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he Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage...

he Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $14 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: $4.9 million with a 0.2 probability, $2.9 million with a 0.5 probability, and $0.7 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 =

Solutions

Expert Solution

Debt/Capital ratio is 0

Total Capital Debt Total equity EBIT Interest expenses EBT Tax expenses Net income
a b c = a - b d e f = d- e g = f * 40% h = f -g
1,40,00,000 0 1,40,00,000 49,00,000 0 49,00,000 19,60,000 29,40,000
1,40,00,000 0 1,40,00,000 29,00,000 0 29,00,000 11,60,000 17,40,000
1,40,00,000 0 1,40,00,000 7,00,000 0 7,00,000 2,80,000 4,20,000
ROE Probability ROE * Probability (Expected ROE - ROE)2 Variance
i = h / c j k = i * j L = (i - 11.31 )2 M = L *j
21 % 0.2 4.2 % 0.00938961 0.001877922
12.42 % 0.5 6.21% 0.00012321 0.000061605
3 % 0.3 0.9% 0.00690561 0.002071683
11.31% 0.00401121

ROE = 11.31 %

SD = Variance ^(1 /2)

= 0.00401121 ^(1/2)

= 0.06333411403

= 6.33 %

CV = SD / Expected ROE

= 6.33 % / 11.31 %

= 0.55

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

Total Capital Debt Total equity EBIT Interest expenses EBT Tax expenses Net income
a b c = a - b d e = b *9% f = d- e g = f * 40% h = f -g
1,40,00,000 14,00,000 1,26,00,000 49,00,000 1,26,000 47,74,000 19,09,600 28,64,400
1,40,00,000 14,00,000 1,26,00,000 29,00,000 1,26,000 27,74,000 11,09,600 16,64,400
1,40,00,000 14,00,000 1,26,00,000 7,00,000 1,26,000 5,74,000 2,29,600 3,44,400
ROE Probability ROE * Probability (Expected ROE - ROE)2 Variance
i = h / c j k = i * j L = (i - 11.959 )2 M = L *j
22.73% 0.2 4.54 % 0.0116014441 0.00232028882
13.20% 0.5 6.6% 0.0001540081 0.00007700405
2.73% 0.3 0.819% 0.0085174441 0.00255523323
11.959% 0.0049525261

ROE = 11.959 %

SD = Variance ^(1 /2)

= 0.0049525261(1/2)

= 0.0703 or 7.03%

CV =SD / ROE

= 7.03 / 11.959

= 0.58

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

Total Capital Debt Total equity EBIT Interest expenses EBT Tax expenses Net income
a b c = a - b d e = b *11% f = d- e g = f * 40% h = f -g
1,40,00,000 70,00,000 70,00,000 49,00,000 7,70,000 41,30,000 16,52,000 24,78,000
1,40,00,000 70,00,000 70,00,000 29,00,000 7,70,000 21,30,000 8,52,000 12,78,000
1,40,00,000 70,00,000 70,00,000 7,00,000 7,70,000 - 70,000 -28,000 -98,000
ROE Probability ROE * Probability (Expected ROE - ROE)2 Variance
i = h / c j k = i * j L = (i - 15.785 )2 M = L *j
35.4% 0.2 7.08 % 0.0350251225 0.0070050245
18.25% 0.5 9.125% 0.0006076225 0.00030381125
-1.4 0.3 -0.42% 0.0295324225 0.00885972675
15.785 0.0161685625

ROE = 15.785

SD = Variance ^(1 /2)

= 0.0161685625 ^(1/2)

= 0.1271 or 12.71 %

CV = SD / ROE

= 12.71 / 15.785

= 0.80

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

Total Capital Debt Total equity EBIT Interest expenses EBT Tax expenses Net income
a b c = a - b d e = b *14% f = d- e g = f * 40% h = f -g
1,40,00,000 84,00,000 56,00,000 49,00,000 11,76,000 37,24,000 14,89,600 22,34,400
1,40,00,000 84,00,000 56,00,000 29,00,000 11,76,000 17,24,000 6,89,600 10,34,400
1,40,00,000 84,00,000 56,00,000 7,00,000 11,76,000 - 4,76,000 -1,90,400 -666400
ROE Probability ROE * Probability (Expected ROE - ROE)2 Variance
i = h / c j k = i * j L = (i - 13.645 )2 M = L *j
39.9% 0.2 7.98 % 0.0689325025 0.0137865005
18.47% 0.5 9.235% 0.0023280625 0.00116403125
-11.9 0.3 -3.57% 0.0652547025 0.01957641075
13.645 0.0345269425

ROE = 13.645

SD =Variance ^(1 /2)

= 0.0345269425^ ( 1/2)

= 0.1858 or 18.58%

CV = SD / ROE

= 18.58 / 13.645

= 1.36


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