Question

Kaelea, Inc., has no debt outstanding and a total market value of $125,000. Earnings before interest and taxes, EBIT, are projected to be $10,400 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 20 percent higher. If there is a recession, then EBIT will be 35 percent lower. Kaelea is considering a $42,000 debt issue with an interest rate of 6 percent. The proceeds will be used to repurchase shares of stock. There are currently 6,250 shares outstanding. Assume Kaelea has a market-to-book ratio of 1.0.

Requirement 1:

(a)	Calculate return on equity, ROE, under each of the three economic scenarios before any debt is issued, assuming no taxes. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	ROE
Recession	%
Normal	%
Expansion	%

(b)	Calculate the percentage changes in ROE when the economy expands or enters a recession, assuming no taxes. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	%?ROE
Recession	%
Expansion	%

Requirement 2:

Assume the firm goes through with the proposed recapitalization and no taxes.

(a)	Calculate return on equity, ROE, under each of the three economic scenarios after the recapitalization. (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

	ROE
Recession	%
Normal	%
Expansion	%

(b)	Calculate the percentage changes in ROE for economic expansion and recession. (Do not roundintermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	%?ROE
Recession	%
Expansion	%

Requirement 3:

Assume the firm has a tax rate of 35 percent.

(a)

Calculate return on equity, ROE, under each of the three economic scenarios before any debt is issued. Also, calculate the percentage changes in ROE for economic expansion and recession. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign.Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	ROE
Recession	%
Normal	%
Expansion	%

	%?ROE
Recession	%
Expansion	%

(b)

Calculate return on equity, ROE, under each of the three economic scenarios after the recapitalization. Also, calculate the percentage changes in ROE for economic expansion and recession, assuming the firm goes through with the proposed recapitalization. (Do not round intermediate calculations. Negative amounts should be indicated by a minus sign. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	ROE
Recession	%
Normal	%
Expansion	%

	%?ROE
Recession	%
Expansion	%

Answer 1

Requirement 1 - no debt and no taxes

a) Since market to book ratio is 1, Market value of firm = Book value of firm

Also, as their is no debt currently, Equity = book value of Equity = $125,000

ROE

Particulars	Normal	Expansion	Recession
EBIT	10400	10,400 x (1 + 0.20) = 12480	10,400 x (1 - 0.35) = 6760
Less: Interest	0	0	0
EBT	10400	12480	6760
Less: Tax	0	0	0
Net Income (a)	10400	12480	6760
Equity (b)	125000	125000	125000
ROE [ (a / b) x 100 ]	8.32%	9.984% or 9.98%	5.408% or 5.41%

b) Change in ROE in case of expansion = (9.984% - 8.32%) / 8.32% = 0.2 or 20.00%

Change in ROE in case of recession = (5.408% - 8.32%) / 8.32% = (-)0.35 or (-)35.00%

Requirement 2 - Debt issued but no taxes

Now, Debt to be issued = $42000

New Value of Equity = $125000 - $42000 = $83000

a)

ROE

Particulars	Normal	Expansion	Recession
EBIT	10400	10,400 x (1 + 0.20) = 12480	10,400 x (1 - 0.35) = 6760
Less: Interest (42000 x 6%)	2520	2520	2520
EBT	7880	9960	4240
Less: Tax	0	0	0
Net Income (a)	7880	9960	4240
Equity (b)	83000	83000	83000
ROE [ (a / b) x 100 ]	9.493975903% or 9.49%	12.00%	5.108433734% or 5.11%

b) Change in ROE in case of expansion = (12% - 9.493975903%) / 9.493975903% = 0.26396 or 26.40%

Change in ROE in case of recession = (5.108433734% - 9.493975903%) / 9.493975903% = (-)0.46193 or (-)46.19%

Requirement 3

a) No debt and tax @35%

ROE

Particulars	Normal	Expansion	Recession
EBIT	10400	10,400 x (1 + 0.20) = 12480	10,400 x (1 - 0.35) = 6760
Less: Interest	0	0	0
EBT	10400	12480	6760
Less: Tax@35%	3640	4368	2366
Net Income (a)	6760	8112	4394
Equity (b)	125000	125000	125000
ROE [ (a / b) x 100 ]	5.408% or 5.41%	6.4896% or 6.49%	3.5152% or 3.52%

Change in ROE in case of expansion = (6.4896% - 5.408%) / 5.408% = 0.20 or 20.00%

Change in ROE in case of recession = (3.5152% - 5.408%) / 5.408% = (-)0.35 or (-)35.00%

b) Debt issued and tax @35%

ROE

Particulars	Normal	Expansion	Recession
EBIT	10400	10,400 x (1 + 0.20) = 12480	10,400 x (1 - 0.35) = 6760
Less: Interest (42000 x 6%)	2520	2520	2520
EBT	7880	9960	4240
Less: Tax@35%	2758	3486	1484
Net Income (a)	5122	6474	2756
Equity (b)	83000	83000	83000
ROE [ (a / b) x 100 ]	6.171084337% or 6.17%	7.80%	3.320481927% or 3.32%

Change in ROE in case of expansion = (7.80% - 6.171084337%) / 6.171084337% = 0.263959 or 26.40%

Change in ROE in case of recession = (3.320481927% - 6.171084337%) / 6.171084337% = (-)0.46193 or (-)46.19%