Question

(EPS with Convertible Bonds, Various Situations) In 2016, Chirac Enterprises issued, at par, 60 \(1,000, 8% bonds, each convertible into 100 shares of common stock. Chirac had revenues of \)17,500 and expenses other than interest andtaxes of $8,400 for 2017. (Assume that the tax rate is 40%.) Throughout 2017, 2,000 shares of common stock were outstanding; none of the bonds was converted or redeemed.

Instructions

a) Compute diluted earnings per share for 2017.

b) Assume the same facts as those assumed for part (a), except that the 60 bonds were issued on September 1, 2017 (rather than in 2016), and none have been converted or redeemed. Compute diluted earnings per share for 2017.

c) Assume the same facts as assumed for part (a), except that 20 of the 60 bonds were actually converted on July 1, 2017. Compute diluted earnings per share for 2017.

Short answer

Diluted earnings per share

a) $0.6825

b) $1.365

c) $0.6825

Step-by-step solution

Meaning of Earnings per Share

Earnings per share is a profitability metric used by the investors that shows the part of the company's profits to be distributed to each share of common stock.

Calculation of diluted earnings per share for 2017 for part a

$\begin{array}{c}\mathbf{Diluted}\mathbf{earnings}\mathbf{per}\mathbf{share}\mathbf{=}\frac{\mathbf{Net}\mathbf{income}\mathbf{+}\mathbf{Interest}\mathbf{\left(}\mathbf{Net}\mathbf{of}\mathbf{tax}\mathbf{\right)}}{\mathbf{Weighted}\mathbf{number}\mathbf{of}\mathbf{shares}\mathbf{outstanding}\mathbf{+}\mathbf{Potentially}\mathbf{dilutive}\mathbf{common}\mathbf{shares}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{2}\mathbf{,}\mathbf{580}\mathbf{+}\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{800}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{40}\mathbf{)}}{\mathbf{2000}\mathbf{+}\mathbf{6000}}\\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{6825}\end{array}$

Working note:

Computation of Net Income

Net Income	$17,500
Less: Other than Interest	$8,400
Less: Bond Interest$\mathbf{(}\mathbf{60}\mathbf{\times }\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{\%}\mathbf{)}$	$4,800
Income before interest and taxes	$4,300
Less: Tax @40%	$1,720
Net Income	$2,580

Step 3:Calculation of diluted earnings per share for 2017 for part b

$\begin{array}{c}\mathbf{D}\mathbf{i}\mathbf{l}\mathbf{u}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{e}\mathbf{a}\mathbf{r}\mathbf{n}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{s}\mathbf{p}\mathbf{e}\mathbf{r}\mathbf{s}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{=}\frac{\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}\mathbf{+}\mathbf{I}\mathbf{n}\mathbf{t}\mathbf{e}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{t}\mathbf{\left(}\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{o}\mathbf{f}\mathbf{t}\mathbf{a}\mathbf{x}\mathbf{\right)}}{\mathbf{W}\mathbf{e}\mathbf{i}\mathbf{g}\mathbf{h}\mathbf{t}\mathbf{e}\mathbf{d}\mathbf{n}\mathbf{u}\mathbf{m}\mathbf{b}\mathbf{e}\mathbf{r}\mathbf{o}\mathbf{f}\mathbf{s}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{o}\mathbf{u}\mathbf{t}\mathbf{s}\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{d}\mathbf{i}\mathbf{n}\mathbf{g}\mathbf{+}\mathbf{P}\mathbf{o}\mathbf{t}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{i}\mathbf{a}\mathbf{l}\mathbf{l}\mathbf{y}\mathbf{d}\mathbf{i}\mathbf{l}\mathbf{u}\mathbf{t}\mathbf{i}\mathbf{v}\mathbf{e}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{m}\mathbf{o}\mathbf{n}\mathbf{s}\mathbf{h}\mathbf{a}\mathbf{r}\mathbf{e}\mathbf{s}}\\ \mathbf{=}\frac{\mathbf{\$}\mathbf{4}\mathbf{,}\mathbf{500}\mathbf{+}\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{600}\mathbf{(}\mathbf{1}\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{40}\mathbf{)}}{\mathbf{2000}\mathbf{+}\mathbf{(}\mathbf{6000}\mathbf{\times }\frac{\mathbf{4}}{\mathbf{12}}\mathbf{)}}\\ \mathbf{=}\mathbf{1}\mathbf{.}\mathbf{365}\end{array}$

Working note:

Computation of Net Income

Net Income	$17,500
Less: Other than Interest	$8,400
Less: Bond Interest$\mathbf{(}\mathbf{60}\mathbf{\times }\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{\%}\mathbf{\times }\frac{\mathbf{4}}{\mathbf{12}}\mathbf{)}$	$1,600
Income before interest and taxes	$7,500
Less: Tax @40%	$3,000
Net Income	$4,500

Calculation of diluted earnings per share for 2017 for part c

Working note:

Computation of Net Income

Net Income	$17,500
Less: Other than Interest	$8,400
Less: Bond Interest$\mathbf{[}\mathbf{(}\mathbf{60}\mathbf{\times }\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{\%}\mathbf{\times }\frac{\mathbf{6}}{\mathbf{12}}\mathbf{)}\mathbf{+}\mathbf{(}\mathbf{40}\mathbf{\times }\mathbf{\$}\mathbf{1}\mathbf{,}\mathbf{000}\mathbf{\times }\mathbf{8}\mathbf{\%}\mathbf{\times }\frac{\mathbf{6}}{\mathbf{12}}\mathbf{)}\mathbf{]}$	$4,000
Income before interest and taxes	$5,100
Less: Tax @40%	$2,040
Net Income	$3,060