Question

Ghost, Inc., has no debt outstanding and a total market value of $369,600. Earnings before interest and taxes, EBIT, are projected to be $51,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 15 percent higher. If there is a recession, then EBIT will be 24 percent lower. The company is considering a $185,000 debt issue with an interest rate of 6 percent. The proceeds will be used to repurchase shares of stock. There are currently 8,400 shares outstanding. Ignore taxes for questions a and b. Assume the company has a market-to-book ratio of 1.0 and the stock price remains constant.

a1.	Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued.
a2.	Calculate the percentage changes in ROE when the economy expands or enters a recession.
b1.	Assume the firm goes through with the proposed recapitalization. Calculate the return on equity (ROE) under each of the three economic scenarios.
b2.	Assume the firm goes through with the proposed recapitalization. Calculate the percentage changes in ROE when the economy expands or enters a recession.

Assume the firm has a tax rate of 24 percent.

c-1.	Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
c-2.	Calculate the percentage changes in ROE when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
c-3.	Calculate the return on equity (ROE) under each of the three economic scenarios assuming the firm goes through with the recapitalization. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
c-4.	Given the recapitalization, calculate the percentage changes in ROE when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Since, the question has multiple sub-parts, I have answered the first four.

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Part a1)

The return on equity (ROE) under each of the three economic scenarios before any debt is issued is determined as below:

ROE (Recession) = Net Income under Recession/Equity*100 = (51,000 - 51,000*24%)/369,600*100 = 10.49%

ROE (Normal) = Net Income under Normal/Equity*100 = 51,000/369,600*100 = 13.80%

ROE (Expansion) = Net Income under Expansion/Equity*100 = (51,000 + 51,000*15%)/369,600*100 = 15.87%

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Tabular Representation:

	ROE
Recession	10.49%
Normal	13.80%
Expansion	15.87%

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Notes:

1) As there is not debt (resulting in no interest) and no taxes, Net Income will be same as EBIT.

2) As market-to-book ratio is 1, market value of equity would be same as book value of equity.

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Part a2)

The percentage changes in ROE when the economy expands or enters a recession is arrived as below:

Percentage Change in ROE (Normal to Recession) = (ROE under Recession - ROE under Normal)/ROE under Normal*100 = (10.49% - 13.80%)/13.80% = -24.00%

Percentage Change in ROE (Normal to Expansion) = (ROE under Expansion - ROE under Normal)/ROE under Normal*100 = (15.87% - 13.80%)/13.80% = 15.00%

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Part b1)

Step 1: Calculate Revised Equity and Net Income under Each Scenario

The revised value of equity and net income under each scenario is determined as below:

Equity = Current Equity - Value of Debt = 369,600 - 185,000 = $184,600

Net Income under Recession = EBIT - Decrease in EBIT - Interest Expense = 51,000 - 51,000*24% - 185,000*6% = $27,660

Net Income under Normal = EBIT - Interest Expense = 51,000 - 185,000*6% = $39,900

Net Income under Expansion = EBIT + Increase in EBIT - Interest Expense = 51,000 + 51,000*15% - 185,000*6% = $47,550

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Step 2: Calculate ROE under Three Economic Scenarios

The value of ROE under three economic scenarios is calculated as follows:

ROE (Recession) = Net Income under Recession/Equity*100 = 27,660/184,600*100 = 14.98%

ROE (Normal) = Net Income under Normal/Equity*100 = 39,900/184,600*100 = 21.61%

ROE (Expansion) = Net Income under Expansion/Equity*100 = 47,550/184,600*100 = 25.76%

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Tabular Representation:

	ROE
Recession	14.98%
Normal	21.61%
Expansion	25.76%

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Part b2)

The percentage changes in ROE when the economy expands or enters a recession is arrived as below:

Percentage Change in ROE (Normal to Recession) = (ROE under Recession - ROE under Normal)/ROE under Normal*100 = (14.98% - 21.61%)/21.61% = -30.68%

Percentage Change in ROE (Normal to Expansion) = (ROE under Expansion - ROE under Normal)/ROE under Normal*100 = (25.76% - 21.61%)/21.61% = 19.17%