Question

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: $4.2 million with a 0.2 probability, $2.9 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

Debt capital Ratio is 0

Calculation of Return on Equity

Calculation of expected EBIT

State	Probability	EBIT A	Expected EBIT B	Variance (A-Sum(B)^2	Pi x var
1	0.2	$4.2	0.84	2.6896	0.53792
2	0.5	$2.9	1.45	0.1156	0.0578
3	0.3	$0.9	0.27	2.7556	0.82668
			2.56		1.4224

= Sq rt 1.4224 = 1.19

CV = Standard deviation /mean = 1.19/2.56 = 0.46

Return on Equity = Equity earnings/Total shares

$2.56 (1-0.4) / $10 = 0.1536 = 15.36%

Debt Capital Ratio 10% interest rate 9%

Debt capital = $10 * 10% = $1 million interest = $1 million * 9% = 0.09 Million

State	Prob	EBIT	Int	EBT	PAT	Pi x EAT	Var^2	Pi X var^2
1	0.2	4.2	0.09	4.11	2.47	0.4932	0.968256	0.193651
2	0.5	2.9	0.09	2.81	1.69	0.8430	0.041616	0.020808
3	0.3	0.9	0.09	0.81	0.49	0.1458	0.992016	0.297605
		8.0			4.64	1.482		0.512064

= Sq rt 0.512064 = 0.72

CV = Standard deviation /mean = 0.72/1.482 = 0.49

Return on Equity = Equity earnings/Total shares

= 1.482/9 million = 0.1646 or 16.46%

Debt Capital Ratio 50% interest rate 11%

Debt capital = $10 * 50% = $5 million interest = $5 million * 11% = 0.55 Million

State	Prob	EBIT	Int	EBT	PAT	Pi x EAT	Var^2	Pi X var^2
1	0.2	4.2	0.55	3.65	2.19	0.438	0.968256	0.193651
2	0.5	2.9	0.55	2.35	1.41	0.7050	0.041616	0.020808
3	0.3	0.9	0.55	0.35	0.21	0.063	0.992016	0.297605
		8.0			3.81	1.206		0.512064

= Sq rt 0.512064 = 0.72

CV = Standard deviation /mean = 0.72/1.206 = 0.59

Return on Equity = Equity earnings/Total shares

= 1.206/5 million = 0.2412 or 24.12%

Debt Capital Ratio 60% interest rate 14%

Debt capital = $10 * 60% = $6 million interest = $6 million * 14% = 0.84 Million

State	Prob	EBIT	Int	EBT	PAT	Pi x EAT	Var^2	Pi X var^2
1	0.2	4.2	0.84	3.36	2.02	0.4032	0.968256	0.193651
2	0.5	2.9	0.84	2.06	1.24	0.6180	0.041616	0.020808
3	0.3	0.9	0.84	0.06	0.04	0.0108	0.992016	0.297605
		8.0			3.29	1.032		0.512064

= Sq rt 0.512064 = 0.72

CV = Standard deviation /mean = 0.72/1.032 = 0.70

Return on Equity = Equity earnings/Total shares

= 1.032/4 million = 0.258 or 25.80%