Question

FINANCIAL LEVERAGE EFFECTS 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: $4.6 million with a 0.2 probability, $1.5 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

Debt/Capital ratio is 0

The value of ROE, standard deviation and and coefficient of variation is arrived as follows:

State	Probability of State (A)	EBIT	Interest	(EBIT-Interest)*(1-Tax Rate)	Equity (16,000,000 - 0%*16,000,000)	ROE (B)	A*B	Variance
1	0.2	4,600,000	0	2,760,000	16,000,000	17.25%	3.45%	0.00213
2	0.5	1,500,000	0	900,000	16,000,000	5.63%	2.81%	0.00009
3	0.3	600,000	0	360,000	16,000,000	2.25%	0.68%	0.00066
						RÔE	6.94%
							Variance	0.00287
							Standard Deviation (σ)	0.054
							Coefficient of Variation (σ/RÔE)	0.77

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Tabular Representation as Required in Question

RÔE =	6.94%
σ =	5.36%
CV =	0.77

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Debt/Capital ratio is 10%, interest rate is 9%

The value of ROE, standard deviation and and coefficient of variation is calculated as follows:

State	Probability of State (C)	EBIT	Interest (16,000,000*10%*9%)	(EBIT-Interest)*(1-Tax Rate)	Equity (16,000,000 - 10%*16,000,000)	ROE (D))	C*D	Variance
1	0.2	4,600,000	144,000	2,673,600	14,400,000	18.57%	3.71%	0.00263
2	0.5	1,500,000	144,000	813,600	14,400,000	5.65%	2.83%	0.00011
3	0.3	600,000	144,000	273,600	14,400,000	1.90%	0.57%	0.00081
						RÔE	7.11%
							Variance	0.00355
							Standard Deviation (σ)	0.060
							Coefficient of Variation (σ/RÔE)	0.84

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Tabular Representation as Required in Question

RÔE =	7.11%
σ =	5.95%
CV =	0.84

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Debt/Capital ratio is 50%, interest rate is 11%

The value of ROE, standard deviation and and coefficient of variation is arrived as below:

State	Probability of State (E)	EBIT	Interest (16,000,000*50%*11%)	(EBIT-Interest)*(1-Tax Rate)	Equity (16,000,000 - 50%*16,000,000)	ROE (F)	E*F	Variance
1	0.2	4,600,000	880,000	2,232,000	8,000,000	27.90%	5.58%	0.00851
2	0.5	1,500,000	880,000	372,000	8,000,000	4.65%	2.33%	0.00034
3	0.3	600,000	880,000	-168,000	8,000,000	-2.10%	-0.63%	0.00264
						RÔE	7.28%
							Variance	0.01149
							Standard Deviation (σ)	0.107
							Coefficient of Variation (σ/RÔE)	1.47

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Tabular Representation as Required in Question

RÔE =	7.28%
σ =	10.72%
CV =	1.47

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Debt/Capital ratio is 60%, interest rate is 14%

The value of ROE, standard deviation and and coefficient of variation is determined as follows:

State	Probability of State (G)	EBIT	Interest (16,000,000*60%*14%)	(EBIT-Interest)*(1-Tax Rate)	Equity (16,000,000 - 60%*16,000,000)	ROE (H)	G*H	Variance
1	0.2	4,600,000	1,344,000	19,53,600	6,400,000	30.53%	6.11%	0.01329
2	0.5	1,500,000	1,344,000	93,600	6,400,000	1.46%	0.73%	0.00054
3	0.3	600,000	1,344,000	-446,400	6,400,000	-6.98%	-2.09%	0.00412
						RÔE	4.74%
							Variance	0.01795
							Standard Deviation (σ)	0.134
							Coefficient of Variation (σ/RÔE)	2.82

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Tabular Representation as Required in Question

RÔE =	4.74%
σ =	13.40%
CV =	2.82

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Notes for all the Parts of Questions

1)

The formula for ROE and RÔE is given as below:

ROE = (EBIT-Interest)*(1-Tax Rate)/Equity

RÔE = ROE under State 1 + ROE under State 2 + ROE under State 3

2)

The formula for variance and standard deviation is provided as follows:

Variance = Probability of State 1*(ROE under State 1 - RÔE)^2 + Probability of State 2*(ROE under State 2 - RÔE)^2 + Probability of State 3*(ROE under State 3 - RÔE)^3

Standard Deviation = (Variance)^(1/2)