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: $5.8 million with a 0.2 probability, $3.4 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: [$ in millions]
Debt	$                     -	$                    -	$                 -
Equity	$              14.00	$             14.00	$          14.00
Total capital	$              14.00	$             14.00	$          14.00
EBIT	$                5.80	$               3.40	$             0.60
Probability	0.2	0.5	0.3
Interest	$                     -	$                    -	$                 -
EBT	$                5.80	$               3.40	$             0.60
Tax at 40%	$                2.32	$               1.36	$             0.24
NI	$                3.48	$               2.04	$             0.36
ROE [NI/Equity] %	24.86	14.57	2.57
Expected ROE %	13.03
Deviations from mean [Expected ROE]	11.83	1.54	-10.46
Deviations^2	139.92	2.38	109.35
Deviations^2*p	27.98	1.19	32.81
Sum of deviations^2*p	61.98
SD = Sum of deviations^0.5 =	7.87
COV = SD/Expected ROE	0.60
Debt/Capital Ratio is 10%: [$ in millions]
Debt	$                1.40	$               1.40	$             1.40
Equity	$              12.60	$             12.60	$          12.60
Total capital	$              14.00	$             14.00	$          14.00
EBIT	$                5.80	$               3.40	$             0.60
Probability	0.2	0.5	0.3
Interest at 9%	$                0.13	$               0.13	$             0.13
EBT	$                5.67	$               3.27	$             0.47
Tax at 40%	$                2.27	$               1.31	$             0.19
NI	$                3.40	$               1.96	$             0.28
ROE [NI/Equity] %	27.02	15.59	2.26
Expected ROE %	13.88
Deviations from mean [Expected ROE]	13.14	1.71	-11.62
Deviations^2	172.73	2.94	135.00
Deviations^2*p	34.55	1.47	40.50
Sum of deviations^2*p	76.52
SD = Sum of deviations^0.5 =	8.75
COV = SD/Expected ROE	0.63
Debt/Capital Ratio is 50%: [$ in millions]
Debt	$                7.00	$               7.00	$             7.00
Equity	$                7.00	$               7.00	$             7.00
Total capital	$              14.00	$             14.00	$          14.00
EBIT	$                5.80	$               3.40	$             0.60
Probability	0.2	0.5	0.3
Interest at 11%	$                0.77	$               0.77	$             0.77
EBT	$                5.03	$               2.63	$           -0.17
Tax at 40%	$                2.01	$               1.05	$           -0.07
NI	$                3.02	$               1.58	$           -0.10
ROE [NI/Equity] %	43.11	22.54	-1.46
Expected ROE %	19.46
Deviations from mean [Expected ROE]	23.66	3.09	-20.91
Deviations^2	559.66	9.52	437.41
Deviations^2*p	111.93	4.76	131.22
Sum of deviations^2*p	247.92
SD = Sum of deviations^0.5 =	15.75
COV = SD/Expected ROE	0.81
Debt/Capital Ratio is 60%: [$ in millions]
Debt	$                8.40	$               8.40	$             8.40
Equity	$                5.60	$               5.60	$             5.60
Total capital	$              14.00	$             14.00	$          14.00
EBIT	$                5.80	$               3.40	$             0.60
Probability	0.2	0.5	0.3
Interest at 14%	$                1.18	$               1.18	$             1.18
EBT	$                4.62	$               2.22	$           -0.58
Tax at 40%	$                1.85	$               0.89	$           -0.23
NI	$                2.77	$               1.33	$           -0.35
ROE [NI/Equity] %	49.54	23.83	-6.17
Expected ROE %	19.97
Deviations from mean [Expected ROE]	29.57	3.86	-26.14
Deviations^2	874.47	14.88	683.45
Deviations^2*p	174.89	7.44	205.03
Sum of deviations^2*p	387.37
SD = Sum of deviations^0.5 =	19.68
COV = SD/Expected ROE	0.99