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Module 18
Earnings per Share
Simple and Complex Capital Structure
Companies are required to disclose earnings per share (EPS), is perhaps the most
important measure investors use to evaluate the performance of a business.
The calculation and reporting of EPS is governed by Statement of Financial Accounting
Standard. It requires companies to calculate two EPS numbers:
 Basic.
 Diluted.
Companies are classified as having a simple or a complex capital structure. A company
has a simple capital structure if it has only common stock outstanding or has no other
securities that can be converted into common stock. In contrast, if a company has any
of the following securities, it has a complex capital structure:
 Convertible preferred stock
 Convertible bonds
 Stock options
 Other securities that can be converted into common stock.
These types of securities can be dilutive securities because they can reduce the EPS
when additional common stock must be issued upon conversion of these securities.
Basic Earnings per Share
All companies must report basic EPS for each comparative income statement presented.
Basic EPS is calculated as follows:
(Net income – Preferred dividends) / Weighted average number of common shares
outstanding
Note that the numerator measures the earnings available to common stockholders.
Furthermore, if the company has noncumulative preferred stock, it deducts only the
dividends declared during a period (if no dividends are declared for noncumulative
preferred stock in the year, they need not be paid in future years and hence do not
represent an obligation related to the current year). If the company has cumulative
preferred stock, however, the dividends for the preferred stock must be deducted
whether they are declared or not (because the arrears must be paid in future years).
The denominator measures the weighted average number of shares outstanding. If a
company has not issued new shares (including any stock splits or stock dividends) or
purchased treasury stock during the period, the denominator is simply the number of
shares outstanding at the beginning of the period.
Weighted Average Number of Shares
If a company issues new shares (for cash or other consideration) during a year, such
shares are weighted only for the part of the year they are outstanding. Thus, if a
company has 10,000 shares outstanding at the beginning of the year and issues an
additional 1,000 shares on October 1, the weighted average number of shares is
calculated as follows:
10,000 shares for full year + 1,000 shares for a quarter of the year
10,000 + (0.25)(1,000) = 10,250
Another way to calculate the weighted average shares outstanding is as follows:
From nine months -January 1 to September 30- the company had 10,000 shares.
For three months -October 1 to December 31- the company had 11,000 shares. Thus,
the number of weighted average shares is calculated as follows:
10,000 x (9/12) + 11,000 x (3/12) = 10,250
To calculate weighted average shares, a table can be set up as follows:
Actual Shares
Fraction of Year
Period
Outstanding
Outstanding
Equivalent Whole Units
A
B
C
D=BxC
1/1 to 9/30
10,000
9/12
10,000 x (9/12) = 7,500
10/1 to 12/31
11,000
3/12
11,000 x (3/12) = 2,750
Total
10,250
Similar calculations are performed when a company purchases treasury stock during a
year.
Weighted Average Shares – Stock Splits and Stock Dividends
When the number of shares outstanding changes during a year as the result of a stock
split or stock dividend, a retroactive recognition of this change is made. That is, the
stock split or stock dividend is assumed to have occurred at the beginning of the period.
Thus, all shares outstanding during the period from the beginning of the year to the date
of the stock split or dividend are multiplied by the appropriate split factor or dividend
percentage.
Example
Garcia Company had 10,000 shares outstanding on January 1, 2002. The following
transactions occurred during the year:
April 1
Issued an additional 2,000 shares to the public
July 1
2-for-1 stock split
October 1
Purchased 3,000 shares as treasury stock
December 1
20% stock dividend
In this example, the stock split and the stock dividend are assumed to have occurred on
January 1, although the 20% stock dividend did not occur until December 1. The impact
of the stock dividend is that where previously there was one share, now there will be 1.2
shares. Thus, the dividend factor is 1.2. For all transactions before December 1, the
company multiplies the number of shares by a factor of 1.2.
In addition, the impact of the stock split is that where previously there was one share,
now there will be two shares. Thus, the split factor is 2. For all transactions before July
1, the company multiplies the number of shares by a factor of 2.
