The Neal Company wants to estimate next year\'s return on equity (ROE) under dif

Question

The Neal Company wants to estimate next year's return on equity (ROE) under different leverage ratios. Neal's total capital is $11 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: $4.5 million with a 0.2 probability, $1.7 million with a 0.5 probability, and $600,000 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. Do not round intermediate calculations. Round your answers to two decimal places at the end of the calculations.

Debt/Capital ratio is 0.

Explanation / Answer

Expected ROE = $2,520,000 / $14,000,000

= 0.18

Net income under state-2: Here the debt portion is 0% and the equity portion is 100% and the Cost of debt is 0%

Expected ROE = $1,680,000 / $14,000,000

= 0.12

Net income under state-3: Here the debt portion is 0% and the equity portion is 100% and the Cost of debt is 0%

Expected ROE = $420,000 / $14,000,000

= 0.03

Therefore, from the table

Column-7 is calculated as 0.2*(0.18-0.105)^2 = 0.00113

Similarly calculating for other states.

Variance = 0.00293

Standard deviation = Square root of variance

= v0.00293

= 0.054 or 5.4%

Co-efficient of variation = Standard deviation / Expected ROE

= 5.4% / 10.5%

= 0.514

Case-2: When the leverage value is 10% the debt is $1,400,000 the equity is $1,260,000 and the Cost of debt is 9%

Variance = 0.00363

Standard deviation = Sqrt(0.00363)

= 0.06 or 6%

Co-efficient of variation = 6% / 11.1%

= 0.54

Case-3: When the leverage value is 50% the debt is $7,000,000 the equity is $7,000,000 and the Cost of debt is 11%

Variance = 0.0117

Standard deviation = Sqrt(0.0117)

= 0.108 or 10.8%

Co-efficient of variation = 10.8% / 14.4%

= 0.750

Case-4: When the leverage value is 60% the debt is $8,400,000 the equity is $5,600,000 and the Cost of debt is 14%

Variance = 0.01827

Standard deviation = Sqrt(0.01827)

= 0.135 or 13.5%

Co-efficient of variation = 13.5% / 13.7%

= 0.985 or 0.99

As leverage increases, the expected return on equity also increases only upto a certain point. But as the risk increases with increased leverage, the cost of debt raises. So after the return on equity peaks it then begins to decrease. As leverage increases, the measure of risk also increases.

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