Question

The Neal Company wants to estimate next year's return on equity (ROE) under different financial leverage ratios. Neal's total capital is $16 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: $5.7 million with a 0.2 probability, $2.1 million with a 0.5 probability, and $0.6 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.
***Please dont Round intermediate Calculations ***
Thanks!!

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 =

Answer 1

ROE (R) = Net income/Equity

Expected ROE (m) = sum of probability weighted ROEs

Standard deviation (SD) = {Sum of [Probability*(R-m)^2]}^0.5

Coefficient of variation (CV) = SD/m

Case 1 - Debt/Capital = 0. In this case, interest expense will be zero and Equity will be equal to Capital which is 16 million.

ROE = 8.8875% , SD - 7.98% CV = 0.90

Case 2 - Debt/Capital = 10%, so Debt amount = 10%*16 = 1.6 million

Equity amount = 16 -1.6 = 14.4 million

Interest expense = 9%*1.6 = 0.144 million

ROE = 9.2750%, SD = 8.53% and CV = 0.92

Case 3 - Debt/Capital = 50%, so Debt amount = 50%*16 = 8 million

Equity amount = 16 -8 = 8 million

Interest expense = 11%*8 = 0.88 million

ROE = 11.1750%, SD = 12.96% CV = 1.16

Case 4 - Debt/Capital = 60%, so Debt amount = 60%*16 = 9.6 million

Equity amount = 16 - 9.6 = 6.4 million

Interest expense = 14%*9.6 = 1.344 million

ROE = 9.6188%, SD = 15.32% and CV = 1.59