The Neal Company wants to estimate next year\'s return on equity (ROE) under dif
ID: 2655543 • Letter: T
Question
The Neal Company wants to estimate next year's return on equity (ROE) under different 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: $4.6 million with a 0.2 probability, $2.3 million with a 0.5 probability, and $900,000 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.
Debt/Capital ratio is 10%, interest rate is 9%.
Debt/Capital ratio is 50%, interest rate is 11%.
Debt/Capital ratio is 60%, interest rate is 14%.
RÔE = % = % CV =Explanation / Answer
Solution-
Debt/Capital ratio is 0
Probability
EBIT
Equity
Debt
Interest
Net income= (EBIT-interest)*(1-tax)
ROE (Net Income / Equity)
0.2
$4,600,000
$16,000,000
0
0
$2,760,000 ($4,600,000-$0)*(1-0.40)
17.25%
0.5
$2,300,000
$16,000,000
0
0
$1,380,000($2,300,000-$0)*(1-0.40)
8.63%
0.3
$900,000
$16,000,000
0
0
$540,000 ($900,000-$0)*(1-0.40)
3.38%
Expected ROE = 0.2*17.25% + 0.5*8.63% +0.3*3.38%
Expected ROE = 8.78%
Standard Deviation = Square root (0.2*(17.25%-8.78%)^2 + 0.5*(8.63%-8.78%)^2 +0.3*(3.38%-8.78%)^2)
Standard Deviation = 4.81%
CV = 4.81% / 8.78%
CV = 0.55
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
$4,600,000
$14,400,000
$1,600,000
$144,000
$2,673,600 ($4,600,000-$144,000)*(1-0.40)
18.57%
0.5
$2,300,000
$14,400,000
$1,600,000
$144,000
$1,293,600($2,300,000-$144,000)*(1-0.40)
8.98%
0.3
$900,000
$14,400,000
$1,600,000
$144,000
$453,600 ($900,000-$144,000)*(1-0.40)
3.15%
Expected ROE = 0.2*18.75% + 0.5*8.98% +0.3*3.15%
Expected ROE = 9.18%
Standard Deviation = Square root (0.2*(18.57%-9.18%)^2 + 0.5*(8.98%-9.18%)^2 +0.3*(3.15%-9.18%)^2)
Standard Deviation = 5.35%
CV = 5.35% / 9.18%
CV = 0.58
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
$4,600,000
$8,000,000
$8,000,000
$880,000
$2,232,000 ($4,600,000-$880,000)*(1-0.40)
27.9%
0.5
$2,300,000
$8,000,000
$8,000,000
$880,000
$852,000($2,300,000-$880,000)*(1-0.40)
10.65%
0.3
$900,000
$8,000,000
$8,000,000
$880,000
$12,000 ($900,000-$880,000)*(1-0.40)
0.15%
Expected ROE = 0.2*27.9% + 0.5*10.65% +0.3*0.15%
Expected ROE = 10.95%
Standard Deviation = Square root (0.2*(27.9%-10.95%)^2 + 0.5*(10.65%-10.95%)^2 +0.3*(0.15%-10.95%)^2)
Standard Deviation = 9.62%
CV = 9.62% / 10.95%
CV = 0.88
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
$4,600,000
$6,400,000
$9,600,000
$1,344,000
$1,953,600 ($4,600,000-$1,344,000)*(1-0.40)
30.53%
0.5
$2,300,000
$6,400,000
$9,600,000
$1,344,000
$573,600($2,300,000-$1,344,000)*(1-0.40)
8.97%
0.3
$900,000
$6,400,000
$9,600,000
$1,344,000
-$266,400 ($900,000-$1,344,000)*(1-0.40)
-4.17%
Expected ROE = 0.2*30.53% + 0.5*8.97% +0.3*-4.17%
Expected ROE = 9.34%
Standard Deviation = Square root (0.2*(30.53%-9.34%)^2 + 0.5*(8.97%-9.34%)^2 +0.3*(-4.17%-9.34%)^2)
Standard Deviation = 12.03%
CV = 12.03% / 9.34%
CV = 1.29
Debt/Capital ratio is 0
Probability
EBIT
Equity
Debt
Interest
Net income= (EBIT-interest)*(1-tax)
ROE (Net Income / Equity)
0.2
$4,600,000
$16,000,000
0
0
$2,760,000 ($4,600,000-$0)*(1-0.40)
17.25%
0.5
$2,300,000
$16,000,000
0
0
$1,380,000($2,300,000-$0)*(1-0.40)
8.63%
0.3
$900,000
$16,000,000
0
0
$540,000 ($900,000-$0)*(1-0.40)
3.38%
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