,600 before interest and taxes. The market expects these earnings to grow at a rate of 2.8% per year. The firm will make no net investments (i.e., capital expenditures will equal depreciation) or changes to net working capital. Assume that the corporate tax rate equals 25%. Right now, the firm has $4,000 in risk-free debt. It plans to keep a constant ratio of debt to equity every year, so that on average the debt will also grow by 2.8% per year. Suppose the risk-free rate equals 4.6667%, and the expected return on the market equals 10.267%. The asset beta for this industry is 1.46. a. If AMC were an all-equity (unlevered) firm, what would its market value be? b. Assuming the debt is fairly priced, what is the amount of interest AMC will pay next year? If AMC's debt is expected to grow by 2.8% per year, at what rate are its interest payments expected to grow? c. Even though AMC's debt is riskless (the firm will not default), the future growth of AMC's debt is uncertain, so the exact amount of the future interest payments is risky. Assuming the future interest payments have the same beta as AMC's assets, what is the present value of AMC's interest tax shield? d. Using the APV method, what is AMC's total market value, V? What is the market value of AMC's equity? e. What is AMC's WACC? (Hint: Work backward from the FCF and V.) f. Using the WACC, what is the expected return for AMC equity? D E g. Show that the following holds for AMC: BA D+EE + D+ EBD h. Assuming that the proceeds from any increases in debt are paid out to equity holders, what cash flows do the equity holders expect to receive in one year? At what rate are those cash flows expected to grow? Use that information plus your answer to part (f) to derive the market value of equity using the FTE method. a. If AMC were an all-equity (unlevered) firm, what would its market value be? If AMC were an all-equity (unlevered) firm, its market value would be $ 11948.46. (Hold all intermediate calculations to at least 6 decimal places and round to the nearest cent.) b. Assuming the debt is fairly priced, what is the amount of interest AMC will pay next year? If AMC's debt is expected to grow by 2.8% per year, at what rate are its interest payments expected to grow? Assuming the debt is fairly priced, the amount of interest AMC will pay next year is $ 186.67. (Round to the nearest cent.) If AMC's debt is expected to grow by 2.8% per year, the rate its interest payments are expected to grow is 2.8 %. (Round to one decimal place.) c. Even though AMC's debt is riskless (the firm will not default), the future growth of AMC's debt is uncertain, so the exact amount of the future interest payments is risky. Assuming the future interest payments have the same beta as AMC's assets, what is the present value of AMC's interest tax shield? The present value of AMC's interest tax shield is $ 464.82. (Hold all intermediate calculations to at least 6 decimal places and round to the nearest cent.) d. Using the APV method, what is AMC's total market value, V-? What is the market value of AMC's equity? AMC's total market value, () is $ 8413.28 (Round to the nearest cent.) In year 1, AMC will earn $3,500 before interest and taxes. The market expects these earnings to grow at a rate of 2.0% per year. The firm will make no net investments (i.e., capital expenditures will equal depreciation) or changes to net working capital. Assume that the corporate tax rate equals 25%. Right now, the firm has $8,750 in risk-free debt. It plans to keep a constant ratio of debt to equity every year, so that on average the debt will also grow by 2.0% per year. Suppose the risk-free rate equals 5%, and the expected return on the market equals 7.333%. The asset beta for this industry is 1.50. a. If AMC were an all-equity (unlevered) firm, what would its market value be? b. Assuming the debt is fairly priced, what is the amount of interest AMC will pay next year? If AMC's debt is expected to grow by 2.0% per year, at what rate are its interest payments expected to grow? c. Even though AMC's debt is riskless (the firm will not default), the future growth of AMC's debt is uncertain, so the exact amount of the future interest payments is risky. Assuming the future interest payments have the same beta as AMC's assets, what is the present value of AMC's interest tax shield? d. Using the APV method, what is AMC's total market value, V-? What is the market value of AMC's equity? e. What is AMC's WACC? (Hint: Work backward from the FCF and VL.) f. Using the WACC, what is the expected return for AMC equity? E D a. Show that the following holds for AMC: B. = B- + d. Using the APV method, what is AMC's total market value, V-? What is the market value of AMC's equity? The APV tells us that the value of a firm with debt equals the sum of the value of an all equity firm and the tax shield. To compute the value of the firm with leverage, we use the following equation: =+PV(Interest tax shield) Therefore, = $40,384.62 + $1,683.08 = $42,067.70 AMC's total market value, () is $42,067.70. To determine the market value of equity, use the following formula: E=V-D a. If AMC were an all-equity (unlevered) firm, what would its market value be? To calculate the market value of an all-equity (unlevered) firm, follow the steps below: First, calculate the FCF using the following formula: FCF Profit (1 - Tax rate) Therefore, = FCF $3,500 x 0.75 = $2,625.00 Next, calculate the unlevered cost of capital using the following formula: ru = r + + B (rm -rf) Therefore, ru = 0.05 +1.50 (0.07333 -0.05) = 0.0850 = 8.50% Finally, calculate the market value using the following formula: = Therefore, FCF ru-g vu: $2,625.00 = $40,384.62 0.0850 0.020 If AMC were an all-equity (unlevered) firm, its market value would be $40,384.62. b. Assuming the debt is fairly priced, what is the amount of interest AMC will pay next year? If AMC's debt is expected to grow by 2.0% per year, at what rate are its interest payments expected to grow? To compute the amount of interest to be paid next year, use the following formula: Interest paid Debt Interest rate Since the debt is risk-free, the interest rate paid on it must equal the risk-free rate of 5% (or else there would be an arbitrage opportunity). Therefore, Interest paid = $8,750 x 0.05 = $437.50 Assuming the debt is fairly priced, the amount of interest AMC will pay next year is $437.50. Interest payments will grow by the same percentage as the debt. If AMC's debt is expected to grow by 2.0% per year, the rate its interest payments are expected to grow is 2.0%. c. Even though AMC's debt is riskless (the firm will not default), the future growth of AMC's debt is uncertain, so the exact amount of the future interest payments is risky. Assuming the future interest payments have the same beta as AMC's assets, what is the present value of AMC's interest tax shield? To calculate the tax shield, use the following formula: Tax shield Interest paid x Tax rate Therefore, the tax shield = $437.50 x 0.25 = $109.4, and it will grow along with the growth of the debt at a rate of 2.0%. But the exact amount of the tax shield is uncertain, since AMC may add new debt or repay some debt during the year, depending on their cash flows. This makes the actual amount of the tax shield risky even though the debt itself is not. Since the beta of the tax shield due to debt is 1.50, the appropriate discount rate: ru = r+x (rm -r) Therefore, ru = 0.05 +1.50 (0.07333 -0.05) = 0.0850 = 8.50% To calculate the present value of the interest tax shield, use the following formula: PV(Interest tax shield) = Tax shield ru-g Therefore, $109.4 PV(Interest tax shield): = = $1,683.08 0.0850 0.020 The present value of AMC's interest tax shield is $1,683.08.