Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $11 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: $4.1 million with a 0.2 probability, $2.8 million with a 0.5 probability, and $300,000 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.

Answer 1

EBIT	4100000	2800000	300000
Less: Interest	0	0	0
EBT	4100000	2800000	300000
-Tax (EBT*0.25)	1025000	700000	75000
EAT	3075000	2100000	225000
Total Capital	11000000	11000000	11000000
ROE [EAT/Total Capital]	0.279545455	0.190909091	0.020454545

Probabilty	ROE	Probability* ROE	ROE- Expected ROE[D]	Probability*D*D
0.2	0.279545	0.055909	0.12204515	0.002979004
0.5	0.190909	0.0954545	0.03340915	0.000558086
0.3	0.0204545	0.00613635	-0.13704535	0.005634428
Expected ROE = Sum of Probabilty*ROE	0.15749985 = 15.75%	Variance =Sum of [D^2]	0.009171518
			Standard Deviation =Variance^1/2	0.095768041 = 9.58%
		Co Efficient of Variation = Standard Deviation/Mean i.e. Expected Return	0.265557903/0.117	0.608051636 = 0.61