Earnings per Share

Question 1

Basic earnings per share

Answer 1

=net inc available to common shareholders (which is NI-pref. shares declared)/weighted avg common shares outstanding

If preferred stock is cumulative, then it must always be subtracted from NI in order to find BEPS

To find the weighted avg CS, take the CS outstanding at each transaction time listed in question multiplied by the number of months out of 12. So if the transaction was in March it would be 3/12; for June 6/12; for Sept 3/12. Once you multiply the CS by the months fraction add them together.

Question 2

Diluted earnings per share w/ convertible bonds

Answer 2

First find basic earnings per share.
Then determine if the convertible element is dilutive.
Calc to find dilutive elements:
1.Calculate:
Numerator: int on bonds x (1 - the tax rate)/
Denominator: #of shares of converted shares.
If less than basic EPS, then they are dilutive.

Ex. NI of $1M, with 100k common shares outstanding, and 50k nonconvertible preferred stock. Declared a $3 per share div on preferred stock. Convertible bond with total face val of $500k at 4%. Each $10k of bonds convertible to 50 common shares. Tax rate is 35%.

1. Basic EPS:
   Numerator: $1M - (50k x $3) = $850k
   Denominator: 100k
   Basic EPS = $850k / 100k = $8.50
2. Numerator: ($500k x 4%) x (1-35%) = $13k
   Denominator: $500k face val/ $10k = 2,500 bonds x 50shares = 2,500 convertible shares
   EPS effect: $13k / 2.5k = $5.20
   The EPS effect is less than the basic EPS, so they are dilutive.
3. Apply dilutive effect elements to basic EPS equation parts.
   Numerator: $850k + $13k = $863k
   Denominator: 100k + 2.5k = 102.5k
   Diluted EPS = $863k / 102.5k = $8.42

Question 3

Diluted earnings per share w/ stock options

Answer 3

In DEPS for stock options, the assumption is the company will use the money received for the options to purchase treasury stock.

First find basic earnings per share.
Then determine if the convertible element is dilutive.
Calc to find dilutive elements:
1.Calculate: Find # of treasury shares company “buys back”
Numerator: #of outstanding options x $option purchase price
Denominator: average mkt stock price
2.Calculate: Diluted earnings per share
Numerator: Basic EPS NI
Denominator: Common stock outstnd + converted stk options - treasury shares.

Ex. NI of $800k, with 190k common shares outstanding, and $70k cash div on nonconvertible preferred stock. 20K of stock options outstanding at $2 each for one share of CS. Avg price of stock for year was $8. Tax rate is 20%.

1. Basic EPS:
   Numerator: $800k - $70k = $730k
   Denominator: 190k
   Basic EPS = $730k / 190k = $3.84
2. Treasury Stock:
   Numerator: 20k x $2 = $40k
   Denominator: $8
   TS = $40k / $8 = 5k shares
3. Diluted EPS:
   Numerator: $730k
   Denominator: 190k + 20k - 5k = 205k
   Diluted EPS = $730k / 205k = $3.56