KFC, Nando's und andere geben Tierwohl-Versprechen für Hühner auf

Let's think step by step. We have the following information: - The firm's expected EBIT is $20,000 per year forever. - The firm's tax rate is 35%. - The firm has debt with a market value of $25,000. - The firm pays an 8% annual coupon on its debt. - The firm's unlevered cost of capital is 10%. We are asked: "What is the firm's levered value?" --- ### Step 1: Understand the firm's cash flows The firm's EBIT is $20,000 per year forever. This is before interest and taxes. Debt interest expense per year = 8% of $25,000 = $2,000. EBT (Earnings Before Tax) = EBIT - Interest = $20,000 - $2,000 = $18,000. Tax = 35% of EBT = 0.35 * $18,000 = $6,300. Net Income = EBT - Tax = $18,000 - $6,300 = $11,700. This net income goes to equity holders. But wait — we need the levered value of the firm, which is V_L = E + D. We can use the APV approach or the FCF approach. Let’s try both. --- ### Step 2: Approach 1: APV (Adjusted Present Value) APV formula: V_L = V_U + PV(interest tax shield) First, find V_U (unlevered value): Unlevered cash flows to firm = EBIT*(1-tax rate) = $20,000*(1-0.35) = $13,000 per year. Unlevered cost of capital = 10%, so V_U = $13,000 / 0.10 = $130,000. Now, tax shield: Interest tax shield per year = Interest expense * tax rate = $2,000 * 0.35 = $700 per year. But what discount rate for tax shield? In a perpetuity, if debt is perpetual and risk-free rate assumption? Often we use the cost of debt if tax shield risk matches debt risk. But here debt is perpetual and risk is same as debt, so discount at cost of debt (8%). PV(tax shield) = $700 / 0.08 = $8,750. So V_L = $130,000 + $8,750 = $138,750. --- ### Step 3: Approach 2: FCF to firm (WACC method) FCF = EBIT*(1-T) + Tax shield from interest? No, FCF to firm is EBIT*(1-T) because tax shield is already incorporated in the tax calculation? Actually standard formula: FCF = EBIT*(1-T) + Depreciation - CapEx - ΔNWC. Here no depreciation, CapEx=0, ΔNWC=0, so FCF = EBIT*(1-T) = $13,000. But if we use WACC, we need levered beta etc. Not straightforward without more info. So APV seems more direct. --- ### Step 4: Check given data We have debt value D = $25,000. Is the debt value given as market value? It says "the firm has debt with a market value of $25,000." So D is $25,000. If D is $25,000, then E = V_L - D. From APV we got V_L = $138,750, so E = $113,750. But is that consistent? Let's check the equity cash flows: Net Income = $11,700 per year to equity. Cost of equity should be r_e = r_0 + (D/E)*(r_0 - r_d)*(1-T). But we don't know r_e yet. Alternatively, if the firm is levered, the equity value should be E = Net Income / r_e. But we don't know r_e. So maybe we need to find r_e first. --- ### Step 5: Use M&M with taxes M&M Proposition I with taxes: V_L = V_U + T_C * D. Here T_C = 35%, D = $25,000. So V_L = $130,000 + 0.35*$25,000 = $130,000 + $8,750 = $138,750. This matches APV above. So the levered value is $138,750. --- ### Step 6: Check consistency with given debt value Debt value is given as $25,000. In M&M, the debt value is given, so D is $25,000. V_L = $138,750, so E = $113,750. Equity cash flow = $11,700. So cost of equity r_e = $11,700 / $113,750 ≈ 10.29%. Unlevered cost of capital is 10%, so it's consistent because levered equity has slightly higher cost due to leverage. --- Therefore, the firm's levered value is $138,750. --- **Final answer:** latex \boxed{138750}

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