These two steps imply that for numbers of stock before July 1, the company multiplies
the number of shares by both the split factor and the dividend factor– that is, by both 1.2
and 2, giving a factor of 2.4. The total weighted average number of shares outstanding is
calculated as follows:
Period
A
1/1 to 3/31
4/1 to 6/30
7/1 to 9/30
10/1 to 11/30
12/1 to 12/31
Total
Actual Shares
Outstanding
B
10,000
12,000
24,000
21,000
25,200
Multiplication
Factor
C
1.2 x 2 = 2.4
1.2 x 2 = 2.4
1.2
1.2
1
Fraction of Year
Outstanding
D
3/12
3/12
3/12
2/12
1/12
Equivalent
Whole Units
E=BxCxD
6,000
7,200
7,200
4,200
2,100
26,700
Review Question 1
1. If a company has common stock and nonconvertible preferred stock, it has a _____
capital structure.
2. If a company has convertible bonds, it has a ________ capital structure.
3. To calculate the numerator for EPS, _____ are subtracted from net income.
4. If a company has _______ preferred stock, it subtracts the dividends only when they
are declared (to calculate the EPS).
5. If a company has experienced a _______ during the year, a retroactive approach is
used to calculate the weighted average number of shares outstanding.
Answers
1. simple
4. noncumulative
2. complex
5. stock split
3. preferred dividends
Diluted EPS–Options
The holder of the option has the right to purchase stock at a set price in the future. If the
option can be exercised at a price lower than the market price, the option is valuable
because stock can be purchased at the lower option price and then sold at the higher
market price. The option price is called the exercise price or strike price.
The exercise of an option does not change the reported net income. However, it can
change the denominator of the EPS calculation (by changing the number of shares).
The treasury stock method is used to calculate the change in the number of shares.
This method assumes that the cash received from option holders is used to buy back
treasury stock. Thus, the number of shares both increase and decrease. They increase
when the options are exercised and new shares are issued; they decrease when the
cash received from the exercise of options is used to buy back treasury shares.
Note the following:
 The total cash proceeds from the exercise of options are calculated based on all
outstanding options and the relevant prices of all such options (different options may
have different exercise prices).
 The relevant price used to calculate the purchase of treasury shares (using the
options’ proceeds) is the average market price.
 Neither of these two transactions actually happens, but both are assumed to happen
solely for the purpose of calculating EPS.
If the option price is less than the average market price, the number of shares issued is
greater than the number of shares bought back. Thus, the number of shares
outstanding will increase.
Example
Smith Company had 20,000 shares outstanding throughout the year ending December
31, 2002. During the year, the company also had 2,000 options with an exercise price of
$20. The average market price was $25. Calculate the number of shares outstanding for
EPS calculations.
Cash proceeds from assumed exercise of options = $20 x 2,000 = $40,000
Number of treasury shares that can be bought back = $40,000/$25 = 1,600
Thus,
Number of new shares issued = 2,000
Number of new treasury shares purchased back = 1,600
Hence, there is a net increase of 400 shares, so the average number of shares
outstanding for the year is 20,000 + 400, or 20,400.
If the option price is higher than the average market price, the options are considered
antidilutive and will not be used to calculate the average number of shares outstanding.
If the company has a loss for the period, the options are ignored because the reported
loss per share will be lower if the options are included in the calculation.
Diluted EPS–Convertible Securities
If a company has convertible preferred stock or convertible bonds, the “if converted”
method is used to calculate diluted EPS. This method assumes that the convertible
securities have been converted.
The effect of using the if-converted method for convertible preferred stock is as follows:


Because the securities have been converted to common stock, there is no need to
pay the preferred dividend. Thus, the numerator of the EPS ratio increases.
Remember that in the numerator for EPS, the preferred dividend is subtracted from
the net income because the preferred dividend need not be subtracted.
Furthermore, the conversion results in an increase in both the number of shares
outstanding and the denominator of the EPS ratio.
The effect of using the if-converted method for convertible bonds is as follows:
 Because the securities have been converted to common stock, there is no need to
pay the interest on the bonds. Thus, interest expense decreases and net income
increases. This, in turn, means that the numerator of the EPS ratio increases.
 Furthermore, the conversion results in an increase in both the number of shares
outstanding and the denominator of the EPS ratio.
Thus, under the if-converted method, both the numerator and the denominator of the
EPS ratio increase. The EPS is calculated assuming conversion. If the effect of including
the convertible securities results in a dilution of EPS, the lower number is reported as
diluted EPS.
For convertible bonds, note the following:
 Interest expense, not cash interest paid, is the significant factor. This becomes
relevant if the bonds have been issued at a discount or premium.
