Question

RAK, Inc., has no debt outstanding and a total market value of $140,000. 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 12 percent higher. If there is a recession, then EBIT will be 30 percent lower. RAK is considering a $115,000 debt issue with an interest rate of 6 percent. The proceeds will be used to repurchase shares of stock. There are currently 7,000 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

ROE = NI/E

a1)

	Recession(-30%)	Normal	Expansion(+12%)
EBIT=NI	$32,000(1 - 0.3) = $22,400	$32,000	$32,000(1 + 0.12) = $35,840
Equity	$140,000	$140,000	$140,000
ROE	$22,400/$140,000 = 0.16, or 16%	$32,000/$140,000 = 0.2286, or 22.86%	$35,480/$140,000 = 0.256, or 25.6%

a2). Sensitivity Analysis: Normal to Recession

%?ROE = (.16 - .2286)/.2286 = -.30 or -30%

Sensitivity Analysis: Normal to Expansion

%?ROE = (.256 - .2286)/.2286 = .12 or 12%

b1). If the firm goes forward with recapitalization, the new equity value will be:

Equity = $140,000 - $115,000 = $25,000

Interest = $115,000 x 6% = $6,900

	Recession(-30%)	Normal	Expansion(+12%)
EBIT	$22,400	$32,000	$35,840
Less: Interest	$ 6,900	$ 6,900	$ 6,900
NI	$15,500	$25,100	$28,940
Equity	$25,000	$25,000	$25,000
ROE	$15,500/$25,000 = 0.62, or 62%	$25,100/$25,000 = 1.004, or 100.40%	$28,940/$25,000 = 1.1576, or 115.76%

b2). Sensitivity Analysis: Normal to Recession

%?ROE = (.62 - 1.004)/1.004 = -.3825 or -38.25%

Sensitivity Analysis: Normal to Expansion

%?ROE = (1.1576 - 1.004)/1.004 = .1530 or 15.30%

c1).

Recession Normal Expansion

EBIT $22,400 $32,000 $35,840

Less:Taxes(@35%) 7,840 11,200 12,544

NI $14,560 $20,800 $23,296

ROE 0.104 0.1486 0.1664

c2). Sensitivity Analysis: Normal to Recession

%?ROE = (.104 - .1486)/.1486 = -.3001 or -30%

Sensitivity Analysis: Normal to Expansion

%?ROE = (.1664 - .1486)/.1486 = .1198 or 12%

c3). Equity = $140,000 - $115,000 = $25,000

Interest = $115,000 x 6% = $6,900

Recession Normal Expansion

EBIT $22,400 $32,000 $35,840

Less: Interest 6,900 6,900 6,900

EBT $15,500 $25,100 $28,940

Less:Taxes(@35%) 5,425 8,785 10,129

NI $10,075 $16,315 $18,811

ROE 0.403 0.6526 0.75244

c4). Sensitivity Analysis: Normal to Recession

%?ROE = (.403 - .6526)/.6526 = -.3825 or -38.25%

Sensitivity Analysis: Normal to Expansion

%?ROE = (.75244 - .6526)/.6526 = .1530 or 15.30%