Question

RAK, Inc., has no debt outstanding and a total market value of $150,000. 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 12 percent higher. If there is a recession, then EBIT will be 20 percent lower. RAK is considering a $90,000 debt issue with an interest rate of 6 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 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

1.

Recession RoE=26000*(1-20%)/150000=13.867%

Normal RoE=26000/150000=17.33%

Expansion RoE=26000*(1+12%)/150000=19.4133%

2.

%change in RoE

Recession: =13.867%/17.33%-1=-20%

Expansion: =19.4133%/17.33%-1=12%

3.

Recession RoE=(26000*(1-20%)-90000*6%)/(150000-90000)=25.67%

Normal RoE=(26000-90000*6%)/(150000-90000)=34.33%

Expansion RoE=(26000*(1+12%)-90000*6%)/(150000-90000)=39.53%

4.

%change in RoE

Recession: =25.67%/34.33%-1=-25.2%

Expansion: =39.53%/34.33%-1=15.1%

5.

Recession RoE=26000*(1-20%)*(1-35%)/150000=9.0133%

Normal RoE=26000*(1-35%)/150000=11.267%

Expansion RoE=26000*(1+12%)*(1-35%)/150000=12.6187%

6.

%change in RoE

Recession: =9.0133%/11.267%-1=-20%

Expansion: =8.834%/7.682%-1=12%

7.

Recession RoE=(26000*(1-20%)-90000*6%)*(1-35%)/(150000-90000)=16.683%

Normal RoE=(26000-90000*6%)*(1-35%)/(150000-90000)=22.3167%

Expansion RoE=(26000*(1+12%)-90000*6%)*(1-35%)/(150000-90000)=25.6967%

8.

%change in RoE

Recession: =16.683%/22.3167%-1=-25.2%

Expansion: =25.6967%/22.3167%-1=15.1%