In: Finance
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 = |
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