Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $18 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: $4.4 million with a 0.2 probability, $1.9 million with a 0.5 probability, and $0.9 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

When Debt capital ratio is 0%
EBIT		2.1
less interest		0
earning before tax		2.1
less tax 40%		0.84
earning available to equity share holders		1.26
Return on equity	(net income/value of equity)*100	7
Probability	expected return	expected return*probability	Expected return- average return	square of (expected return- average return)	probability*square of (expected return- average return)
0.2	4.4	0.88	-1.22	1.4884	0.298
0.5	1.9	0.95	-1.15	1.3225	0.661
0.3	0.9	0.27	-1.83	3.3489	1.005
average return or EBIT	sum of expected return*probability	2.1		Variance =sum of probability*square of (expected return- average return)	1.964
				standard deviation = square root of variance	1.401
				coefficient of variance =(standard deviation /average return)*100	66.714
When Debt capital ratio is 10%
EBIT		2.1
less interest	(18*10%)*9%	0.162
earning before tax		1.938
less tax 40%		0.7752
earning available to equity share holders		1.628
Return on equity	(net income/value of equity)*100 =[1.628/(18-1.8)]*100	10.04938
Probability	expected return	expected return*probability	Expected return- average return	square of (expected return- average return)	probability*square of (expected return- average return)
0.2	4.4	1.02	-1.22	1.4884	0.298
0.5	1.9	1.6	-1.15	1.3225	0.661
0.3	0.9	0.27	-1.83	3.3489	1.005
average return	sum of expected return*probability	2.1		Variance =sum of probability*square of (expected return- average return)	1.964
				standard deviation = square root of variance	1.401
				coefficient of variance	66.714
When Debt capital ratio is 50%
EBIT		2.1
less interest	(18*50%)*11%	0.99
earning before tax		1.11
less tax 40%		0.444
earning available to equity share holders		0.666
Return on equity	(net income/value of equity)*100 =[0.666/(18-9)]*100	7.4
Probability	expected return	expected return*probability	Expected return- average return	square of (expected return- average return)	probability*square of (expected return- average return)
0.2	4.4	0.88	-1.22	1.4884	0.298
0.5	1.9	0.95	-1.15	1.3225	0.661
0.3	0.9	0.27	-1.83	3.3489	1.005
average return	sum of expected return*probability	2.1		Variance =sum of probability*square of (expected return- average return)	1.964
				standard deviation = square root of variance	1.401
				coefficient of variance	66.714
When Debt capital ratio is 60%
EBIT		2.1
less interest	(18*60%)*14%	1.512
earning before tax		0.588
less tax 40%		0.2352
earning available to equity share holders		0.3528
Return on equity	(net income/value of equity)*100 =[0.3528/(18-10.8)]*100	4.9
Probability	expected return	expected return*probability	Expected return- average return	square of (expected return- average return)	probability*square of (expected return- average return)
0.2	4.4	0.88	-1.22	1.4884	0.298
0.5	1.9	0.95	-1.15	1.3225	0.661
0.3	0.9	0.27	-1.83	3.3489	1.005
average return	sum of expected return*probability	2.1		Variance =sum of probability*square of (expected return- average return)	1.964
				standard deviation = square root of variance	1.401
				coefficient of variance	66.714