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 $17 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: $4.7 million with a 0.2 probability, $2.8 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	$          17.00	$          17.00	$           17.00
Total capital	$          17.00	$          17.00	$           17.00
EBIT	$             4.70	$            2.80	$             0.50
Probability	0.20	0.50	0.30
Interest	$                 -	$                 -	$                  -
EBT	$             4.70	$            2.80	$             0.50
Tax at 40%	$             1.88	$            1.12	$             0.20
NI	$             2.82	$            1.68	$             0.30
ROE [NI/Equity] %	16.59	9.88	1.76
Expected ROE %	8.79
Deviations from mean [Expected ROE]	7.80	1.09	-7.02
Deviations^2	60.84	1.20	49.33
Deviations^2*p	12.17	0.60	14.80
Sum of deviations^2*p	27.57
SD = [Sum of deviations^2*p]^0.5 =	5.25
COV = SD/Expected ROE	0.60
Debt/Capital Ratio is 10%: [$ in millions]
Debt	$             1.70	$            1.70	$             1.70
Equity	$          15.30	$          15.30	$           15.30
Total capital	$          17.00	$          17.00	$           17.00
EBIT	$             4.70	$            2.80	$             0.50
Probability	0.20	0.50	0.30
Interest at 9%	$             0.15	$            0.15	$             0.15
EBT	$             4.55	$            2.65	$             0.35
Tax at 40%	$             1.82	$            1.06	$             0.14
NI	$             2.73	$            1.59	$             0.21
ROE [NI/Equity] %	17.83	10.38	1.36
Expected ROE %	9.16
Deviations from mean [Expected ROE]	8.67	1.22	-7.80
Deviations^2	75.11	1.48	60.90
Deviations^2*p	15.02	0.74	18.27
Sum of deviations^2*p	34.03
SD = [Sum of deviations^2*p]^0.5 =	5.83
COV = SD/Expected ROE	0.64
Debt/Capital Ratio is 50%: [$ in millions]
Debt	$             8.50	$            8.50	$             8.50
Equity	$             8.50	$            8.50	$             8.50
Total capital	$          17.00	$          17.00	$           17.00
EBIT	$             4.70	$            2.80	$             0.50
Probability	0.2	0.5	0.3
Interest at 11%	$             0.94	$            0.94	$             0.94
EBT	$             3.77	$            1.87	$           -0.44
Tax at 40%	$             1.51	$            0.75	$           -0.17
NI	$             2.26	$            1.12	$           -0.26
ROE [NI/Equity] %	26.58	13.16	-3.07
Expected ROE %	10.98
Deviations from mean [Expected ROE]	15.60	2.19	-14.05
Deviations^2	243.36	4.79	197.32
Deviations^2*p	48.67	2.39	59.20
Sum of deviations^2*p	110.26
SD = [Sum of deviations^2*p]^0.5 =	10.50
COV = SD/Expected ROE	0.96
Debt/Capital Ratio is 60%: [$ in millions]
Debt	$          10.20	$          10.20	$           10.20
Equity	$             6.80	$            6.80	$             6.80
Total capital	$          17.00	$          17.00	$           17.00
EBIT	$             4.70	$            2.80	$             0.50
Probability	0.2	0.5	0.3
Interest at 14%	$             1.43	$            1.43	$             1.43
EBT	$             3.27	$            1.37	$           -0.93
Tax at 40%	$             1.31	$            0.55	$           -0.37
NI	$             1.96	$            0.82	$           -0.56
ROE [NI/Equity] %	28.87	12.11	-8.19
Expected ROE %	9.37
Deviations from mean [Expected ROE]	19.50	2.74	-17.56
Deviations^2	380.25	7.48	308.31
Deviations^2*p	76.05	3.74	92.49
Sum of deviations^2*p	172.28
SD = [Sum of deviations^2*p]^0.5 =	13.13
COV = SD/Expected ROE	1.40