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 $14 million, it currently uses only common equity, it has no future plans to use preferred stock in its capital structure, and its federalplusstate tax rate is 40%. The CFO has estimated next year's EBIT for three possible states of the world: $4.2 million with a 0.2 probability, $2.8 million with a 0.5 probability, and $700,000 with a 0.3 probability. Calculate Neal's expected ROE, standard deviation, and coefficient of variation for each of the following debttocapital ratios; then evaluate the results:
Debt/Capital Ratio  Interest Rate 
0%  — 
10  9% 
50  11 
60  14 
To identify: The expected return on equity, standard deviation, and coefficient of variance from the given situation.
Introduction:
Return on Equity:
The return, which is generated on the equity that is invested by the stockholders is known as return on equity.
The capital ratio at 0% and none interest rate.
Compute the expected return on equity.
State1
Compute the net income.
Given,
The probability is 0.2.
The EBIT is $4,200,000.
Formula to calculate the net income,
Where,
Substitute $4,200,000 for EBIT, 0 for I and 0.40 for T.
The net income of state 1 is $2,520,000.
Compute the return on equity of state 1.
The net income is $2,520,000. (Calculated above)
The equity is $14,000,000. (Given)
Formula to calculate the return on equity,
Substitute $2,520,000 for net income and $14,000,000 for equity.
The return on equity of state 1 is 18%.
State2
Compute the net income.
Given,
The probability is 0.5.
The EBIT is $2,800,000.
Formula to calculate the net income,
Where,
Substitute $2,800,000 for EBIT, 0 for I and 0.40 for T.
The net income of state 2 is $1,680,000.
Compute the return on equity of state 2.
The net income is $1,680,000. (Calculated above)
The equity is $14,000,000. (Given)
Formula to calculate the return on equity,
Substitute $1,680,000 for net income and $14,000,000 for equity.
The return on equity on state 2 is 12%.
State3
Compute the net income.
Given,
The probability is 0.3.
The EBIT is $700,000.
Formula to calculate the net income,
Where,
Substitute $700,000 for EBIT, 0 for I and 0.40 for T.
The net income of state 3 is $420,000.
Compute the return on equity of state 3.
The net income is $420,000. (Calculated above)
The equity is $14,000,000. (Given)
Formula to calculate the return on equity,
Substitute $420,000 for net income and $14,000,000 for equity.
The return on equity on state 3 is 3%.
Compute the expected return on equity of 3 states.
The return on equity of state 1 is18%. (Calculated in equation (1))
The return on equity of state 2 is 12%. (Calculated in equation (2))
The return on equity of state 3 is 3%. (Calculated in equation (3))
The probability of state 1 is 0.2. (Given)
The probability of state 2 is 0.5. (Given)
The probability of state 3 is 0.3. (Given)
Formula to calculate the expected return on earnings,
Substitute 0.2, 0.5 and 0.3 for probability and 18%, 12% and 3% for return on earnings.
The expected return on earnings is 10.50%.
Compute the standard deviation.
State  Probability 
Return on Equity (ROE) 
Expected Return on Equity (EROE) 
Deviation

1  0.2  18%  10.50%  11.25% 
2  0.5  12%  10.50%  1.125% 
3  0.3  3%  10.50%  16.88% 
Variance  29.25% 
Table (1)
The variance is 29.25%. (Calculated above)
Formula to calculate the standard deviation,
Substitute 29.25% for variance.
The standard deviation is 5.408%.
Compute the coefficient of deviation.
The standard deviation is 5.408%.
The expected return on equity is 10.50%.
Formula to calculate the coefficient of variance,
Where,
Substitute 5.408% for standard deviation and 10.25% for EROE.
The coefficient of variance is 0.515.
The capital ratio at 10% and interest rateis 9%.
Compute the expected return on equity
Statement to show the computation of return on equity of each state
Table (2)
Compute expected return on equity of 3 states.
The return on equity of state 1 is 19.40%. (Calculated above)
The return on equity of state 2 is 12.73%. (Calculated above)
The return on equity of state 3 is 2.73%. (Calculated above)
The probability of state 1 is 0.2. (Given)
The probability of state 2 is 0.5. (Given)
The probability of state 3 is 0.3. (Given)
Formula to calculate the expected return on earnings,
Substitute 0.2, 0.5 and 0.3 for probability and 19.40%, 12.73% and 2.73% for return on earnings.
The expected return on earnings is 11.07%.
Compute the standard deviation
State  Probability 
Return on Equity (ROE) 
Expected Return on Equity (EROE) 
Deviation

1  0.2  19.40%  11.07%  13.88% 
2  0.5  12.73%  11.07%  1.378% 
3  0.3  2.73%  11.07%  20.87% 
Variance  36.128% 
Table 3
The variance is 36.128%. (Calculated above)
Formula to calculate the standard deviation,
Substitute 36.128% for variance.
The standard deviation is 6.01%.
Compute the coefficient of deviation.
The standard deviation is 6.01%.
The expected return on equity is 11.07%.
Formula to calculate the coefficient of variance,
Where,
Substitute 6
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