Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $20 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 million with a 0.2 probability, $1.9 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.

a) Debt/Capital ratio is 0.
RÔE =
σ =   
CV =

b) Debt/Capital ratio is 10%, interest rate is 9%.
RÔE =
σ =
CV =

c) Debt/Capital ratio is 50%, interest rate is 11%.
RÔE =   
σ =   
CV =

d) Debt/Capital ratio is 60%, interest rate is 14%.
RÔE =   
σ =
CV =

Answer 1

Question a.

Debt = $0 and Equity = $20,000,000
State	Probability	EBIT	EBT	Earning after tax	ROEs	(Prob. * ROE)	( ROEs - ROE)	Prob. ( ROE - ROE)2
1	0.2	$5,000,000	$5,000,000	$3,000,000	15.00%	3.00%	0.00711	0.00142
2	0.5	$1,900,000	$1,900,000	$1,140,000	5.70%	2.85%	0.00325	0.00162
3	0.3	$800,000	$800,000	$480,000	2.40%	0.72%	0.00058	0.00017
Total						6.57%		0.00322

EBT = EBIT - Interest expenses

ROE = Earning after tax / Total Equity

Standard deviation = Under root Variance

Variance = 0.00322

CV = Standard deviation / ROE

= 5.6% / 6.57%

= 0.852

RÔE = 6.57%
σ = 5.6%
CV = 0.852

Question b.

Total capital = $20 million

Debt = $20 million * 10% = $2 million.

Equity = $18 million.

Interest expenses = ( $2 million* 9% ) = $0.18 million or $180,000

Debt = $2,000,000 and Equity = $18,000,000
State	Probability	EBIT	EBT	Earning after tax	ROEs	(Prob. * ROE)	( ROEs - ROE)	Prob. ( ROE - ROE)
1	0.2	$5,000,000	$4,820,000	$2,892,000	16.07%	3.21%	0.00877	0.00175
2	0.5	$1,900,000	$1,720,000	$1,032,000	5.73%	2.87%	0.00329	0.00164
3	0.3	$800,000	$620,000	$372,000	2.07%	0.62%	0.00043	0.00013
Total						6.70%		0.00353

Variance = 0.00353

CV = Standard deviation / ROE

= 5.9% / 6.70%

= 0.887

RÔE = 6.70%
σ = 5.9%
CV = 0.887