1. finance
2. investing
3. options

Earnings Per Share (EPS)
RCJ Chapter 15
(836-842)
Key Issues
1.
2.
3.
4.
5.
6.
7.
8.
Basic EPS
Weighted average common shares
Pecking order
Treasury stock transactions
Dilution
Diluted EPS
options and warrants: treasury stock method
Convertible bonds and preferred stock: if converted
method
9. Determining dilution vs anti-dilution
Paul Zarowin
2
Basic EPS
Basic EPS 


Net income - Preferred dividends
Weighted average number of common stock outstandin g
weight shares outstanding by fraction of year;
changes due to share repos, issuances, option
exercises, etc..
Paul Zarowin
3
Basic EPS - Example

On January 1, 2001 Solomon Corporation had:





160,000 common shares outstanding.
10,000 preferred shares, $100 par value, 7%
On September 1, 2001 the company issued 40,000
additional common shares.
The net income for 2001: $1,257,331
What is the basic EPS?
Preferred dividends = 10,000 x 100 x0.07 = $70,000
(a) Shares (b) Portion Weighted shares
Time span
outstanding of year
(col. a x col. b)
Jan 1 - Aug 31
160,000
2/3
106,667
Sep1 - Dec 31
200,000
1/3
66,667
173,333
Basic EPS 
$1,257,331 - $70,000
 $6.85 per share
173,334 shares
4
Basic EPS (cont’d)
EPS is from common shareholders’ viewpoint
Pecking order of suppliers of capital:
1. Debt holders
2. Preferred stock holders
3. Common stock holders

Why are preferred dividends subtracted, but not
bond interest?
Ex. E15-14; P15-4
Paul Zarowin
5
Effect of Treasury Stock Transactions
1. Purchase of treasury shares:
DR Treasury stock (contra O/E A/C)
CR
Cash
2. resale of treasury shares:
or
DR Cash
DR APC
CR
CR
Treasury stock (at cost, from 1.)
APC
DR (or CR) to APC is economic loss (or gain) that is not
recognized in accounting
Paul Zarowin
6
Effect of Treasury Stock Transactions (cont’d)
Key point:
Transactions in own common stock don’t affect NI
(proprietary viewpoint), only affect number of shares
outstanding; so firms can manipulate EPS
Q:How does transaction timing during the year affect
EPS?
Ex. E15-16; P15-8
Paul Zarowin
7
Diluted EPS

SFAS No. 128 requires companies with complex capital
structures to compute another measure called diluted
earnings per share.
Diluted EPS =
Income adjustments due to
Net income - Preferred dividends + dilutive financial instruments
Weighted average number of
common shares outstanding

+
Newly issuable shares due to
dilutive financial instruments
(1) Options; and (2) Convertible securities can:
Only dilutive securities
 Decrease EPS  dilutive
are included in the diluted
 Increase EPS  anti-dilutive
EPS calculation
Paul Zarowin
8
Conversion Ratio
Conversion ratio =
Income adjustments due to
dilutive financial instruments
Newly issuable shares due to
dilutive financial instruments

The dilutive effect of financial instruments (for
example, options warrants, and convertible bonds)
on EPS is calculated starting with the instrument with
the lowest conversion rate (i.e. most dilutive), and
working up to the instrument with the highest
conversion rate (i.e. least dilutive).
Paul Zarowin
9
Step 1: calculate the effect of options and
warrants on EPS

Treasury Method:
Q: Option exercise price < Market price
No
Yes
Options have dilutive effect  include
them in diluted EPS:
1. Assume all options are exercised 
add new shares.
2. Assume proceeds (# shares x
exercise price) are used to repurchase
previously issued common shares 
subtract these shares.
Paul Zarowin
Options do not
have dilutive
effect  not
included in
diluted EPS.
10

Example: Now assume that Solomon Corporation issued
options to buy 20,000 shares of common stock at $100
per share. The market price is $114. What is the diluted
EPS?



Option exercise price 100$ < Market price 114$
Upon full exercise of option  additional 20,000
shares
The proceeds 20,000 X $100 = $2,000,000
are assumed to be used to repurchase previously
issued common shares at the $114 market price.
$2,000,000
 17,544 shares
$114 per share

The dilution effect: 20,000 – 17,544 = 2,456 shares
Diluted EPS 
$1,257,331 - 70,000
 $6.75 per share
173,334  2,456
Step 2: calculate effect of convertible
securities on EPS
‘if-converted method’ (one convertible security)
Increase in EPS denominator: calculate additional shares under
full conversion.
 Increase in EPS numerator: Calculate increase in net income if
interest had not been paid on the convertible bonds/preferred
shares.
increase in (after tax ) net income
 Diluted EPS After step 1
Conversion ratio=
# shares converted

Yes
Dilutive effect: Add increase
in numerator and Denominator to
Dilutive EPS.
No
No dilutive effect: leave
Dilutive EPS after step 1 as-is.
Paul Zarowin
12

Example cont’: Solomon Corporation also has:




$1,000,000 of 5% convertible bonds, with par (face) value of
$1,000 per bond
Each $1,000 bond pays interest of $50 per year and is
convertible into 10 shares of common stock.
35% tax rate
What is the dilutive EPS now?

Increase in denominator: 1,000 x 10 = 10,000 shares

Increase in numerator: 1000 x $50 x (1-0.35)=$32,500
32,500
 3.25  6.75
10,000
Diluted EPS 
$1,257,331 - 70,000  32,500
 $6.57 per share
173,334  2,456  10,000
Summary of example
Basic EPS = $6.85
(slide #4)
1. After considering effect of
options = $6.75
(slide #11)
2. After considering effect of
convertible bonds = $6.57
(slide #13)
Q: Why does dilution effect of options always come before convertibles?
Paul Zarowin
14
If converted method with multiple
convertible securities
Rank all convertible securities by conversion ratio; take
convertible with lowest conversion ratio*
For the chosen convertible security check:
increase in (after tax ) net income
 Diluted EPS After step 1
# shares converted
Yes: Dilutive
No: Anti-dilutive
Calculate New EPS
Stop
Take the convertible with the
next lowest conversion ratio
* Options have lower conversion ratio, therefore come before convertibles.
Paul Zarowin
15
Exercises

E15-14

P15-4

P15-12
Paul Zarowin
16