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: $4.6 million with a 0.2 probability, $3.4 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.

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	$               16.00	$          16.00	$           16.00
Total capital	$               16.00	$          16.00	$           16.00
EBIT	$                 4.60	$            3.40	$             0.50
Probability	0.20	0.50	0.30
Interest	$                      -	$                 -	$                  -
EBT	$                 4.60	$            3.40	$             0.50
Tax at 40%	$                 1.84	$            1.36	$             0.20
NI	$                 2.76	$            2.04	$             0.30
ROE [NI/Equity] %	17.25	12.75	1.88
Expected ROE %	10.39
Deviations from mean [Expected ROE]	6.86	2.36	-8.51
Deviations^2	47.09	5.58	72.46
Deviations^2*p	9.42	2.79	21.74
Sum of deviations^2*p	33.95
SD = Sum of deviations^0.5 =	5.83
COV = SD/Expected ROE	0.56
Debt/Capital Ratio is 10%: [$ in millions]
Debt	$                 1.60	$            1.60	$             1.60
Equity	$               14.40	$          14.40	$           14.40
Total capital	$               16.00	$          16.00	$           16.00
EBIT	$                 4.60	$            3.40	$             0.50
Probability	0.20	0.50	0.30
Interest at 9%	$                 0.14	$            0.14	$             0.14
EBT	$                 4.46	$            3.26	$             0.36
Tax at 40%	$                 1.78	$            1.30	$             0.14
NI	$                 2.67	$            1.95	$             0.21
ROE [NI/Equity] %	18.57	13.57	1.48
Expected ROE %	10.94
Deviations from mean [Expected ROE]	7.63	2.63	-9.46
Deviations^2	58.14	6.89	89.46
Deviations^2*p	11.63	3.45	26.84
Sum of deviations^2*p	41.91
SD = Sum of deviations^0.5 =	6.47
COV = SD/Expected ROE	0.59
Debt/Capital Ratio is 50%: [$ in millions]
Debt	$                 8.00	$            8.00	$             8.00
Equity	$                 8.00	$            8.00	$             8.00
Total capital	$               16.00	$          16.00	$           16.00
EBIT	$                 4.60	$            3.40	$             0.50
Probability	0.2	0.5	0.3
Interest at 11%	$                 0.88	$            0.88	$             0.88
EBT	$                 3.72	$            2.52	$           -0.38
Tax at 40%	$                 1.49	$            1.01	$           -0.15
NI	$                 2.23	$            1.51	$           -0.23
ROE [NI/Equity] %	27.90	18.90	-2.85
Expected ROE %	14.18
Deviations from mean [Expected ROE]	13.73	4.73	-17.03
Deviations^2	188.38	22.33	289.85
Deviations^2*p	37.68	11.16	86.96
Sum of deviations^2*p	135.79
SD = Sum of deviations^0.5 =	11.65
COV = SD/Expected ROE	0.82
Debt/Capital Ratio is 60%: [$ in millions]
Debt	$                 9.60	$            9.60	$             9.60
Equity	$                 6.40	$            6.40	$             6.40
Total capital	$               16.00	$          16.00	$           16.00
EBIT	$                 4.60	$            3.40	$             0.50
Probability	0.2	0.5	0.3
Interest at 14%	$                 1.34	$            1.34	$             1.34
EBT	$                 3.26	$            2.06	$           -0.84
Tax at 40%	$                 1.30	$            0.82	$           -0.34
NI	$                 1.95	$            1.23	$           -0.51
ROE [NI/Equity] %	30.53	19.28	-7.91
Expected ROE %	13.37
Deviations from mean [Expected ROE]	17.16	5.91	-21.28
Deviations^2	294.34	34.88	452.89
Deviations^2*p	58.87	17.44	135.87
Sum of deviations^2*p	212.18
SD = Sum of deviations^0.5 =	14.57
COV = SD/Expected ROE	1.09