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 $16 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: $5.8 million with a 0.2 probability, $3 million with a 0.5 probability, and $0.8 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

Neal's total capital is $16 million

federal-plus-state tax rate is 40%.

EBIT for three possible states of the world: $5.8 million with a 0.2 probability, $3 million with a 0.5 probability, and $0.8 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

1. Debt/Capital ratio is 0.

There is no debt, so interest is nil

EBIT (million)	Interest (million)	EBT (million)	Tax (million)	Net income (million)	Equity (million)	ROE=Net income / Equity ( R )	Proba Bility ( p)	R*P
$ 5.8	0	$ 5.8	5.8*40% =2.32	5.8-2.32 =3.48	$ 16	3.48/16 =0.2175	0.2	0.2175* 0.2 =0.0435
$ 3	0	$ 3	1.2	=1.8	$16	=0.1125	0.5	=0.05625
$ 0.8	0	$ 0.8	0.32	=0.48	$16	=0.03	0.3	=0.009

Expected ROE = Total sum of ( R*P )

Expected ROE = 0.0435 + 0.05625 + 0.009 = 0.10875 = 10.875%

ROE=Net income / Equity ( R )	EROE (ER)	(R-ER)	(R-ER)2	(R-ER)2 * ( p)
=0.2175	0.10875	= 0.10875	=0.01183	0.002365
=0.1125	0.10875	=0.00375	=0.000014	0.000007031
=0.03	0.10875	=-0.07875	=0.00620	0.001860468
			Total	0.00423281

standard deviation (σ) = root off total sum of (R-ER)2 * ( p)

standard deviation (σ) = root off 0.00423281

standard deviation (σ) = 0.065   = 6.5%

coefficient of variation (CV) = standard deviation / Expected ROE

coefficient of variation (CV) = 0.065 / 0.10875   = 0.5977

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

Debt = 16 * 10% = 1.6 million   Equity = 14.40 million

Interest = 1.6 * 9% = 0.144 million

EBIT (million)	Interest (million)	EBT (million)	Tax (million)	Net income (million)	Equity (million)	ROE=Net income / Equity ( R )	Proba Bility ( p)	R*P
$ 5.8	0.144	=5.656	=2.2624	=3.3936	$ 14.4	=0.23567	0.2	=0.04713
$ 3	0.144	$ 2.856	1.1424	=1.7136	$14.4	=0.119	0.5	=0.0595
$ 0.8	0.144	$ 0.656	0.2624	=0.3936	$14.4	=0.02733	0.3	=0.0082

Expected ROE = Total sum of ( R*P )

Expected ROE = 0.04713 + 0.0595+ 0.0082  = 0.1148 = 11.48%

ROE=Net income / Equity ( R )	EROE (ER)	(R-ER)	(R-ER)2	(R-ER)2 * ( p)
=0.23567	0.1148	= 0.12084	=0.014602	0.0029203
=0.119	0.1148	=0.0042	=0.000017	0.00000882
=0.02733	0.1148	=-0.08747	=0.007651	0.0022953
			Total	0.00522442

standard deviation (σ) = root off total sum of (R-ER)2 * ( p)

standard deviation (σ) = root off 0.00522442

standard deviation (σ) = 0.07228   = 7.23%

coefficient of variation (CV) = standard deviation / Expected ROE

coefficient of variation (CV) = 7.23% / 11.48%   = 0.63

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

Debt = 16 * 50% = 8 million   Equity = 8 million

Interest = 8 * 11% = 0.88 million

EBIT (million)	Interest (million)	EBT (million)	Tax (million)	Net income (million)	Equity (million)	ROE=Net income / Equity ( R )	Proba Bility ( p)	R*P
$ 5.8	0.88	=4.92	=1.968	=2.952	$ 8	=0.369	0.2	=0.0738
$ 3	0.88	$ 2.12	0.848	=1.272	$ 8	=0.159	0.5	=0.0795
$ 0.8	0.88	$ -0.08	0.032	=-0.48	$ 8	=-0.006	0.3	=-0.0018

Expected ROE = Total sum of ( R*P )

Expected ROE = 0.0738 + 0.0795+ -0.0018  = 0.1515 = 15.15%

ROE=Net income / Equity ( R )	EROE (ER)	(R-ER)	(R-ER)2	(R-ER)2 * ( p)
=0.369	0.1515	= 0.2175	=0.047306	0.00946125
=0.159	0.1515	=0.0075	=0.000056	0.000028125
=-0.006	0.1515	=-0.1575	=0.024806	0.007441875
			Total	0.01693125

standard deviation (σ) = root off total sum of (R-ER)2 * ( p)

standard deviation (σ) = root off 0.01693125

standard deviation (σ) = 0.1301   = 13.01%

coefficient of variation (CV) = standard deviation / Expected ROE

coefficient of variation (CV) = 13.01% / 15.15%   = 0.86

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

Debt = 16 * 60% = 9.6 million   Equity = 6.4 million

Interest = 9.6 * 14% = 1.344 million

EBIT (million)	Interest (million)	EBT (million)	Tax (million)	Net income (million)	Equity (million)	ROE=Net income / Equity ( R )	Proba Bility ( p)	R*P
$ 5.8	1.344	$ 4.456	1.7824	=2.6736	$ 6.4	=0.41775	0.2	=0.08355
$ 3	1.344	$ 1.656	0.6624	=0.9936	$6.4	=0.15525	0.5	=0.07762
$ 0.8	1.344	$-0.544	0.2176	=-0.3264	$6.4	=-0.051	0.3	=-0.0153

Expected ROE = Total sum of ( R*P )

Expected ROE = 0.08355 + 0.07762+ -0.0153  = 0.14587 = 14.59%

ROE=Net income / Equity ( R )	EROE (ER)	(R-ER)	(R-ER)2	(R-ER)2 * ( p)
=0.41775	0.14587	= 0.27188	=0.073918	0.014783746
=0.15525	0.14587	=0.00938	=0.000088	0.000043992
=-0.051	0.14587	=-0.19687	=0.038757	0.011627338
			Total	0.026455076

standard deviation (σ) = root off total sum of (R-ER)2 * ( p)

standard deviation (σ) = root off 0.026455076

standard deviation (σ) = 0.16265   = 16.26%

coefficient of variation (CV) = standard deviation / Expected ROE

coefficient of variation (CV) = 16.26% / 14.59%   = 1.114