Answer:
a. We have:
EPS under normal = $1.09 per share
EPS under expansion = $1.34 per share
EPS under recession = $0.74 per share
b. We have:
Percentage changes in EPS when the economy expands = 23%
Percentage changes in EPS when the economy enters recession = –32%
c. We have:
EPS under normal after recapitalization = $1.24
EPS under expansion after recapitalization = $1.59 per share
EPS under recession after recapitalization = $0.75 per share
d. We have:
Percentage changes in EPS after recapitalization when the economy expands = 28.23%
Percentage changes in EPS when the economy enters recession = –39.52%
Explanation:
a. Calculate earnings per share, EPS, under each of the three economic scenarios before any debt is issued.
Shares outstanding = 5,400
Net income under normal = EBIT under normal - (EBIT under normal * Tax rate) = $9,800 - ($9,800 * 40%) = $5,880
EPS under normal = Net income under normal / Shares outstanding = $5,880 / 5,400 = $1.09 per share
Net income under expansion = (EBIT under normal * (100% + Percentage increase in EBIT)) - ((EBIT under normal * (100% + Percentage increase in EBIT)) * Tax rate) = ($9,800 * (100% + 23%)) – (($9,800 * (100% + 23%))* 40%) = $7,232.40
EPS under expansion = Net income under expansion / Shares outstanding = $7,232.40 / 5,400 = $1.34 per share
Net income under recession = (EBIT under normal * (100% - Percentage decrease in EBIT)) - ((EBIT under normal * (100% - Percentage decrease in EBIT)) * Tax rate) = ($9,800 * (100% - 32%)) – (($9,800 * (100% - 32%))* 40%) = $3,998.40
EPS under recession = Net income under recession / Shares outstanding = $3,998.40 / 5,400 = $0.74 per share
b. Calculate the percentage changes in EPS when the economy expands or enters a recession.
Percentage changes in EPS when the economy expands = ((EPS under expansion - EPS under normal) / EPS under normal) * 100 = (($1.34 - $1.09) / $1.09) * 100 = 23%
Percentage changes in EPS when the economy enters recession = ((EPS under recession - EPS under normal) / EPS under normal) * 100 = (($0.74 - $1.09) / $1.09) * 100 = –32%
c. Calculate earnings per share, EPS, under each of the three economic scenarios after the recapitalization.
Market price per share = Total market value / Shares outstanding before recapitalization = $81,000 / 5,400 = $15
Number of shares to repurchase = Debt amount / Market price per share = $23,100 / $15 = 1,540
Shares outstanding after recapitalization = Shares outstanding before recapitalization - Number of shares to repurchase = 5,400 – 1,540 = 3,860
Interest on debt = Debt amount * Interest rate = $23,100 * 8% = $1,848
Net income under normal after recapitalization = EBIT under normal – Interest on debt - ((EBIT under normal – Interest on debt) * Tax rate) = $9,800 - $1,848 - (($9,800 - $1,848) * 40%) = $4,771.20
EPS under normal after recapitalization = Net income under normal after recapitalization / Shares outstanding after recapitalization = $4,771.20 / 3,860 = $1.24
EBIT under expansion = EBIT under normal * (100% + Percentage increase in EBIT) = ($9,800 * (100% + 23%)) = $12,054
Net income under expansion after recapitalization = EBIT under expansion – Interest on debt – ((EBIT under expansion – Interest on debt) * Tax rate) = $12,054 - $1,848 - (($12,054 - $1,848) * 40%) = $6,123.60
EPS under expansion after recapitalization = Net income under expansion after recapitalization / Shares outstanding after recapitalization = $6,123.60 / 3,860 = $1.59 per share
EBIT under recession = EBIT under normal * (100% - Percentage decrease in EBIT) = ($9,800 * (100% - 32%)) = $6,664
Net income under recession after recapitalization = EBIT under recession – Interest on debt – ((EBIT under recession – Interest on debt) * Tax rate) = $6,664 - $1,848 - (($6,664 - $1,848) * 40%) = $2,889.60
EPS under recession after recapitalization = Net income under recession after recapitalization / Shares outstanding after recapitalization = $2,889.60 / 3,860 = $0.75 per share
d. Calculate the percentage changes in EPS when the economy expands or enters a recession.
Percentage changes in EPS after recapitalization when the economy expands = ((EPS under expansion after recapitalization - EPS under normal after recapitalization) / EPS under normal after recapitalization) * 100 = (($1.59 - $1.24) / $1.24) * 100 = 28.2%
Percentage changes in EPS when the economy enters recession = ((EPS under recession - EPS under normal) / EPS under expansion) * 100 = (($0.75 - $1.24) / $1.24) * 100 = –39.52%
