Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $19 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 25%. The CFO has estimated next year's EBIT for three possible states of the world: $5 million with a 0.2 probability, $3.2 million with a 0.5 probability, and $700,000 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.

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 = 0
EBIT	5.00	3.20	0.70
Interest	0.00	0.00	0.00
EBT	5.00	3.20	0.70
Tax@25%	1.25	0.80	0.18
PAT	3.75	2.40	0.53
Probability	0.20	0.50	0.30
Debt	0	0	0
Equity	19	19	19
Capital	19	19	19	Avg
ROE	19.74%	12.63%	2.76%	11.09%
				Variance
P*(ROE-Avg)^2	0.15%	0.01%	0.21%	0.37%
			Std dev	6.08%
			COV	54.80%
Debt/Capital = 10%, interest = 9%
EBIT	5.00	3.20	0.70
Interest	0.17	0.17	0.17
EBT	4.83	3.03	0.53
Tax@25%	1.21	0.76	0.13
PAT	3.62	2.27	0.40
Probability	0.20	0.50	0.30
Debt	1.9	1.9	1.9
Equity	17.1	17.1	17.1
Capital	19	19	19	Avg
ROE	21.18%	13.29%	2.32%	11.57%
				Variance
P*(ROE-Avg)^2	0.18%	0.01%	0.26%	0.46%
			Std dev	6.75%
			COV	58.35%
Debt/Capital = 50%, interest = 11%
EBIT	5.00	3.20	0.70
Interest	1.05	1.05	1.05
EBT	3.96	2.16	-0.35
Tax@25%	0.99	0.54	-0.09
PAT	2.97	1.62	-0.26
Probability	0.20	0.50	0.30
Debt	9.5	9.5	9.5
Equity	9.5	9.5	9.5
Capital	19	19	19	Avg
ROE	31.22%	17.01%	-2.72%	13.93%
				Variance
P*(ROE-Avg)^2	0.60%	0.05%	0.83%	1.48%
			Std dev	12.16%
			COV	87.24%
Debt/Capital = 60%, interest = 14%
EBIT	5.00	3.20	0.70
Interest	1.60	1.60	1.60
EBT	3.40	1.60	-0.90
Tax@25%	0.85	0.40	-0.22
PAT	2.55	1.20	-0.67
Probability	0.20	0.50	0.30
Debt	11.4	11.4	11.4
Equity	7.6	7.6	7.6
Capital	19	19	19	Avg
ROE	33.59%	15.83%	-8.84%	11.98%
				Variance
P*(ROE-Avg)^2	0.93%	0.07%	1.30%	2.31%
			Std dev	15.20%
			COV	126.83%