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Question

# 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 federal-plus-state 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 debt-to-capital ratios; then evaluate the results: $$ \begin{matrix} \text{Debt/Capital Ratio} & \text{Interest Rate}\\ \text{0\\%} & \text{--}\\ \text{10} & \text{9\\%}\\ \text{50} & \text{11}\\ \text{60} & \text{14}\\ \end{matrix} $$

Solution

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1 of 12This problem is asking us to find the expected ROE, standard deviation and coefficient of variation for several different debt/capital ratio and interest rate scenarios.

We need to find the $\textbf{expected ROE}$ for each of the three probabilities and then add them together which will give us the final expected ROE

Once we have each of the ROEs we can find the $\textbf{deviation}$ for each of the probabilities which when added together will give us the variance.

$\textbf{Standard deviation}$ can be determined by taking the square root of this variance

Finally we can determine the $\textbf{coefficient of variation}$ by dividing the standard deviation by the expected ROE

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