 Interest is tax deductible. Thus, net income increases only by the after-tax amount of
the interest expense. For example, assume that interest expense is $1,000 and the
tax rate is 30%. If interest is not paid (because of the assumed conversion of the
bond) the net income before taxes will increase by $1,000. This, in turn, leads to a
$300 ($1,000 x 0.30) increase in tax expense. Hence, the net income after taxes
increases only by $700, or (1 – 0.30) times the interest expense.
Under the if-converted method assumes that the conversion occurred at the beginning of
the earliest period for which the income statement is presented. Thus, if two years’
income statements are reported in comparative financial statements, the conversion
must be assumed for both years. The exception to this rule is that if the actual dilutive
securities are issued at a later date (that is, sometime after the beginning date of the
earliest income statement presented), the conversion is assumed to occur on the day
the securities are issued. Note that for all calculations under the if-converted method,
the conversions are only assumed to have occurred; actual conversion need not occur.
Multiple Dilutive Securities
When multiple potentially dilutive securities exist, some securities that, by themselves
are dilutive, may become antidilutive in combination with other securities. With multiple
potentially dilutive securities, the calculation of diluted EPS proceeds as follows.
Step 1.
Calculate the basic EPS.
Step 2.
Calculate the numerator effect (that is, the iincrease in the earnings available to common
stockholders) and the denominator effect (the increase in the weighted average number
of common shares outstanding) for each potentially dilutive security.
Step 3.
Calculate the ratio of the numerator effect to the denominator effect for each potentially
dilutive security. Call this the impact for each security.
Step 4.
Rank order the results from step 3 in increasing order –start with the lowest number and
go in ascending order.
Step 5.
Calculate the diluted EPS, assuming that only the security with the lowest impact is
converted.
Step 6.
Check the EPS calculated in step 5 with the next lowest impact number. If it is higher
than the revised EPS (calculated in step 5), stop: The security is antidilutive. If the next
lowest impact is lower than the revised EPS, go back to step 5 and assume that this
security has been converted and recalculate the EPS.
Note
A company’s options are always considered first because as long as the exercise price
of an option is lower than the average market price, the average number of shares
outstanding always increases. As noted previously, the numerator effect is zero, and the
denominator effect is positive. Thus, the impact is always zero, and options always lead
to lower EPS (as long as net income is positive).
Example
Hunter Company had net income of $40,000 and basic EPS of $10 for the most recent
fiscal year. The company had some convertible securities and options. The numerator
and denominator effect of these securities are as follows:
Numerator Effect Denominator Effect
Rank for
Security Type
($)
(number of shares)
Ratio
Entry to EPS
A
B
C
D = B/C
Calculations
Convertible
bonds
17,000
2,000
8.50
3
Convertible
preferred stock
2,000
1,000
2.00
2
Options
0
1,000
0.00
Because net income is $40,000 and EPS is $10, the weighted average number of
shares outstanding for the year is $40,000/$10, or 4,000.
Step 1.
Consider the effect of options.
Diluted EPS after options are considered is ($40,000 + 0)/(4,000 + 1,000) or $8
Step 2.
1
Compare the EPS from step 1 to the next lowest ratio in the table.
As convertible preferred stock has a ratio of 2.00, which is lower than the EPS from step
1 ($8), include convertible preferred stock in diluted EPS calculation.
Diluted EPS after convertible preferred stock is considered as
=($40,000 + 0 + $2,000)/(4,000+ 1,000 + 1,000), or $7.
Step 3.
Compare the EPS from step 2 to the next lowest ratio in the table.
As convertible bonds have a ratio of 8.50, which is higher than the EPS from step 1 ($8),
stop. Do not include convertible bonds in diluted EPS calculation because the
convertible bonds have become antidilutive.
Thus, diluted EPS for the year = $7.
Review Question 2
1. The ________ method is used to account for options in diluted EPS calculations.
2. The ________ method is used to account for convertible bonds in diluted EPS
calculations.
3. If the exercise price of options is more than the average market price, the options are
considered to be _______.
4. If a company has reported a loss, options are considered to be ________.
5. When considering convertible preferred stock, the numerator effect equals the amount
of the _______.
