Thank you. Financial leverage effects The Neal Company wants to estimate next ye

Question

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Financial leverage effects The Neal Company wants to estimate next year's return on equity (ROE) under different leverage ratios. Neal's total capital is $13 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federal-plus-state tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.8 million with a 0.2 probability, $2.2 million with a 0.5 probability, and $800,000 with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debt-to-capital ratios. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations. Debt/Capital ratio is 0. ROE = CV= Debt/Capital ratio is 10%, interest rate is 9%. CV Debt/Capital ratio is 50%, interest rate is 11%. Debt/Capital ratio is 60%, interest rate is 14%. ROE = CV=

Explanation / Answer

Debt/Capital ratio = 0: % Debt 0 0% Equity 13000000 100% Total capital 13000000 State 1 State 2 State 3 Probability 0.2 0.5 0.3 EBIT 4800000 2200000 800000 Interest 0 0 0 EBT 4800000 2200000 800000 Tax at 40% 1920000 880000 320000 NI 2880000 1320000 480000 ROE = NI/Equity 0.2215 0.1015 0.0369 ROE*p 0.0443 0.0508 0.0111 0.1062 Expected ROE 0.1062 = 10.62% Answer d = ROE - E[ROE] 0.1153 -0.0047 -0.0693 d^2 0.0133 0.0000 0.0048 p*d^2 0.0027 0.0000 0.0014 0.0041 SD = 0.0041^0.5 = 6.41% Answer COV = 6.40/10.62 = 0.60 Answer Debt/Capital ratio = 10%: % Debt 1300000 10% Equity 11700000 90% Total capital 13000000 State 1 State 2 State 3 Probability 0.2 0.5 0.3 EBIT 4800000 2200000 800000 Interest [9%] 117000 117000 117000 EBT 4683000 2083000 683000 Tax at 40% 1873200 833200 273200 NI 2809800 1249800 409800 ROE = NI/Equity 0.2402 0.1068 0.0350 ROE*p 0.0480 0.0534 0.0105 0.1119 Expected ROE 0.1119 = 11.19% Answer d = ROE - E[ROE] 0.1283 -0.0051 -0.0769 d^2 0.0164 0.0000 0.0059 p*d^2 0.0033 0.0000 0.0018 0.0051 SD = 0.0051^0.5 = 7.12% Answer COV = 7.12/11.19 = 0.64 Answer Debt/Capital ratio = 50%: % Debt 6500000 50% Equity 6500000 50% Total capital 13000000 State 1 State 2 State 3 Probability 0.2 0.5 0.3 EBIT 4800000 2200000 800000 Interest [11%] 715000 715000 715000 EBT 4085000 1485000 85000 ` Tax at 40% 1634000 594000 34000 NI 2451000 891000 51000 ROE = NI/Equity 0.3771 0.1371 0.0078 ROE*p 0.0754 0.0685 0.0024 0.1463 Expected ROE 0.1463 = 14.63% Answer d = ROE - E[ROE] 0.2308 -0.0092 -0.1385 d^2 0.0533 0.0001 0.0192 p*d^2 0.0107 0.0000 0.0058 0.0164 SD = 0.0164^0.5 = 12.82% Answer COV = 12.82/14.63 = 0.88 Answer ` Debt/Capital ratio = 60%: % Debt 7800000 60% Equity 5200000 40% Total capital 13000000 State 1 State 2 State 3 Probability 0.2 0.5 0.3 EBIT 4800000 2200000 800000 Interest [14%] 1092000 1092000 1092000 EBT 3708000 1108000 -292000 ` Tax at 40% 1483200 443200 -116800 NI 2224800 664800 -175200 ROE = NI/Equity 0.4278 0.1278 -0.0337 ROE*p 0.0856 0.0639 -0.0101 0.1394 Expected ROE 0.1394 = 13.94% Answer d = ROE - E[ROE] 0.2884 -0.0116 -0.1731 d^2 0.0832 0.0001 0.0300 p*d^2 0.0166 0.0001 0.0090 0.0257 SD = 0.0257^0.5 = 16.03% Answer COV = 16.03/13.94 = 1.15 Answer `

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