Question

Castle, Inc., has no debt outstanding and a total market value of $250,000. Earnings before interest and taxes, EBIT, are projected to be $42,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 18 percent higher. If there is a recession, then EBIT will be 30 percent lower. The firm is considering a debt issue of $100,000 with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 10,000 shares outstanding. Ignore taxes for questions a and b. Assume the stock price remains constant.

a-1. Calculate return on equity (ROE) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	ROE
Recession	%
Normal	%
Expansion	%

a-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. Enter your answers as a percent rounded to the nearest whole number, e.g., 32.)

  

	% change in ROE
Recession	%
Expansion	%

Assume the firm goes through with the proposed recapitalization.

b-1. Calculate the return on equity (ROE) under each of the three economic scenarios. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	ROE
Recession	%
Normal	%
Expansion	%

b-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. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	% change in ROE
Recession	%
Expansion	%

Assume the firm has a tax rate of 35 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. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	ROE
Recession	%
Normal	%
Expansion	%

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. Enter your answers as a percent rounded to the nearest whole number, e.g., 32.)

	% change in ROE
Recession	%
Expansion	%

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. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	ROE
Recession	%
Normal	%
Expansion	%

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. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

	% change in ROE
Recession	%
Expansion	%

Answer 1

Before Recapitalization

No of shares = 10,000 => Given

Equity = $2,50,000 => Given

Hence Price per share = $2,50,000 / 10,000

EBIT = $42,000 => Given

a-1

	Change in EBIT	EBIT	ROE
Recession	-30%	$   29,400.00	11.76%
a2-Normal	0	$   42,000.00	16.80%
Expansion	18%	$   49,560.00	19.82%

Change in EBIT is given , i.e. In case of Recession reduction by 30% , and In case of expansion , EBIT is 18% higher.
Hence to calculate EBIT in Recession => $42,000 less 30% of $42,000 = 42000 - 12600 = $29,400.
Hence to calculate EBIT in Expansion => $42,000 plus 18% of $42,000 = 42000 + 7560 = $49,560.

ROE in case of Recession Economy = $29,400 / $2,50,000 = 11.76%
ROE in case of Normal Economy = $42,000 / $2,50,000 = 16.80%
ROE in case of Expansion Economy = $49,560 / $2,50,000 = 19.82%

a-2

	ROE	Change in ROE
Recession	11.76%	-5.04%	From 16.80% to 11.76%
Expansion	19.82%	3.02%	From 16.80% to 19.82%

In case of Recession ROE reduced from 16.80% to 11.76% which is negative change of 5.76%
In case of Expansion ROE increased from 16.80% to 19.82% which is positive change of 3.02%

a-3

After recapitalization
Debt	$ 1,00,000.00	New Debt Taken
Interest Rate	8%	Interest Rate Given
No of shares	6000	Calculated as $150,000/$25
Equity	$ 1,50,000.00	Equity reduced from 250,000 to 150,000 after debt is taken
Per Share price	$             25.00	Calculated earlier

Calculation of EBIT after DEBT
EBIT	$       42,000.00	Given
Less:Interest	$          8,000.00	Calculated as 100,000 * 8%
Earnings After Tax	$       34,000.00	Calculated as 42000-8000

	Change in EBIT	EBIT	ROE
Recession	-30%	$   23,800.00	15.87%
Normal	0%	$   34,000.00	22.67%
Expansion	18%	$   40,120.00	26.75%

Change in EBIT is given , i.e. In case of Recession reduction by 30% , and In case of expansion , EBIT is 18% higher.
Hence to calculate EBIT in Recession => $34,000 less 30% of $10,200 = 34000 - 10200 = $23,800.
Hence to calculate EBIT in Expansion => $34,000 plus 18% of $34,000 = 34000 + 6120 = $40,120.

a-4

	ROE	Change in ROE
Recession	15.87%	-6.80%	From 22.67% to 15.87%
Expansion	26.75%	4.08%	From 22.67% to 26.75%

In case of Recession ROE reduced from 22.67% to 15.87% which is negative change of -6.80%
In case of Expansion ROE increased from 22.67% to 26.75% which is positive change of 4.08%