Answers
1. treasury stock
4. antidilutive
2. If-converted
5. preferred dividend
3. dilutive
Glossary

Antidilutive security is a security whose inclusion in the EPS calculations leads to a
higher EPS.

Complex capital structure describes a company that has securities (such as
options, convertible preferred stock, or convertible bonds) that can be converted into
common stock.

Dilutive securities are securities whose conversion into common stock reduces the
EPS.

If-converted method assumes that convertible securities have been converted and
accordingly calculates the diluted EPS.

Simple capital structure describes a company that has only common stock
outstanding or no other securities that can be converted into common stock.

Treasury stock method as the method used to account for the effect of options in
calculating diluted EPS. The options are assumed to be exercised, and the
proceeds from such issue of stock assumed to be used to purchase treasury stock.
Demonstration Problem 1
Trevino Company
Trevino Company had 10,000 shares outstanding as of January 1, 2002. The following
transactions took place during 2002:
Date
Event
February 1
2-for-1 stock split
April 1
5,000 new shares issued
July 1
20% stock dividend issued
October 1
Purchased 2,000 shares of treasury stock
Solution to Demonstration Problem 1, Trevino Company
Period
1/1 to 1/31
2/1 to 3/31
4/1 to 6/30
7/1 to 9/30
10/1 to 12/31
Total
Actual
Shares
Outstanding
10,000
20,000
25,000
30,000
28,000
Assumed Shares
Outstanding
10,000 x 2 x 1.2 =
24,000
20,000 x 1.2 = 24,000
25,000 x 1.2 = 30,000
30,000
28,000
Fraction of
Year
1/12
Equivalent
Shares
2,000
2/12
3/12
3/12
3/12
4,000
7,500
7,500
7,000
28,000
Demonstration Problem 2
Williams Company
Williams Company had 20,000 shares of common stock ($1 par value) outstanding as of
January 1, 2002. During the year, the company had the following transactions related to
common stock:
Date
Event
April 1
7,000 new shares issued
July 1
2-for-1 stock split
October 1
Purchased 2,000 shares of treasury stock
The company also had 1,000 shares of 6%, $100 par preferred stock outstanding
through the year and declared and paid preferred dividends. For the year ended
December 31, 2002, the following data are available:
a. Income from continuing operations, $100,000.
b. Extraordinary gain (net of taxes), $20,000.
c. Net income, $120,000.
Calculate the earnings per share for the year ended December 31, 2002.
Solution to Demonstration Problem 2, Williams Company
Step 1.
Calculate the Weighted average number of shares.
Actual Shares
Assumed Shares
Period
Outstanding
Outstanding
1/1 to 3/31
20,000
20,000 x 2 = 40,000
4/1 to 9/30
27,000
27,000 x 2 = 54,000
10/1 to 12/31
52,000
52,000
Total
Fraction of
Year
3/12
6/12
3/12
Equivalent
Shares
10,000
27,000
13,000
50,000
Step 2.
Calculate net income available for common stockholders.
Preferred dividends = 1,000 x 0.06 x $100 = $6,000
Net income available for common stockholders = $120,000 – $6,000 = $114,000
Note: To present the EPS numbers, preferred dividends must be subtracted from all
relevant EPS numbers. As a result, income from continuing operations = $100,000 –
6,000 = $94,000.
Step 3.
Calculate earnings per share.
Income per share from continuing operations = $94,000/50,000 = $1.88
Extraordinary gain per share = $20,000/50,000 = $0.40
Net income per share = $2.28
Demonstration Problem 3
Parker Company
The net income of Parker Company for the year ended December 31, 2002 was
$200,000. The following additional information is available about the company:
a. The weighted average number of shares outstanding during the year was 48,000.
b. During the year, 2,000 shares of $100 par, 4% convertible preferred stock were
outstanding. Each preferred stock is convertible into two shares of common stock.
c. During the year, 500 bonds each of $1,000 face value were outstanding. The bonds
were issued at par, pay 9% interest per year, and are convertible to 20 shares of
common stock.
d. There were 10,000 options outstanding, with an option price of $16 each. The
average market price for the period was $20.
Calculate the basic and diluted earnings per share, assuming that the tax rate for the
Company is 20%. Round your answers to the nearest cent per share.
Solution to Demonstration Problem 3, Parker Company
Step 1.
