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 $12 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, $2.5 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 =

Answer 1

Ans.

Debt/Capital ratio is 0
Probability	EBIT	Equity	Debt	Interest	Net income= (EBIT-interest)*(1-tax)	ROE (Net Income / Equity)
0.2	$5,700,000	$12,000,000	0	0	$3,420,000 ($5,700,000-$0)*(1-0.40)	28.50%
0.5	$2,500,000	$12,000,000	0	0	$1,500,000($2,500,000-$0)*(1-0.40)	12.50%
0.3	$300,000	$12,000,000	0	0	$180,000 ($300,000-$0)*(1-0.40)	1.50%

Expected ROE = 0.2*28.50% + 0.5*12.50% +0.3*1.50%

Expected ROE = 5.70% + 6.25% + 0.45% = 12.40%

Standard Deviation = Square root (0.2*(28.50%-12.40%)2 + 0.5*(12.50%-12.40%)2 +0.3*(1.50%-12.40%)2)

Standard Deviation = 9.35%

CV = Standard Deviation/Expected ROE = 9.35% / 12.40%

CV = 0.75

Debt/Capital ratio is 10%, interest rate is 9%
Probability	EBIT	Equity	Debt	Interest	Net income= (EBIT-interest)*(1-tax)	ROE (Net Income / Equity)
0.2	$5,700,000	$10,800,000	$1,200,000	$108,000	$3,555,200 ($5,700,000-$108,000)*(1-0.40)	31.07%
0.5	$2,500,000	$10,800,000	$1,200,000	$108,000	$1,435,200($2,500,000-$108,000)*(1-0.40)	13.29%
0.3	$300,000	$10,800,000	$1,200,000	$108,000	$115,200 ($300,000-$108,000)*(1-0.40)	1.07%

Expected ROE = 0.2*31.07% + 0.5*13.29% +0.3*1.07%

Expected ROE = 6.21% + 6.64% + 0.32% = 13.18%

Standard Deviation = Square root (0.2*(31.07%-13.18%)2 + 0.5*(13.29%-13.18%)2 +0.3*(1.07%-13.18%)2)

Standard Deviation = 10.39%

CV = 10.39% / 13.18%

CV = 0.79

Debt/Capital ratio is 50%, interest rate is 11%
Probability	EBIT	Equity	Debt	Interest	Net income= (EBIT-interest)*(1-tax)	ROE (Net Income / Equity)
0.2	$5,700,000	$6,000,000	$6,000,000	$660,000	$3,024,200 ($5,700,000-$660,000)*(1-0.40)	50.40%
0.5	$2,500,000	$6,000,000	$6,000,000	$660,000	$1,104,000($2,500,000-$660,000)*(1-0.40)	18.40%
0.3	$300,000	$6,000,000	$6,000,000	$660,000	- $216,000 ($300,000-$660,000)*(1-0.40)	-3.60%

Expected ROE = 0.2*50.40% + 0.5*18.40% +0.3* (- 3.60)%

Expected ROE = 10.08% + 9.20 % - 1.08 % = 18.20%

Standard Deviation = Square root (0.2*(50.40%-18.20%)2 + 0.5*(18.40% - 18.20%)2 +0.3*(-3.60%-18.20%)2)

Standard Deviation = 18.70%

CV = 18.70% / 18.20%

CV = 1.03

Debt/Capital ratio is 60%, interest rate is 14%
Probability	EBIT	Equity	Debt	Interest	Net income= (EBIT-interest)*(1-tax)	ROE (Net Income / Equity)
0.2	$5,700,000	$4,800,000	$7,200,000	$1,008,000	$2,815,200 ($5,700,000-$1,008,000)*(1-0.40)	58.65%
0.5	$2,500,000	$4,800,000	$7,200,000	$1,008,000	$895,200($2,500,000-$1,008,000)*(1-0.40)	18.65%
0.3	$300,000	$4,800,000	$7,200,000	$1,008,000	- $424,800 ($300,000-$1,008,000)*(1-0.40)	-8.85%

Expected ROE = 0.2*58.65% + 0.5*18.65% +0.3*(-8.85)%

Expected ROE = 11.73% + 9.33 % - 2.66 % = 18.40%

Standard Deviation = Square root (0.2*(58.65%-18.40%)2 + 0.5*(18.65%-18.40%)2 +0.3*(-8.85% - 18.40 %)2)

Standard Deviation = 23.38%

CV = 23.38% / 18.40%

CV = 1.27