Question

This is my 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: $5.7 million with a 0.2 probability, $3.1 million with a 0.5 probability, and $0.9 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 =

This is same question and its answer which could be as reference：

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $20 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: $4.1 million with a 0.2 probability, $1.9 million with a 0.5 probability, and $0.5 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. ROE = = 5.8 3.7 X% % CV = 0.85 X Debt/Capital ratio is 10%, interest rate is 9%. RÔE - 0 CV- 5.8 4.2 0.71 % % Debt/Capital ratio is 50%, Interest rate is 11%. ROE - O CV - 4.9 X% 7.5 % 1.52 Debt/Capital ratio is 60%, Interest rate is 14%. RÕE = 1.8 % CV = 5.43 x

Thanks for your help！

Answer 1

Please see the table below. Yellow colored cells contain your answers. I have kept them to two places of decimal, as your question wants it. You can round them off as per your requirement.

Sub part have been solved in the same sequence as they appear in the question.

Debt to capital ratio is 0%: Debt = 0; Equity = $ 16,000,000;
State	Ps	EBIT	(EBIT - rdD)(1 - T)	ROEs	Ps(ROE)	Ps(ROEs - ROE)^2
1	0.2	5,700,000	3,420,000	0.21	0.04	0.00211
2	0.5	3,100,000	1,860,000	0.12	0.06	0.00001
3	0.3	900,000	540,000	0.03	0.01	0.00179
				Average	0.11
					Variance	0.00392
					Standard deviation	0.063
ROE	11.10%
σ2	0.00392
σ	6.26%
CV = σ / ROE	0.56
Debt to capital ratio is 10%: Debt = 1,600,000; Equity = $ 14,400,000; interest rate = 9%
State	Ps	EBIT	(EBIT - rdD)(1 - T)	ROEs	Ps(ROE)	Ps(ROEs - ROE)^2
1	0.2	5,700,000	3,333,600	0.23	0.05	0.00261
2	0.5	3,100,000	1,773,600	0.12	0.06	0.00002
3	0.3	900,000	453,600	0.03	0.01	0.00221
				Average	0.12
					Variance	0.00483
					Standard deviation	0.070
ROE	11.73%
σ2	0.00483
σ	6.95%
CV = σ / ROE	0.59
Debt to capital ratio is 50%: Debt = 8,000,000; Equity = $ 8,000,000; interest rate = 11%
State	Ps	EBIT	(EBIT - rdD)(1 - T)	ROEs	Ps(ROE)	Ps(ROEs - ROE)^2
1	0.2	5,700,000	2,892,000	0.36	0.07	0.00845
2	0.5	3,100,000	1,332,000	0.17	0.08	0.00006
3	0.3	900,000	12,000	0.00	0.00	0.00716
				Average	0.16
					Variance	0.01566
					Standard deviation	0.125
ROE	15.60%
σ2	0.01566
σ	12.51%
CV = σ / ROE	0.80
Debt to capital ratio is 60%: Debt = 9,600,000; Equity = $ 6,400,000; interest rate = 14%
State	Ps	EBIT	(EBIT - rdD)(1 - T)	ROEs	Ps(ROE)	Ps(ROEs - ROE)^2
1	0.2	5,700,000	2,613,600	0.41	0.08	0.01320
2	0.5	3,100,000	1,053,600	0.16	0.08	0.00009
3	0.3	900,000	(266,400)	(0.04)	(0.01)	0.01119
				Average	0.15
					Variance	0.02447
					Standard deviation	0.156
ROE	15.15%
σ2	0.02447
σ	15.64%
CV = σ / ROE	1.03