Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $15 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: $5.4 million with a 0.2 probability, $3.1 million with a 0.5 probability, and $0.3 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.

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%.

Would really appreciate some help with this question, I have the answers but I don't understand how to calculate the standard deviation and coefficient of variation. Those are the two I'm struggling with a lot and I don't understand the formula for the standard deviation so any explanation would be really appreciated.

Answer 1

A brief explanation with formula for Expected return, standard deviation and coefficient of variation provided below:

Expected Return:

It is sum product of Probability and return in each situation. It is also called mean return.

where,

E(R) = Expected Return

Ri = Return in each states

Pi = Probability of each states

Standard deviation

It is measure of dispersion which means how data (returns) deviated from mean (expected return). It is also called volatility.

where,

standard deviation

E(R) = Expected Return

Ri = Return in each states

Pi = Probability of each states

Coefficient of variation

It is ratio of standard deviation and expected return. it represent how much risk taken for one unit of return.

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

Cell reference -