Question

RAK, Inc., has no debt outstanding and a total market value of $240,000. Earnings before interest and taxes, EBIT, are projected to be $26,000 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 20 percent lower. RAK is considering a $150,000 debt issue with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 15,000 shares outstanding. Ignore taxes for questions a and b. Assume the company has a market-to-book ratio of 1.0.

  

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. (Negative amounts 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 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. (Negative amounts 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. (Negative amounts 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	%

  

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. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. (e.g., 32.16))

  

	% change in ROE
Recession	%
Expansion	%

Answer 1

a-1.

	ROE
Recession	8.67 %
Normal	10.83 %
Expansion	12.78 %

a-2.

	% change in ROE
Recession	- 19.94 %
Expansion	18.01 %

b-1.

	ROE
Recession	9.78 %
Normal	15.56 %
Expansion	20.76 %

Workings:

After the proposed recapitalization,

Equity = $ 240,000 - 150,000 = $ 90,000

Interest expense = $ 150,000 x 8% = $ 12,000

Normal ROE = Net Income / Equity = $ ( 26,000 - 12,000) / $ 90,000 = 15.56 %

Recession ROE = $ (20,800 -12,000) / $ 90,000 = 9.78 %

Expansion ROE = $ ( 30,680 - 12,000) / $ 90,000 = 20.76 %

b-2.

	% change in ROE
Recession	- 37.15 %
Expansion	33.42 %

c-1.

	ROE
Recession	5.63 %
Normal	7.04 %
Expansion	8.31 %

Workings:

Equity = $ 240,000.

Normal ROE = $ 26,000 x ( 1 - 0.35) / $ 240,000 = 7.04 %

Recession ROE = $ 20,800 x ( 1- 0.35) / $ 240,000 = 5.63 %

Expansion ROE = $ 30,680 x ( 1 - 0.35) / $ 240,000 = 8.31 %

c-2.

	% change in ROE
Recession	- 20.03 %
Expansion	18.04 %

c-3.

	ROE
Recession	6.36 %
Normal	10.11 %
Expansion	13.49 %

After the proposed recapitalization,

Equity = $ 90,000.

Normal ROE = $ ( 26,000 - 12,000) x 0.65 / $ 90,000 = 10.11 %

Recession ROE = $ ( 20,800 - 12,000) x 0.65 / $ 90,000 = 6.36 %

Expansion ROE = $ ( 30,680 - 12,000) x 0.65 / $ 90,000 = 13.49 %

c-4.

	% change in ROE
Recession	- 37.09 %
Expansion	33.43 %