Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $14 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: $5.7 million with a 0.2 probability, $1.5 million with a 0.5 probability, and $0.3 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 =

Continue without saving

Answer 1

a) When Debt/Capital ratio is 0

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
$14.00	$0.00	$14.00	A	0.2	$5.70	$0.00	$5.70	$2.28	$3.42	24.429%	4.89%	2.56%	0.0051
$14.00	$0.00	$14.00	B	0.5	$1.50	$0.00	$1.50	$0.60	$0.90	6.429%	3.21%	4.23%	0.0212
$14.00	$0.00	$14.00	C	0.3	$0.30	$0.00	$0.30	$0.12	$0.18	1.286%	0.39%	7.06%	0.0212
										Expected ROE	8.49%	Variance	0.0475
										(sum of all 3 pROEs above)		(sum of all 3 variances above)

Attaching a picture here as well for ease in putting formulae:

RÔE = 8.49%

σ = = 0.217877 or 21.78%

CV =σ/RÔE= 21.787%/8.49%=2.566

b) Debt/Capital ratio is 10%,interest rate is 9%.

Scenario 2 : 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
$14.00	$1.40	$12.60	A	0.2	$5.70	$0.13	$5.57	$2.23	$3.34	26.543%	5.31%	2.14%	0.0043
$14.00	$1.40	$12.60	B	0.5	$1.50	$0.13	$1.37	$0.55	$0.82	6.543%	3.27%	4.18%	0.0209
$14.00	$1.40	$12.60	C	0.3	$0.30	$0.13	$0.17	$0.07	$0.10	0.829%	0.25%	7.20%	0.0216
										Expected ROE	8.83%	Variance	0.0468
										(sum of all 3 pROEs above)		(sum of all 3 variances above)

Attaching a picture here as well for ease in putting formulae:

RÔE = 8.83%

σ = = 0.216219 or 21.62%

CV =σ/RÔE= 21.6219%/8.83%=2.448

c) Debt/Capital ratio is 50%,interest rate is 11%.

Scenario 3 : Debt/Capital ratio is 50%,interest rate is 11%.​​​​​ 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
$14.00	$7.00	$7.00	A	0.2	$5.70	$0.77	$4.93	$1.97	$2.96	42.257%	8.45%	-1.00%	-0.0020
$14.00	$7.00	$7.00	B	0.5	$1.50	$0.77	$0.73	$0.29	$0.44	6.257%	3.13%	4.32%	0.0216
$14.00	$7.00	$7.00	C	0.3	$0.30	$0.77	-$0.47	-$0.19	-$0.28	-4.029%	-1.21%	8.66%	0.0260
										Expected ROE	10.37%	Variance	0.0456
										(sum of all 3 pROEs above)		(sum of all 3 variances above)

Attaching a picture here as well for ease in putting formulae:

RÔE = 10.37%

σ = = 0.213426 or 21.34%

CV =σ/RÔE= 21.3426%/10.37%=2.0581

d) Debt/Capital ratio is 60%,interest rate is 14%.

Scenario 4 : Debt/Capital ratio is 60%,interest rate is 14%.​​​​​ 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
$14.00	$8.40	$5.60	A	0.2	$5.70	$1.18	$4.52	$1.81	$2.71	48.471%	9.69%	-2.25%	-0.0045
$14.00	$8.40	$5.60	B	0.5	$1.50	$1.18	$0.32	$0.13	$0.19	3.471%	1.74%	5.71%	0.0286
$14.00	$8.40	$5.60	C	0.3	$0.30	$1.18	-$0.88	-$0.35	-$0.53	-9.386%	-2.82%	10.26%	0.0308
										Expected ROE	8.61%	Variance	0.0549
										(sum of all 3 pROEs above)		(sum of all 3 variances above)

Attaching a picture here as well for ease in putting formulae:

RÔE = 8.61%

σ = = 0.234202 or 23.42%

CV =σ/RÔE= 23.4202%/8.61%=2.7201