7. Problem 13.07 Problem 13-7 Financial leverage effects The Neal Company wants

Question

7. Problem 13.07 Problem 13-7 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 $12 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: $4.2 million with a 0.2 probability, $3.4 million with a 0.5 probability, and $900,000 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 o ROE = CV= Debt/Capital ratio is 10%, interest rate is 9%. ROE = CV= Debt/Capital ratio is 50%, interest rate is 11%. ROE = CV= Debt/Capital ratio is 60%, interest rate is 14%. ROE = CV=

Explanation / Answer

Debt/Capital ratio = 0: % Debt 0 0% Equity 12000000 100% Total capital 12000000 State 1 State 2 State 3 Probability 0.2 0.5 0.3 EBIT 4200000 3400000 900000 Interest 0 0 0 EBT 4200000 3400000 900000 Tax at 40% 1680000 1360000 360000 NI 2520000 2040000 540000 ROE = NI/Equity 0.2100 0.1700 0.0450 ROE*p 0.042 0.085 0.0135 0.1405 Expected ROE 14.05% Answer d = ROE - E[ROE] 0.0695 0.0295 -0.0955 d^2 0.0048 0.0009 0.0091 p*d^2 0.0010 0.0004 0.0027 0.0041 SD = 0.0041^0.5 = 6.40% Answer COV = 6.40/14.05 = 0.46 Answer Debt/Capital ratio = 10%: % Debt 1200000 10% Equity 10800000 90% Total capital 12000000 State 1 State 2 State 3 Probability 0.2 0.5 0.3 EBIT 4200000 3400000 900000 Interest [9%] 108000 108000 108000 EBT 4092000 3292000 792000 Tax at 40% 1636800 1316800 316800 NI 2455200 1975200 475200 ROE = NI/Equity 0.2273 0.1829 0.0440 ROE*p 0.0455 0.0914 0.0132 0.1501 Expected ROE 15.01% Answer d = ROE - E[ROE] 0.0772 0.0328 -0.1061 d^2 0.0060 0.0011 0.0113 p*d^2 0.0012 0.0005 0.0034 0.0051 SD = 0.0051^0.5 = 7.15% Answer COV = 7.15/15.01 = 0.48 Answer Debt/Capital ratio = 50%: % Debt 6000000 50% Equity 6000000 50% Total capital 12000000 State 1 State 2 State 3 Probability 0.2 0.5 0.3 EBIT 4200000 3400000 900000 Interest [11%] 660000 660000 660000 EBT 3540000 2740000 240000 ` Tax at 40% 1416000 1096000 96000 NI 2124000 1644000 144000 ROE = NI/Equity 0.3540 0.2740 0.0240 ROE*p 0.0708 0.1370 0.0072 0.2150 Expected ROE 21.50% Answer d = ROE - E[ROE] 0.1390 0.0590 -0.1910 d^2 0.0193 0.0035 0.0365 p*d^2 0.0039 0.0017 0.0109 0.0165 SD = 0.0165^0.5 = 12.86% Answer COV = 12.86/21.50 = 0.60 Answer ` Debt/Capital ratio = 60%: % Debt 7200000 60% Equity 4800000 40% Total capital 12000000 State 1 State 2 State 3 Probability 0.2 0.5 0.3 EBIT 4200000 3400000 900000 Interest [14%] 1008000 1008000 1008000 EBT 3192000 2392000 -108000 ` Tax at 40% 1276800 956800 0 NI 1915200 1435200 -108000 ROE = NI/Equity 0.3990 0.2990 -0.0225 ROE*p 0.0798 0.1495 -0.0068 0.2226 Expected ROE 22.26% Answer d = ROE - E[ROE] 0.1764 0.0764 -0.2451 d^2 0.0311 0.0058 0.0601 p*d^2 0.0062 0.0029 0.0180 0.0272 SD = 0.0272^0.5 = 16.49% Answer COV = 16.49/22.26 = 0.74 Answer ` Note: Tax has not been calculated for EBIT of $900,000 under 60% Debt ratio as EBT is negative.

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