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

(a1) Normal EBIT = $ 26000, Expansionary EBIT = 18% higher = 1.18 x 26000 = $ 30680 and Recessionary EBIT = 20 % lower = 0.8 x 26000 = $ 20800

In all three cases interest expenses (I) and taxes are zero, as the firm is all equity financed and taxes are not being considered.

Therefore, EBIT = Net Income for all three cases. Further, Equity Value = Total Firm Value for all three cases as the firm is all equity financed.

Equity Value = $ 240000

Therefore, Expansion ROE = (30680 / 240000) x 100 ~ 12.78 %

Recession ROE = (20800 / 240000) x 100 ~ 8.67 %

Normal ROE = (26000 / 240000) x 100 ~ 10.83 %

(a2) % Change in Recession = (8.67 - 10.83) / 10.83 ~ - 0.199446 or -19.95 %

% Change in Expansion = (12.78 - 10.83) / 10.83 ~ 0.18 or 18 %

(b1) Post proposed recapitalization, the firm value remains at $ 240000 as there are no value additive impact of interest tax shields owing to absence of taxes. However, the EBIT and Net Income are not equal anymore owing to interest expenses.

Debt Raised = $ 150000 and Interest Rate = 8 % , Interest Expense = 0.08 x 150000 = $ 12000

Normal Net Income = Normal EBIT - Interest Expense = 260000 - 12000 = $ 14000

Similarly, Recessionary Net Income = 20800 - 12000 = $ 8800 and Expansionary Net Income = 30680 - 12000 = $ 18680

Therefore, Normal ROE = (14000 / 240000) x 100 ~ 5.83 %, Expansionary ROE = (18680 / 240000) x 100 ~ 7.78 % and Recessionary ROE = (8800 / 240000) x 100 ~ 3.67 %

(b2) % Change in Expansion = ((7.78 - 3.67) / 3.67) x 100 ~ 33.43 %

% Change in Recession = ((3.67 - 5.83) / 5.83) x 100 ~ - 37.14 %

NOTE: Please raise separate queries for solutions to the remaining sub-parts as one query is limited to the solution of only one question upto a maximum of four sub-parts.