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 = EBIT*(1-tax rate)/Market value

Recession

ROE = EBIT*(1-recession impact%)*(1-tax rate)/market value

ROE=26000*(1-0.2)*(1-0)/240000

ROE=8.67

Normal

ROE = EBIT*(1-tax rate)/Market value

ROE=26000*(1-0)/240000

ROE=10.83

Expansion

ROE = EBIT*(1+Growth impact%)*(1-tax rate)/Market value

ROE=26000*(1+0.18)*(1-0)/240000

ROE=12.78

a-2

%age change in ROE for Recession

=(ROE recession/ROE normal-1)*100

=(0.0867/0.1083-1)*100

=-20%

%age change in ROE for Growth

=(ROE Growth/ROE normal-1)*100

=(0.1278/0.1083-1)*100

=18.01%

b-1

New market value = old market value-debt

=240000-150000

=90000

ROE = (EBIT-debt*interest%)*(1-tax rate)/new market value

Recession

ROE = (EBIT*(1-recession impact%)-debt*interest %age)*(1-tax rate)/new market value

ROE=(26000*(1-0.2)-150000*0.08)*(1-0)/90000

ROE=9.78

Normal

ROE = (EBIT-debt*interest%)*(1-tax rate)/new market value

ROE=(26000-150000*0.08)*(1-0)/90000

ROE=15.56

Expansion

ROE= (EBIT*(1+growth impact%)-debt*interest %age)*(1-tax rate)/new market value

ROE=(26000*(1+0.18)-150000*0.08)*(1-0)/90000

ROE=20.76

b-2

%age change in ROE for Recession

=(ROE recession/ROE normal-1)*100

=(0.0978/0.1556-1)*100

=-37.15%

%age change in ROE for Growth

=(ROE Growth/ROE normal-1)*100

=(0.2076/0.1556-1)*100

=33.42%

c-1

ROE = EBIT*(1-tax rate)/Market value

Recession

ROE = EBIT*(1-recession impact%)*(1-tax rate)/market value

ROE=26000*(1-0.2)*(1-0.35)/240000

ROE=5.63

Normal

ROE = EBIT*(1-tax rate)/Market value

ROE=26000*(1-0.35)/240000

ROE=7.04

Expansion

ROE = EBIT*(1+Growth impact%)*(1-tax rate)/Market value

ROE=26000*(1+0.18)*(1-0.35)/240000

ROE=8.31

c-2

%age change in ROE for Recession

=(ROE recession/ROE normal-1)*100

=(0.0563/0.0704-1)*100

=-20%

%age change in ROE for Growth

=(ROE Growth/ROE normal-1)*100

=(0.0831/0.0704-1)*100

=18.04%

c-3

New market value = old market value-debt

=240000-150000

=90000

ROE = (EBIT-debt*interest%)*(1-tax rate)/new market value

Recession

ROE = (EBIT*(1-recession impact%)-debt*interest %age)*(1-tax rate)/new market value

ROE=(26000*(1-0.2)-150000*0.08)*(1-0.35)/90000

ROE=6.36

Normal

ROE = (EBIT-debt*interest%)*(1-tax rate)/new market value

ROE=(26000-150000*0.08)*(1-0.35)/90000

ROE=10.11

Expansion

ROE= (EBIT*(1+growth impact%)-debt*interest %age)*(1-tax rate)/new market value

ROE=(26000*(1+0.18)-150000*0.08)*(1-0.35)/90000

ROE=13.49

c-4

%age change in ROE for Recession

=(ROE recession/ROE normal-1)*100

=(0.0636/0.1011-1)*100

=-37.09%

%age change in ROE for Growth

=(ROE Growth/ROE normal-1)*100

=(0.1349/0.1011-1)*100

=33.43%