Calculate the numerator effect, denominator effect, and the ratio of these two for
convertible preferred stock, convertible bonds, and options.
a. Convertible preferred stock
Numerator effect (dividends that need not be paid) = $100 x 0.04 x 2,000 = $8,000
Denominator effect (to be issued upon conversion) = 4,000 shares
b. Convertible bonds
Interest that need not be paid if conversion is assumed = $1,000 x 0.09 x 500 = $45,000
Numerator effect = (1 – tax rate) x $45,000 = (1 – 0.20) x $45,000 = $36,000
Denominator effect (to be issued upon conversion) = 500 x 20 = 10,000 shares
c. Options
Denominator effect for options:
Proceeds from exercising options = $160,000 ($16 x 10,000)
Number of treasury shares assumed to be purchased = $160,000/$20 = 8,000
Thus, increase in number of shares = 2,000
Item
Convertible
preferred stock
Convertible bond
Numerator
Effect
Denominator
Effect
(no. of shares)
Ratio
Rank
$ 8,000
4,000
$2.00
2
36,000
10,000
3.60
3
Options
0
2,000
0
1
Thus, the order of inclusion for diluted EPS calculation is options first, convertible
preferred stock second, and convertible bonds last.
Basic EPS
= (Net income – Preferred dividends)/Weighted avg. shares outstanding
= ($200,000 – 8,000)/48,000
= $192,000/48,000
= $4.00 per share
Diluted EPS:
Step 1.
Assume that options are exercised.
EPS = ($192,000 + 0)/(48,000 + 2,000)
= $192,000/50,000
`
= $3.84 per share
Step 2.
Assume that convertible preferred stock is converted.
EPS = ($192,000 + 0 + $8,000)/(48,000 + 2,000 + 4,000)
= $200,000/54,000
= $ 3.70 per share
Step 3.
Assume that convertible bonds are converted.
EPS = ($192,000 + 0 + $8,000 + $36,000)/(48,000 + 2,000 + 4,000 + 10,000)
= $236,000/64,000
= $ 3.69 per share
Diluted EPS reported is $3.69 per share.
Practice Problem 1
Woods Company
Woods Company had 20,000 shares outstanding as of January 1, 2002. The following
transactions took place during 2002:
Event
Date
April 1
4,000 new shares issued
May 1
10% stock dividend issued
July 1
2-for-1 stock split
November 1
Purchased 1,800 shares of treasury stock
Solution to Practice Problem 1, Woods Company
Period
1/1 to 3/31
Actual
Shares
Outstanding
20,000
4/1 to 4/30
24,000
5/1 to 6/30
7/1 to 10/31
11/1 to 12/31
Total
26,400
52,800
51,000
Assumed Shares
Outstanding
20,000 x 1.1 x 2 =
44,000
24,000 x 1.1 x 2 =
52,800
26,400 x 2 = 52,800
52,800
51,000
Fraction of
Year
3/12
Equivalent
Shares
11,000
1/12
4,400
3/12
3/12
2/12
13,200
13,200
8,500
50,300
Practice Problem 2
Lewis Company
Lewis Company had 10,500 shares of common stock ($1 par value) outstanding as of
January 1, 2002. During the year, the company had the following transactions related to
common stock:
Date
Event
May 1
20% stock dividend issued
July 1
6,000 new shares issued
November 1
Purchased 3,600 shares of treasury stock
The company also had 500 shares of 8%, $100 par preferred stock outstanding through
the year and declared and paid preferred dividends. For the year ended December 31,
2002, the following data are available:
a. Income from continuing operations, $64,000.
b. Loss from discontinued operations (net of taxes), $15,000.
c. Net income, $49,000.
Calculate the earnings per share for the year ended December 31, 2002.
Solution to Practice Problem 2, Lewis Company
Step 1.
Calculate the weighted average number of shares.
Actual Shares
Assumed Shares
Period
Outstanding
Outstanding
1/1 to 6/30
10,500
10,500 x 1.2 = 12,600
7/1 to 10/31
18,600
18,600
11/1 to 12/31
15,000
15,000
Total
Fraction of
Year
6/12
4/12
2/12
Equivalent
Shares
6,300
6,200
2,500
15,000
Step 2.
Calculate net income available for common stockholders.
Preferred dividends = 500 x 0.08 x $100 = $4,000
Net income available for common stockholders = $49,000 – $4,000 = $45,000
Note: To present the EPS numbers, preferred dividends must be subtracted from all
relevant EPS numbers. As a result, income from continuing operations = $64,000 –
4,000 = $60,000.
