Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $14 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: $4.7 million with a 0.2 probability, $1.7 million with a 0.5 probability, and $0.6 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

Part a) Debt/captial ratio is 0

Probability	EBIT	EAT = EBIT*(1-tax)	Expected EAT (EAT* Probability)	(EAT-ΣExpected EAT)	(EAT-ΣExpected EAT)^2	[(EAT-ΣExpected EAT)^2]* Probability
0.2	4.7	4.7*(1-0.4) = 2.82	0.564	1.638	2.683044	0.5366088
0.5	1.7	1.7*(1-0.4) = 1.02	0.51	-0.162	0.026244	0.013122
0.3	0.6	0.8*(1-0.4) = 0.36	0.108	-0.822	0.675684	0.2027052
			1.182			0.752436

Mean = ΣExpected EAT = 1.182

ROE = ΣExpected EAT/total capital = 1.182million/14million = 8.44%

Standard deviation = ΣProbability*[(EAT-ΣExpected EAT)^2] = 75.24%

Coefficient of variance = Standard deviation/Mean = 0.752436/1.182 = 0.6366

Part b) Debt/Capital ratio is 10%, interest rate is 9%

Debt = 10% on capital = 10%*14 million = 1.4 million

Interest (I) = 1.4million*9% = 0.126million

Equity = Capital-debbt = 14million-1.4million = 12.6million

Possibility	EBIT	EBT = (EBIT-I)	EAT = EBT*(1-tax)	Expected EAT (EAT* Probability)	(EAT-ΣExpected EAT)	(EAT-ΣExpected EAT)^2	[(EAT-ΣExpected EAT)^2]* Probability
0.2	4.7	4.574	2.7444	0.54888	1.638	2.683044	0.5366088
0.5	1.7	1.574	0.9444	0.4722	-0.162	0.026244	0.013122
0.3	0.6	0.474	0.2844	0.08532	-0.822	0.675684	0.2027052
				1.1064			0.752436

Mean = ΣExpected EAT = 1.1064

ROE = ΣExpected EAT/equity = 1.1064million/12.6million = 8.78%

Standard deviation = ΣProbability*[(EAT-ΣExpected EAT)^2] = 75.24%

Coefficient of variance = Standard deviation/Mean = 0.752436/1.1064 = 0.68

Part c) Debt/Capital ratio is 50%, interest rate is 11%

Debt = 50% on capital = 50%*14 million = 7 million

Interest (I) = 7million*11% = 0.77million

Equity = Capital-debbt = 14million-7million = 7million

Possibility	EBIT	EBT = (EBIT-I)	EAT = EBT*(1-tax)	Expected EAT (EAT* Probability)	(EAT-ΣExpected EAT)	(EAT-ΣExpected EAT)^2	[(EAT-ΣExpected EAT)^2]*Probability
0.2	4.7	3.93	2.358	0.47160	1.638	2.683044	0.5366088
0.5	1.7	0.93	0.558	0.279	-0.162	0.026244	0.013122
0.3	0.6	-0.17	-0.102	-0.0306	-0.822	0.675684	0.2027052
				0.72			0.752436

Mean = ΣExpected EAT = 0.72

ROE = ΣExpected EAT/equity = 0.72million/7million = 10.29%

Standard deviation = ΣProbability*[(EAT-ΣExpected EAT)^2] = 75.24%

Coefficient of variance = Standard deviation/Mean = 0.752436/0.72 = 1.0451

Part d) Debt/Capital ratio is 60%, interest rate is 14%

Debt = 60% on capital = 60%*14 million = 8.4 million

Interest (I) = 8.4million*14% = 1.176million

Equity = Capital-debbt = 14million-8.4million = 5.6million

Possibility	EBIT	EBT = (EBIT-I)	EAT = EBT*(1-tax)	Expected EAT (EAT* Probability)	(EAT-ΣExpected EAT)	(EAT-ΣExpected EAT)^2	[(EAT-ΣExpected EAT)^2]*Probability
0.2	4.7	3.524	2.1144	0.42288	1.638	2.683044	0.5366088
0.5	1.7	0.524	0.3144	0.1572	-0.162	0.026244	0.013122
0.3	0.6	-0.576	-0.3456	-0.10368	-0.822	0.675684	0.2027052
				0.4764			0.752436

Mean = ΣExpected EAT = 0.4764

ROE = ΣExpected EAT/equity = 0.4764million/5.6million = 8.51%

Standard deviation = ΣProbability*[(EAT-ΣExpected EAT)^2] = 75.24%

Coefficient of variance = Standard deviation/Mean = 0.752436/0.4764 = 1.5794