Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $15 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: $5.2 million with a 0.2 probability, $2.4 million with a 0.5 probability, and $0.7 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	$              15.00	$             15.00	$          15.00
Total capital	$              15.00	$             15.00	$          15.00
EBIT	$                5.20	$               2.40	$             0.70
Probability	0.2	0.5	0.3
Interest	$                     -	$                    -	$                 -
EBT	$                5.20	$               2.40	$             0.70
Tax at 40%	$                2.08	$               0.96	$             0.28
NI	$                3.12	$               1.44	$             0.42
ROE [NI/Equity] %	20.80	9.60	2.80
Expected ROE %	9.80
Deviations from mean [Expected ROE]	11.00	-0.20	-7.00
Deviations^2	121.00	0.04	49.00
Deviations^2*p	24.20	0.02	14.70
Sum of deviations^2*p	38.92
SD = Sum of deviations^0.5 =	6.24
COV = SD/Expected ROE	0.64
Debt/Capital Ratio is 10%: [$ in millions]
Debt	$                1.50	$               1.50	$             1.50
Equity	$              13.50	$             13.50	$          13.50
Total capital	$              15.00	$             15.00	$          15.00
EBIT	$                5.20	$               2.40	$             0.70
Probability	0.2	0.5	0.3
Interest at 9%	$                0.14	$               0.14	$             0.14
EBT	$                5.07	$               2.27	$             0.57
Tax at 40%	$                2.03	$               0.91	$             0.23
NI	$                3.04	$               1.36	$             0.34
ROE [NI/Equity] %	22.51	10.07	2.51
Expected ROE %	10.29
Deviations from mean [Expected ROE]	12.22	-0.22	-7.78
Deviations^2	149.38	0.05	60.49
Deviations^2*p	29.88	0.02	18.15
Sum of deviations^2*p	48.05
SD = Sum of deviations^0.5 =	6.93
COV = SD/Expected ROE	0.67
Debt/Capital Ratio is 50%: [$ in millions]
Debt	$                7.50	$               7.50	$             7.50
Equity	$                7.50	$               7.50	$             7.50
Total capital	$              15.00	$             15.00	$          15.00
EBIT	$                5.20	$               2.40	$             0.70
Probability	0.2	0.5	0.3
Interest at 11%	$                0.83	$               0.83	$             0.83
EBT	$                4.38	$               1.58	$           -0.13
Tax at 40%	$                1.75	$               0.63	$           -0.05
NI	$                2.63	$               0.95	$           -0.08
ROE [NI/Equity] %	35.00	12.60	-1.00
Expected ROE %	13.00
Deviations from mean [Expected ROE]	22.00	-0.40	-14.00
Deviations^2	484.00	0.16	196.00
Deviations^2*p	96.80	0.08	58.80
Sum of deviations^2*p	155.68
SD = Sum of deviations^0.5 =	12.48
COV = SD/Expected ROE	0.96
Debt/Capital Ratio is 60%: [$ in millions]
Debt	$                9.00	$               9.00	$             9.00
Equity	$                6.00	$               6.00	$             6.00
Total capital	$              15.00	$             15.00	$          15.00
EBIT	$                5.20	$               2.40	$             0.70
Probability	0.2	0.5	0.3
Interest at 14%	$                1.26	$               1.26	$             1.26
EBT	$                3.94	$               1.14	$           -0.56
Tax at 40%	$                1.58	$               0.46	$           -0.22
NI	$                2.36	$               0.68	$           -0.34
ROE [NI/Equity] %	39.40	11.40	-5.60
Expected ROE %	11.90
Deviations from mean [Expected ROE]	27.50	-0.50	-17.50
Deviations^2	756.25	0.25	306.25
Deviations^2*p	151.25	0.13	91.88
Sum of deviations^2*p	243.25
SD = Sum of deviations^0.5 =	15.60
COV = SD/Expected ROE	1.31