Step 3.
Calculate earnings per share.
Income per share from continuing operations = $60,000/15,000 = $4.00
Extraordinary gain per share = $15,000/15,000 = $1.00
Net income per share = $45,000/15,000 = $3.00
Practice Problem 3
Charles Company
The net income of Charles Company for the year ended December 31, 2002 was
$100,000. The following additional information is available about the Company:
a. The weighted average number of shares outstanding during the year was 19,000.
b. During the year 1,000 shares of $100 par, 5% convertible preferred stock were
outstanding. Each preferred stock is convertible into one share of common stock.
c. During the year, 100 bonds each of $1,000 face value were outstanding. The bonds
were issued at par, pay 12% interest per year, and are convertible into 20 shares of
common stock.
d. There were 5,000 options outstanding, with an option price of $20 each. The
average market price for the period was $25.
Calculate the basic and diluted earnings per share, assuming that the tax rate for the
company is 30%.
Solution to Practice Problem 3, Charles Company
Step 1.
Calculate the numerator effect, denominator effect, and the ratio of these two for
convertible preferred stock, convertible bonds, and options.
a. Convertible preferred stock
Numerator effect (dividends that need not be paid) = $100 x 0.05 x 1,000 = $5,000
Denominator effect (to be issued upon conversion) = 1,000 shares
b. Convertible bonds
Interest that need not be paid, if conversion is assumed = $1,000 x 0.12 x 100 = $12,000
Numerator effect = (1 – tax rate) x $12,000 = (1 – 0.30) x $12,000 = $8,400
Denominator effect (to be issued upon conversion) = 100 x 20 = 2,000 shares
c. Options
Denominator effect for options:
Proceeds from exercising options = $100,000 ($20 x 5,000)
Number of treasury shares assumed to be purchased = $100,000/$25 = 4,000
Thus, increase in number of shares = 1,000
Item
Convertible
preferred stock
Convertible bond
Numerator
Effect
Denominator
Effect
(no. of shares)
Ratio
Rank
$5,000
1,000
$5.00
3
8,400
2,000
4.20
2
Options
0
1,000
0
1
Thus, the order of inclusion for diluted EPS calculation is options first, convertible bonds
second, and convertible preferred stock last.
Basic EPS
= (Net income – Preferred dividends)/Weighted. avg. shares outstanding
= ($100,000 – 5,000)/19,000
= $95,000/19,000
= $5.00 per share
Diluted EPS
Step 1.
Assume that options are exercised.
EPS = ($95,000 + 0)/(19,000 + 1,000)
= $95,000/20,000
`
= $4.75 per share
Step 2.
Assume that convertible bonds are converted.
EPS = ($95,000 + 0 + $8,400)/(19,000 + 1,000 + 2,000)
= $103,400/22,000
= $4.70 per share
The EPS after step 2 ($4.70) is lower than the ratio of numerator effect to denominator
effect for the convertible preferred stock ($5.00). Hence, convertible preferred stocks
are antidilutive. Thus, they will not be assumed to have been converted, and the diluted
EPS reported is $4.70 per share.
Practice Problem 4
1. The numerator of EPS is
a. Net income.
b. Net income less income tax expense.
c. Income before taxes less interest.
d. Net income less preferred dividends.
2. Faldo Company had 1,000 shares of common stock outstanding at the beginning of
the year. On October 1, the company issued an additional 400 shares of common stock.
The weighted average number of shares for EPS calculations is
a. 1,000.
b. 1,100.
c. 1,200.
d. 1,400.
3. The net income of Woods Company for the year ending December 31, 2002, was
$8,000. The company had 100 shares of 5%, $100 par preferred stock and 200 bonds
(issued at par) each with a face value of $1,000 and a stated rate of 10%. If the
weighted average number of shares outstanding for the year is 1,000, the basic EPS for
the year is
a. $5.50.
b. $6.00.
c. $7.50.
d. $8.00.
4. Which of the following is not potentially dilutive?
a. Stock options.
b. Preferred stock.
c. Convertible bonds.
d. Convertible preferred stock.
5. In calculating diluted EPS, the numerator effect for convertible preferred stock is
a. Interest expense.
b. Interest expense, net of tax.
c. Preferred dividends.
d. Cash interest paid.
