Question

5- The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $10 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: $4.3 million with a 0.2 probability, $2.4 million with a 0.5 probability, and $0.7 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

1)

Total capital =10 mil

Debt/ capital = 0

Debt = 0 and interest =0

So .Equity =10- 0 =10 mil

The calculations are shown below,

Prob (P)	EBIT	Int	EBIT - Int= EBT	EBT(1- tax)= NI	NI/ Equity= ROE	P * ROE	(ROE - Exp ROE)^2	P * (ROE - Exp ROE)^2
0.2	4.3	0	4.3	2.58	0.258	0.0516	0.01483524	0.002967048
0.5	2.4	0	2.4	1.44	0.144	0.072	0.00006084	0.00003042
0.3	0.7	0	0.7	0.42	0.042	0.0126	0.00887364	0.002662092
					Exp ROE =	0.1362	Variance=	0.00565956
							SD=	0.075230047
							CV=	0.552349833

ROE =13.62%

SD =7.52%

CV=0.55

2)

Total capital =10 mil

Debt/ capital = 0.1

Debt = 0.1*10 =1  and interest =0.09 *1= 0.09 mil

.Equity =10- 1 = 9

The calculations are shown below,

Prob (P)	EBIT	Int	EBIT - Int= EBT	EBT(1- tax)= NI	NI/ Equity= ROE	P * ROE	(ROE - Exp ROE)^2	P * (ROE - Exp ROE)^2
0.2	4.3	0.09	4.21	2.526	0.280667	0.056133	0.018315111	0.003663022
0.5	2.4	0.09	2.31	1.386	0.154	0.077	0.000075111	0.000037556
0.3	0.7	0.09	0.61	0.366	0.040667	0.0122	0.010955111	0.003286533
					Exp ROE =	0.145333	Variance=	0.006987111
							SD=	0.083588941
							CV=	0.575153266

ROE =14.53%

SD =8.36%

CV=0.58

3)

Total capital =10 mil

Debt/ capital = 0.5

Debt = 0.5*10 =5 and interest =0.11 *5= 0.55 mil

.Equity =10- 5 = 5 mil

The calculations are shown below,

Prob (P)	EBIT	Int	EBIT - Int= EBT	EBT(1- tax)= NI	NI/ Equity= ROE	P * ROE	(ROE - Exp ROE)^2	P * (ROE - Exp ROE)^2
0.2	4.3	0.55	3.75	2.25	0.45	0.09	0.05934096	0.011868192
0.5	2.4	0.55	1.85	1.11	0.222	0.111	0.00024336	0.00012168
0.3	0.7	0.55	0.15	0.09	0.018	0.0054	0.03549456	0.010648368
					Exp ROE =	0.2064	Variance=	0.02263824
							SD=	0.150460094
							CV=	0.728973325

ROE =20.64%

SD =15.05%

CV=0.73

4)

Total capital =10 mil

Debt/ capital = 0.6

Debt = 0.6*10 =6 and interest =0.14 *6= 0.84 mil

.Equity =10- 6 = 4 mil

The calculations are shown below,

Prob (P)	EBIT	Int	EBIT - Int= EBT	EBT(1- tax)= NI	NI/ Equity= ROE	P * ROE	(ROE - Exp ROE)^2	P * (ROE - Exp ROE)^2
0.2	4.3	0.84	3.46	2.076	0.519	0.1038	0.09272025	0.01854405
0.5	2.4	0.84	1.56	0.936	0.234	0.117	0.00038025	0.000190125
0.3	0.7	0.84	-0.14	-0.084	-0.021	-0.0063	0.05546025	0.016638075
					Exp ROE =	0.2145	Variance=	0.03537225
							SD=	0.188075118
							CV=	0.876807077

ROE =21.45%

SD =18.81%

CV=0.88