Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $16 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: $4.5 million with a 0.2 probability, $2.2 million with a 0.5 probability, and $0.4 million 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. RÔE = % σ = % CV = Debt/Capital ratio is 10%, interest rate is 9%. RÔE = % σ = % CV = Debt/Capital ratio is 50%, interest rate is 11%. RÔE = % σ = % CV = Debt/Capital ratio is 60%, interest rate is 14%. RÔE = % σ = % CV =

Answer 1

Ans

Debt/Capital ratio is 0
Probability	EBIT	Equity	Debt	Interest	Net income= (EBIT-interest)*(1-tax)	ROE (Net Income / Equity)
0.2	$          4,500,000	$              16,000,000	$ 0	$ 0	$2,700,000 ($4,500,000-$0)*(1-0.40)	16.88%
0.5	$          2,200,000	$              16,000,000	$ 0	$ 0	$1,320,000($2,200,000-$0)*(1-0.40)	8.25%
0.3	$            400,000	$              16,000,000	$ 0	$ 0	$240,000 ($400,000-$0)*(1-0.40)	1.50%

Expected ROE = 0.2*16.88% + 0.5*8.25% +0.3*1.50%

Expected ROE = 3.375% + 4.125% + 0.45% = 7.95%

Standard Deviation = Square root (0.2*(16.88%-7.95%)^2 + 0.5*(8.25%-7.95%)^2 +0.3*(1.50%-7.95%)^2)

Standard Deviation = 5.33%

CV = 5.33% / 7.95%

CV = 0.67

Debt/Capital ratio is 10%, interest rate is 9%
Probability	EBIT	Equity	Debt	Interest	Net income= (EBIT-interest)*(1-tax)	ROE (Net Income / Equity)
0.2	$          4,500,000	$14,400,000	$1,600,000	$144,000	$2,613,600 ($4,500,000-$144,000)*(1-0.40)	18.15%
0.5	$          2,200,000	$14,400,000	$1,600,000	$144,000	$1,233,600($2,200,000-$144,000)*(1-0.40)	8.57%
0.3	$            400,000	$14,400,000	$1,600,000	$144,000	$153,600 ($400,000-$144,000)*(1-0.40)	1.07%

Expected ROE = 0.2*18.15% + 0.5*8.57% +0.3*1.07%

Expected ROE = 3.63% + 4.28% + 0.32% = 8.23%

Standard Deviation = Square root (0.2*(18.15%-8.23%)^2 + 0.5*(8.57%-8.23%)^2 +0.3*(1.07%-8.23%)^2)

Standard Deviation = 5.93%

CV = 5.93% / 8.23%

CV = 0.72

Debt/Capital ratio is 50%, interest rate is 11%
Probability	EBIT	Equity	Debt	Interest	Net income= (EBIT-interest)*(1-tax)	ROE (Net Income / Equity)
0.2	$          4,500,000	$8,000,000	$8,000,000	$ 880,000	$2,172,000 ($4,500,000-$880,000)*(1-0.40)	27.15%
0.5	$          2,200,000	$8,000,000	$8,000,000	$ 880,000	$792,00($2,200,000-$$880,000)*(1-0.40)	9.90%
0.3	$            400,000	$8,000,000	$8,000,000	$ 880,000	- $288,000 ($400,000-$$880,000)*(1-0.40)	-3.60%

Expected ROE = 0.2*27.15% + 0.5*9.90% +0.3*(-3.6)%

Expected ROE = 5.43% + 4.95% - 1.08% = 9.3%

Standard Deviation = Square root (0.2*(27.15%-9.3%)^2 + 0.5*(9.90%-9.30%)^2 +0.3*(-3.6%-9.3%)^2)

Standard Deviation = 10.67%

CV = 10.67% / 9.3%

CV = 1.15

Debt/Capital ratio is 60%, interest rate is 14%
Probability	EBIT	Equity	Debt	Interest	Net income= (EBIT-interest)*(1-tax)	ROE (Net Income / Equity)
0.2	$          4,500,000	$6,400,000	$9,600,000	$1,344,000	$1,893,600 ($4,500,000-$1,344,000)*(1-0.40)	29.59%
0.5	$          2,200,000	$6,400,000	$9,600,000	$1,344,000	$513,600($2,200,000-$1,344,000)*(1-0.40)	8.03%
0.3	$            400,000	$6,400,000	$9,600,000	$1,344,000	- $566,400 ($400,000-$1,344,000)*(1-0.40)	-8.85%

Expected ROE = 0.2*29.59% + 0.5*8.03% +0.3*(-8.85)%

Expected ROE = 5.9175% + 4.0125% - 2.655% = 7.28%

Standard Deviation = Square root (0.2*(29.59%-7.28%)^2 + 0.5*(8.03%-7.28%)^2 +0.3*(-8.85%-7.28%)^2)

Standard Deviation = 13.34%

CV = 13.34% / 7.28%

CV = 1.83