6. In calculating diluted EPS, the numerator effect for stock options is
a. Interest expense.
b. Interest expense, net of tax.
c. Cash interest paid, net of tax.
d. zero.
7. Surrey Company has 1,000 stock options outstanding, each with an exercise price of
$25. If the closing market price is $50 and the average market price for the period is
$40, under the treasury stock method, the number of shares outstanding will
a. Increase by 375.
b. Decrease by 500.
c. Decrease by 375.
d. Increase by 500.
8. To calculate diluted EPS, dividends on nonconvertible noncumulative preferred stock
are
a. deducted only when dividends are declared.
b. deducted regardless of whether dividends are declared.
c. added back to the numerator only when dividends are declared.
d. added back to the numerator regardless of whether dividends are declared.
Homework Problem 1
Geiger Company
Geiger Company had 30,000 shares outstanding as of January 1, 2002. The following
transactions took place during 2002:
Date
Event
March 1
6,000 new shares issued
June 1
15 % stock dividend issued
September 1
Purchased 2,400 shares of treasury stock
December 1
2-for-1 stock split
Solution to Homework Problem 1, Geiger Company
Period
1/1 to 2/28
3/1 to 5/31
6/1 to 8/31
9/1 to 11/30
12/1 to 12/31
Total
Actual
Shares
Outstanding
30,000
36,000
41,400
39,000
78,000
Assumed Shares
Outstanding
30,000 x 1.15 x 2 = 69,000
36,000 x 1.15 x 2 = 82,800
41,400 x 2 = 82,800
39,000 x 2 = 78,000
78,000
Fraction of
Year
2/12
3/12
3/12
3/12
1/12
Equivalent
Shares
11,500
20,700
20,700
19,500
6,500
78,900
Homework Problem 2
Harman Company
Harman Company had 40,000 shares of common stock ($1 par value) outstanding as of
January 1, 2002. During the year, the company had the following common stock related
transactions:
Date
Event
April 1
Issued 8,000 new shares
October 1
Purchased 12,000 new shares as treasury stock
December 1
2-for-1 stock split
The company also had 1,000 shares of 7%, $100 par preferred stock outstanding
through the year and declared and paid preferred dividends. For the year ended
December 31, 2002, the following data are available:
a. Income from continuing operations, $153,200.
b. Extraordinary Loss (net of taxes), $17,200.
c. Net income, $136,000.
Calculate the earnings per share for the year ended December 31, 2002.
Solution to Practice Problem 2, Harman Company
Step 1.
Calculate the Weighted average number of shares.
Actual Shares
Assumed Shares
Period
Outstanding
Outstanding
1/1 to 3/31
40,000
40,000 x 2 = 80,000
4/1 to 9/30
48,000
48,000 x 2 = 96,000
11/1 to 12/31
36,000
36,000 x 2 = 72,000
Total
Fraction of
Year
3/12
6/12
3/12
Equivalent
Shares
20,000
48,000
18,000
86,000
Step 2.
Calculate net income available for common stockholders.
Preferred dividends = 1,000 x 0.07 x $100 = $7,000
Net income available for common stockholders = $136,000 – $7,000 = $129,000
Note: To present the EPS numbers, preferred dividends must be subtracted from all
relevant EPS numbers.
As a result, income from continuing operations = $153,200 – $7,000 = $146,000.
Step 3.
Calculate earnings per share.
Income per share from continuing operations = $146,200/86,000 = $1.70
Extraordinary gain per share = $17,200/86,000 = $0.20
Net income per share = $129,000/86,000 = $1.50
Homework Problem 3
Bowles Company
The net income of Bowles Company for the year ended December 31, 2002 was
$50,000. The following additional information is available about the Company:
a. The weighted average number of shares outstanding during the year was 4,000.
b. During the year, 400 shares of $100 par, 5% convertible preferred stock were
outstanding. These preferred shares are convertible into a total of 1,250 shares of
common stock.
c. During the year, 200 bonds each of $1,000 face value were outstanding. The bonds
were issued at par, pay 10% interest per year, and are convertible to 15 shares of
common stock.
d. There were 4,000 options outstanding, with an option price of $9 each. The average
market price for the period was $12.
