The Neal Company wants to estimate next year\'s return on equity (ROE) under dif

Question

The Neal Company wants to estimate next year's return on equity (ROE) under different leverage ratios. Neal's total capital is $11 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: $4.3 million with a 0.2 probability $1.7 million with a 0.5 probability, and $500,000 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% ROE = CV Debt/Capital ratio is 50%, interest rate is 11%. ROE = Debt/Capital ratio is 60%, interest rate is 14%. ROE = = CV

Explanation / Answer

D/C = 0

At p = 0.2

ROE = ((1-40%)*4.3 / 11) = 23.45%

At p = 0.5

ROE = ((1-40%)*1.7 / 11) = 9.27%

At p = 0.3

ROE = ((1-40%)*0.5 / 11) = 2.73%

Expected ROE = 0.2*23.45% + 0.5*9.27% + 0.3*2.73% = 10.14%

SD = SQRT(0.2*(23.45%-10.14%)2 + 0.5*(9.27%-10.14%)2 + 0.3*(2.73%-10.14%)2 ) = 7.23%

CV = 7.23% / 10.14% = 0.71

D/C = 10%

D = 10%*11 = 1.1, E = 11-1.1 = 9.9

Interest = 9%*1.1 = 0.099

At p = 0.2

ROE = ((1-40%)*(4.3-0.099) / 9.9) = 25.46%

At p = 0.5

ROE = ((1-40%)*(1.7-0.099) / 9.9) = 9.70%

At p = 0.3

ROE = ((1-40%)*(0.5-0.099) / 9.9) = 2.43%

Expected ROE = 0.2*25.46% + 0.5*9.7% + 0.3*2.43% = 10.67%

SD = SQRT(0.2*(25.46%-10.67%)2 + 0.5*(9.7%-10.67%)2  + 0.3*(2.43%-10.67%)2 ) = 8.04%

CV = 8.04% / 10.67% = 0.75

D/C = 50%

D = 50%*11 = 5.5, E = 11-5.5 = 5.5

Interest = 11%*5.5 = 0.605

At p = 0.2

ROE = ((1-40%)*(4.3-0.605) / 5.5) = 40.31%

At p = 0.5

ROE = ((1-40%)*(1.7-0.605) / 5.5) = 11.95%

At p = 0.3

ROE = ((1-40%)*(0.5-0.605) / 5.5) = -1.15%

Expected ROE = 0.2*40.31% + 0.5*11.95% + 0.3*-1.15% = 13.69%

SD = SQRT(0.2*(40.31%-13.69%)2 + 0.5*(11.95%-13.69%)2  + 0.3*(-1.15%-13.69%)2 ) = 14.47%

CV = 14.47% / 13.69% = 1.06

D/C = 60%

D = 60%*11 = 6.6, E = 11-6.6 = 4.4

Interest = 14%*4.4 = 0.616

At p = 0.2

ROE = ((1-40%)*(4.3-0.616) / 4.4) = 50.24%

At p = 0.5

ROE = ((1-40%)*(1.7-0.616) / 4.4) = 14.78%

At p = 0.3

ROE = ((1-40%)*(0.5-0.616) / 4.4) = -1.58%

Expected ROE = 0.2*50.24% + 0.5*14.78% + 0.3*-1.58%= 16.96%

SD = SQRT(0.2*(50.24%-16.96%)2 + 0.5*(14.78%-16.96%)2  + 0.3*(-1.58%-16.96%)2 ) = 18.08%

CV = 18.08% / 16.96% = 1.07

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