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: $4.8 million with a 0.2 probability, $2.7 million with a 0.5 probability, and $0.4 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. ROE = CV = Debt/Capital ratio is 10%, interest rate is 9%. RÔE = % CV = Debt/Capital ratio is 50%, interest rate is 11%. RÔE = 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.

Formula Probability (P) EBIT | Interest (0) 0.2 0.5 EBIT- EBT 4.8 2.7 0.4 40%*EBT EBT-Tax Tax @ 40% Net income (NI) 1.92 2.88 1.08 1.62 0.16 0.24 NI/Equity ROE ('R) 18.00% 10.13% 1.50% Expected ROE (m) P ROE 0.0360 0.0506 0.0045 P*(R-m)^2 0.0016 0.0001 0.0017 0 0 0.3 0.4 0.0034 9.11% Standard Deviation (SD) 5.80% 0.64

ROE = 9.11%; Standard deviation = 5.80%; CV = 0.64

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

| Formula Probability (P) 0.2 0.5 0.3 EBIT 4.8 2.7 0.4 9%*Debt Interest (0)| 0.144 0.144 0.144 EBIT- EBT 4.656 2.556 0.256 40%*EBT EBT-Tax Tax @ 40% Net income (NI) 1.8624 2.7936 1.0224 1.5336 0.1024 0.1536 NI/Equity ROE (R) 19.40% 10.65% 1.07% Expected ROE (m) P ROE 0.0388 0.0533 0.0032 P*(R-m)^2 0.0021 0.0001 0.0019 0.0042 9.53% Standard Deviation (SD) 6.46% 0.68 CV

ROE = 9.53%; Standard deviation = 6.46%; CV = 0.68

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

Formula Probability (P) EBITI 4.8 02 11%*Debt Interest (0) 0.88 0.88 0.88 EBIT-1 | 40%*EBT EBT-Tax EBT Tax @ 40% Net income (NI) 3.921 1.568 2.352 1.821 0.728 1.092 -0.48 -0.192 -0.288 P*ROE 0.0588 0.0683 -0.0108 NI/Equity ROE ('R) 29.40% 13.65% -3.60% Expected ROE (m) P*(R-m)^2 0.0082 0.0010 0.0048 05 2.7 0.3 0.4 0.0141 11.63% Standard Deviation (SD) CV 11.88% 1.02

ROE = 11.63%; Standard deviation = 11.88%; CV = 1.02

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

Formula Probability (p) | 02 EBIT 4.8 2.7 0.4 14%*Debt Interest 1.344 1.344 1.344 EBIT-1 | 40%*EBT EBT-Tax EBT Tax @ 40% Net income (NI) 3.456 1.3824 2.0736 1.356 0.5424 0.8136 -0.944 -0.3776 -0.5664 NI/Equity ROE (R) 32.40% 12.71% -8.85% Expected ROE (m) P*ROE 0.0648 0.0636 -0.0266 P*(R-m)^2 0.0108 0.0006 0.0097 05 0.3 0.0212 10.18% Standard Deviation (SD) CV 14.55% 1.43

ROE = 10.18%; Standard deviation = 14.55%; CV = 1.43