Calculate the basic and diluted earnings per share, assuming that the tax rate for the
Company is 25%. Round your answers to the nearest cent per share.
Solution to Homework Problem 3, Bowles Company
Step 1.
Calculate the numerator effect, denominator effect and the ratio of these two for
convertible preferred stock, convertible bonds, and options.
a. Convertible preferred stock
Numerator effect (dividends that need not be paid) = $100 x 0.05 x 400 = $2,000
Denominator effect (to be issued upon conversion) =1,250 shares
b. Convertible bonds
Interest that need not be paid, if conversion is assumed = $1,000 x 0.10 x 200 = $20,000
Numerator effect = (1 – tax rate) x $20,000 = (1 – 0.25) x $20,000 = $15,000
Denominator effect (to be issued upon conversion) = 200 x 15 = 3,000 shares
c. Options
Denominator effect for options:
Proceeds from exercising options = $36,000 ($9 x 4,000)
Number of treasury shares assumed to be purchased = $36,000/$12 = 3,000
Thus, increase in number of shares = 1,000
Item
Convertible
preferred stock
Convertible bond
Numerator
Effect
Denominator
Effect
(no. of shares)
Ratio
Rank
$ 2,000
1,250
$1.60
2
15,000
3,000
5.00
3
Options
0
1,000
0.00
1
Thus, the order of inclusion for diluted EPS calculation is options first, convertible
preferred stock second, and convertible bonds last.
Basic EPS
= (Net income – Preferred dividends)/Weighted avg. shares outstanding
= ($50,000 – 2,000)/4,000
= $48,000/4,000
= $12.00 per share
Diluted EPS:
Step 1.
Assume that options are exercised.
EPS = ($48,000 + 0)/(4,000 + 1,000)
= $48,000/5,000
= $9.60 per share
Step 2.
Assume that convertible preferred stock are converted.
EPS = ($48,000 + 0 + $2,000)/(4,000 + 1,000 + 1,250)
= $50,000/6,250
= $8.00 per share
Step 3.
Assume that convertible bonds are converted.
EPS = ($48,000 + 0 + $2,000 + $15,000)/(4,000 + 1,000 + 1,250 + 3,000)
= $65,000/9,250
= $7.03 per share
Diluted EPS reported is $7.03 per share.
Homework Problem 4
1. The denominator of EPS is
a. Number of shares outstanding at the end of the period.
b. Number of shares outstanding at the beginning of the period.
c. Average of shares outstanding at the end of the period.
d. Weighted average number of shares outstanding for the period.
2. Palmer Company had 3,000 shares of common stock outstanding at the beginning of
the year. On April 1, the company purchased 400 shares as treasury stock. The
weighted average number of shares for EPS calculations is
a. 2,600.
b. 2,800.
c. 2,700.
d. 2,600.
3. The net income of Palmer Company for the year ending December 31, 2002, was
$12,000. The company had 300 shares of 5%, $100 par preferred stock and 100 bonds
(issued at par) each with a face value of $1,000 and a stated rate of 10%. If the
weighted average number of shares outstanding for the year is 1,000, the basic EPS for
the year is
a. $12.00.
b. $11.00.
c. $10.50.
d. $9.50.
4. Assuming that a company has positive net income, which of the following enters the
diluted EPS calculation first?
a. Stock options.
b. Preferred stock.
c. Convertible bonds.
d. Convertible preferred stock.
5. In calculating diluted EPS, the numerator effect for convertible bonds is
a. Interest expense.
b. Interest expense, net of tax.
c. Preferred dividends.
d. Cash interest paid, net of tax.
6. Options are considered dilutive if
a. average market price is lower than the exercise price of options.
b. closing market price is higher than the exercise price of options.
c. average market price is higer than the exercise price of options.
d. closing market price is lower than the exercise price of options.
7. Widener Company has 2,000 stock options outstanding, each with an exercise price
of $16. If the closing market price is $20 and the average market price for the period is
$25, under the treasury stock method, the number of shares outstanding will
a. Increase by 400.
b. Decrease by 400.
c. Decrease by 720.
d. Increase by 720.
8. To calculate basic EPS, dividends on nonconvertible cumulative preferred stock are
a. deducted only when dividends are declared.
b. deducted regardless of whether dividends are declared.
c. added back to the numerator only when dividends are declared.
d. added back to the numerator regardless of whether dividends are declared.