Question

Problem 14-3 ROE and Leverage

Beckett, Inc., has no debt outstanding and a total market value of $240,000. Earnings before interest and taxes, EBIT, are projected to be $32,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 15 percent higher. If there is a recession, then EBIT will be 30 percent lower. Beckett is considering a $80,000 debt issue with an interest rate of 7 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 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. (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent.)

  

	% 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 and round your final answers 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.)

  

	% 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. 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

a-1).

Normal EBIT = $32,000

Since, there is no debt and no taxes (as questions states to ignore taxes for part a & b), then EBIT will be Net Income.

Return on Equity(ROE) = Net Income/Shareholder's Equity

Shareholder's Equity = $240,000

Normal ROE = 32000/240000

= 13.33%

-- EBIT will increase when economy expands = 15%

Expanded EBIT = 32000(1+0.15)

= $ 36,800

Expanded ROE = 36800/240000

= 15.33%

-- EBIT will decrease when economy comes in recession = 30%

Expanded EBIT = 32000(1-0.30)

= $ 22,400

Expanded ROE = 22400/240000

= 9.33%

ROE
Recession	9.33 %
Normal	13.33 %
Expansion	15.33 %

a-2). Calculating the percentage changes in ROE when the economy expands or enters a recession:-

-- When economy expands = [(ROE in Expansion - ROE in Normal)/ROE in Normal]*100

= [(15.33-13.33)/13.33]*100

= 15%

-- When economy enters recession = [(ROE in Recession - ROE in Normal)/ROE in Normal]*100

   = [(9.33-13.33)/13.33]*100

= -30%

% change in ROE
Recession	-30%
Expansion	15%

b-1). Calculating the return on equity (ROE) under each of the three economic scenarios when firm goes through with the proposed recapitalization:-

Particular	Expansion (amt in $)	Normal(amt in $)	Recession (amt in $)
EBIT	36,800	32,000	22,400
Less: Interest (80,000*7%)	(5600)	(5600)	(5600)
EBT	31200	26400	16800
Less: Tax@0%	0	0	0
Net Income (a)	31200	26400	16800
Shareholder's Equity ($240,000-$80,000)*	160,000	160,000	160,000
ROE [(a)/(b)]	19.5%	16.5%	10.5%

*- Since the proceeds of Debt is used to repurchase the shares it will decrease the shareholder;s equity.

ROE
Recession	10.5 %
Normal	16.5 %
Expansion	19.5 %

b-2). Calculating the percentage changes in ROE when the economy expands or enters a recession:-

-- When economy expands = [(ROE in Expansion - ROE in Normal)/ROE in Normal]*100

= [(19.5-16.5)/16.5]*100

= 18.18%

-- When economy enters recession = [(ROE in Recession - ROE in Normal)/ROE in Normal]*100

   = [(10.5-16.5)/16.5]*100

= -36.36%

% change in ROE
Recession	-36.36%
Expansion	18.18%

Now, taking tax rate as 35% to calculate further parts.

c-1). Normal EBIT = $32,000

Since, there is no debt and tax rate is 35%, calculating ROE under three different scenarios:-

Particular	Expansion (amt in $)	Normal(amt in $)	Recession (amt in $)
EBIT	36,800	32,000	22,400
Less: Interest	0	0	0
EBT	36800	32000	22400
Less: Tax@35%	(12880)	(11200)	(7840)
Net Income (a)	23920	20800	14560
Shareholder's Equity	240000	240000	240000
ROE [(a)/(b)]	9.97%	8.67%	6.07%

ROE
Recession	6.07 %
Normal	8.67%
Expansion	9.97 %

c-2). Calculating the percentage changes in ROE when the economy expands or enters a recession:-

-- When economy expands = [(ROE in Expansion - ROE in Normal)/ROE in Normal]*100

= [(9.97-8.67)/8.67]*100

= 15%

-- When economy enters recession = [(ROE in Recession - ROE in Normal)/ROE in Normal]*100

   = [(6.07-8.67)/8.67]*100

= -30%

% change in ROE
Recession	-30%
Expansion	15%

c-3). Calculating the return on equity (ROE) under each of the three economic scenarios when firm goes through with the proposed recapitalization:-

Particular	Expansion (amt in $)	Normal(amt in $)	Recession (amt in $)
EBIT	36,800	32,000	22,400
Less: Interest (80,000*7%)	(5600)	(5600)	(5600)
EBT	31200	26400	16800
Less: Tax@35%	(10920)	(9240)	(5880)
Net Income (a)	20280	17160	10920
Shareholder's Equity ($240,000-$80,000)*	160,000	160,000	160,000
ROE [(a)/(b)]	12.68%%	10.73%	6.83%

*- Since the proceeds of Debt is used to repurchase the shares it will decrease the shareholder;s equity.

ROE
Recession	6.83 %
Normal	10.73 %
Expansion	12.68 %

c-4). Calculating the percentage changes in ROE when the economy expands or enters a recession:-

-- When economy expands = [(ROE in Expansion - ROE in Normal)/ROE in Normal]*100

= [(12.68-10.73)/10.73]*100

= 18.18%

-- When economy enters recession = [(ROE in Recession - ROE in Normal)/ROE in Normal]*100

   = [(6.83-10.73)/10.73]*100

= -36.36%

% change in ROE
Recession	-36.36%
Expansion	18.18%

If you need any clarification regarding this solution, then you can ask in comments

If you like my answer then please Up-vote as it will be motivating.