Solutions to Exercises Session 2 (Capital Structure) 14-1QBE = [pic] QBE = [pic] QBE = 500,000 units.

14-4From the Hamada equation, b = bU[1 + (1 – T)(D/E)], we can calculate bU as bU = b/[1 + (1 – T)(D/E)]. bU = 1. 2/[1 + (1 – 0. 4)($2,000,000/$8,000,000)] bU = 1. 2/[1 + 0. 15] bU = 1. 0435.

14-8Facts as given: Current capital structure: 25% debt, 75% equity; rRF = 5%; rM – rRF = 6%; T = 40%; rs = 14%. Step 1:Determine the firm’s current beta. rs= rRF + (rM – rRF)b 14%= 5% + (6%)b 9%= 6%b 1. 5= b. Step 2:Determine the firm’s unlevered beta, bU. bU= bL/[1 + (1 – T)(D/E)] 1. 5/[1 + (1 – 0.

4)(0. 25/0. 75)] = 1. 5/1. 20 = 1. 25. Step 3:Determine the firm’s beta under the new capital structure.

bL= bU[1 + (1 – T)(D/E)] = 1. 25[1 + (1 – 0. 4)(0. 5/0. 5)] = 1. 25(1. 6) = 2.

Step 4:Determine the firm’s new cost of equity under the changed capital structure. rs= rRF + (rM – rRF)b = 5% + (6%)2 = 17%. 14-9a. a. If net income = $1,000,000 and dividend payout ratio = 40%, then the total amount of dividend paid in Year 0 was 40% x $1,000,000 = $400,000. Therefore, the current dividend per share, D0, = $400,000/200,000 shares = $2. 0.

D1 = $2. 00(1. 05) = $2. 10. Therefore, P0 = D1/(rs – g) = $2. 10/(0. 134 – 0.

05) = $25. 00. b. Step 1:Calculate EBIT before the recapitalization: The firm is 100% equity financed, so there is no interest expense. (EBIT = EBT NI = EBT – Taxes = EBT – EBT(T) = EBT (1-T) ? EBIT = EBT = NI/ (1-T) = $1,000,000/(1 – T) = $1,000,000/0. 6 = $1,666,667. Step 2:Calculate net income after the recapitalization: EBT = EBIT – Interest expense = $1,666,667 – 11%($1,000,000) $1,666,667 - $110,000 = $1,566,667 NI = EBT (1–T) = $1,566,667(.

) = $934,000 Step 3:Calculate the number of shares outstanding after the recapitalization: The company takes out a $1,000,000 to repurchase stock currently prices at $25. Number of shares after recapitalization: 200,000 – ($1,000,000/$25) = 160,000 shares. Step 4:Calculate D1 after the recapitalization: Given the 40% payout ratio: D0 = 40%($934,000/160,000) = $2. 335. D1 = $2. 335(1. 05) = $2.

45175. Step 5:Calculate P0 after the recapitalization: P0 = D1/(rs – g) = $2. 45175/(0. 145 – 0. 05) = $25. 8079 ( $25. 81.

14-4From the Hamada equation, b = bU[1 + (1 – T)(D/E)], we can calculate bU as bU = b/[1 + (1 – T)(D/E)]. bU = 1. 2/[1 + (1 – 0. 4)($2,000,000/$8,000,000)] bU = 1. 2/[1 + 0. 15] bU = 1. 0435.

14-8Facts as given: Current capital structure: 25% debt, 75% equity; rRF = 5%; rM – rRF = 6%; T = 40%; rs = 14%. Step 1:Determine the firm’s current beta. rs= rRF + (rM – rRF)b 14%= 5% + (6%)b 9%= 6%b 1. 5= b. Step 2:Determine the firm’s unlevered beta, bU. bU= bL/[1 + (1 – T)(D/E)] 1. 5/[1 + (1 – 0.

4)(0. 25/0. 75)] = 1. 5/1. 20 = 1. 25. Step 3:Determine the firm’s beta under the new capital structure.

bL= bU[1 + (1 – T)(D/E)] = 1. 25[1 + (1 – 0. 4)(0. 5/0. 5)] = 1. 25(1. 6) = 2.

Step 4:Determine the firm’s new cost of equity under the changed capital structure. rs= rRF + (rM – rRF)b = 5% + (6%)2 = 17%. 14-9a. a. If net income = $1,000,000 and dividend payout ratio = 40%, then the total amount of dividend paid in Year 0 was 40% x $1,000,000 = $400,000. Therefore, the current dividend per share, D0, = $400,000/200,000 shares = $2. 0.

D1 = $2. 00(1. 05) = $2. 10. Therefore, P0 = D1/(rs – g) = $2. 10/(0. 134 – 0.

05) = $25. 00. b. Step 1:Calculate EBIT before the recapitalization: The firm is 100% equity financed, so there is no interest expense. (EBIT = EBT NI = EBT – Taxes = EBT – EBT(T) = EBT (1-T) ? EBIT = EBT = NI/ (1-T) = $1,000,000/(1 – T) = $1,000,000/0. 6 = $1,666,667. Step 2:Calculate net income after the recapitalization: EBT = EBIT – Interest expense = $1,666,667 – 11%($1,000,000) $1,666,667 - $110,000 = $1,566,667 NI = EBT (1–T) = $1,566,667(.

) = $934,000 Step 3:Calculate the number of shares outstanding after the recapitalization: The company takes out a $1,000,000 to repurchase stock currently prices at $25. Number of shares after recapitalization: 200,000 – ($1,000,000/$25) = 160,000 shares. Step 4:Calculate D1 after the recapitalization: Given the 40% payout ratio: D0 = 40%($934,000/160,000) = $2. 335. D1 = $2. 335(1. 05) = $2.

45175. Step 5:Calculate P0 after the recapitalization: P0 = D1/(rs – g) = $2. 45175/(0. 145 – 0. 05) = $25. 8079 ( $25. 81.