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: $4.2 million with a 0.2 probability, $2 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 =

Answer 1

Scenario 1 : Debt/Capital ratio is 0. All dollar figures in millions, unless stated
Total Capital	Debt	Equity	Possible states	Probability	EBIT	Interest on debt	EBIT - Interest expenses	Taxes @40%	Net income = Column I-taxes	ROE=Net income/ equity	pROE= Probability x ROE	(Expected ROE- pROE)^2	Variance= prob. *column N
$17.00	$0.00	$17.00	A	0.2	$4.20	0	$4.20	$1.68	$2.52	0.1482	0.030	0.0448	0.0090
$17.00	$0.00	$17.00	B	0.5	$2.00	0	$2.00	$0.80	$1.20	0.0706	0.035	0.0392	0.0196
$17.00	$0.00	$17.00	C	0.3	$0.90	0	$0.90	$0.36	$0.54	0.0318	0.010	0.0649	0.0195
										Expected ROE	0.0745	Variance	0.0480
										(sum of all 3 prob x ROEs above i.e. (0.03+0.035+0.01)		(sum of all 3 variances above)

Also, attaching the picture showing above calculations, for ease in using formulae

Hence, the answers are as follows, for Debt/Capital ratio is 0 case

RÔE or Expected ROE = 7.45%

σ² or variance = 0.0480

σ =square root of Variance = = 0.21917 or 21.917%

CV =σ/RÔE= 21.917%/7.45%=2.943

b) When Debt/Capital ratio is 10%, interest rate is 9% scenario, we have following calculations:

Scenario 2 : When Debt/Capital ratio is 10%, interest rate is 9% . All dollar figures in millions, unless stated
Total Capital	Debt	Equity	Possible states	Probability	EBIT	Interest on debt	EBIT - Interest expenses	Taxes @40%	Net income = Column I-taxes	ROE=Net income/ equity	pROE= Probability x ROE	(Expected ROE- pROE)^2	Variance= prob. *column N
$17.00	$1.70	$15.30	A	0.2	$4.20	$0.15	$4.05	$1.62	$2.43	15.871%	3.17%	4.27%	0.0085
$17.00	$1.70	$15.30	B	0.5	$2.00	$0.15	$1.85	$0.74	$1.11	7.243%	3.62%	3.83%	0.0191
$17.00	$1.70	$15.30	C	0.3	$0.90	$0.15	$0.75	$0.30	$0.45	2.929%	0.88%	6.57%	0.0197
										Expected ROE	7.67%	Variance	0.0474
										(sum of all 3 prob x ROEs above i.e. (0.03+0.035+0.01)		(sum of all 3 variances above)

Also, attaching the picture showing above calculations, for ease in using formulae:

Hence, the answers are as follows, for scenario 2

RÔE or Expected ROE = 7.67%

σ² or variance = 0.0474

σ =square root of Variance = = 0.21767 or 21.767%

CV =σ/RÔE= 21.767%/7.67%=2.8378