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CHAPTER 18
QUESTIONS
1. Earnings per share information is used by
investors to evaluate the results of operations of a business and estimate future
earnings. Because earnings are an important determinant of the market price of a
company’s common stock, the EPS measurement will aid the investor in determining the attractiveness of an investment in a
company’s stock.

6. When a company issues a stock dividend,
a stock split, or a reverse stock split, the
number of shares of stock is changed, but
there is no other effect on the corporation’s
resources. To meaningfully compare EPS
figures in the current period with earlier periods, the new capital structure should be
reflected retroactively in all prior periods.
The unit in which EPS is measured always
should be uniform across accounting periods.

2. Earnings per share data have the same limitations that any income figure has under
current generally accepted accounting principles. The alternative methods available
for computing net income sometimes make
comparison among companies difficult, and
the condensed EPS figure does not remove
this difficulty. In some cases, the existence
of EPS data even increases the lack of
comparability because EPS information is
frequently disclosed separately from any
note disclosure describing the accounting
methods employed.

7. The two-class method is a technique for allocating earnings per share to two different
classes of stock that both have ownership
privileges. The two-class method is used
when a company has two classes of common stock with different dividend rights or
when a company has participating preferred stock in addition to its common
stock.
8. Dilution of EPS refers to the effect that certain types of securities—whose terms enable their holders to acquire common
shares—will have on EPS data if these securities are converted into common stock. If
in a complex capital structure, conversion
of convertible securities or exercise of options, warrants, or rights would reduce the
EPS from what it would have been using
only common shares outstanding, dilution
of EPS has occurred.

3. The investor uses EPS to help forecast the
future profitability of an investment. If potential future common stock transactions dilute the investor’s ownership interest in the
company, future EPS will decline relative to
the past figures under the same conditions.
By preparing predictive EPS, the potential
impact of conversion of convertible securities and exercise of stock options, warrants, or rights can be captured in the EPS
figure.

9. An antidilutive security is one whose terms
permit it to be exercised or converted into
common stock, but if converted, the EPS
would be increased or the loss per share
decreased from what it would have been
using only common shares outstanding.
Because of changing economic conditions,

a security may be dilutive in one accounting
period but antidilutive in another. If stock
options, warrants, rights, or convertible securities are antidilutive, they are ignored in
computing EPS. Antidilutive securities are
ignored for two reasons. First, by doing so,
diluted EPS gives a worst-case scenario for
existing stockholders. Second, the economic
terms of antidilutive securities suggest that

4. A simple capital structure consists only of
common or common and preferred stock
and includes no convertible securities, options, warrants, or rights that upon conversion or exercise would in the aggregate dilute EPS. A complex capital structure includes securities and rights that would have
a dilutive effect on EPS if converted or exercised.
5. The amount of shares that should be used
in the computation of EPS is 30,000
(10,000 3). The split should be accounted
for as if it had taken place on January 1 of
the earliest year presented.

805


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Chapter 18

the probability that they will be converted
soon is low.
10. The treasury stock method is a means of

determining the extent of dilution in EPS
arising from options, warrants, and rights.
Under the treasury stock method, EPS is
computed as though the options, warrants,
and rights were exercised at the beginning
of the period or at time of issuance, whichever comes later, and as though the funds
obtained thereby were applied to the reacquisition of common stock at the market
price for that period. The computation is
necessary whenever the market price of
the obtainable stock exceeds the exercise
price of the options, warrants, or rights during the period.
11. The interest expense related to convertible
debt, net of taxes, should be added back to
income (in the numerator) for the computation of EPS.
12. The if-converted method assumes conversion of the security as of the beginning of
the fiscal year or as of the date of issue,
whichever comes later. It is used to compute EPS “as if” the securities were converted.
13. When stock options are exercised, the new
shares actually issued are included in the
computation of all EPS amounts. The diluted
EPS is computed as if the exercise took

‡

Relates to Expanded Material.

place as of the beginning of the year. In
computing diluted EPS, the stock price at
exercise date is used to compute the incremental number of shares assumed to be
issued prior to the exercise date.

14. The inclusion of stock options and convertible securities in the computation of EPS
decreases the absolute value of the EPS.
When a company experiences a net loss,
the inclusion of these securities decreases
the loss per share just as it decreases the
income per share. Thus, inclusion of stock
options and convertible securities would
always be antidilutive under loss conditions.
‡

15. To obtain the lowest possible EPS amount,
a company with multiple potentially dilutive
securities first includes any dilutive stock
options, warrants, or rights in the computations. If there are several convertible securities, the impact of each on EPS must
be considered on an individual basis. The
EPS amount can then be computed by including the convertible securities one at a
time beginning with the security having the
lowest incremental EPS. When the recomputed EPS is less than the incremental EPS
of the next security, no additional convertible
securities are considered in computing EPS.


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Chapter 18

807

PRACTICE EXERCISES
PRACTICE 18–1 SHARES OUTSTANDING: ISSUANCE AND REACQUISITION
Period

Jan. 1–Apr. 1
Apr. 1–Aug. 1
Aug. 1–Dec. 31
Total

Fraction of
the Year
3/12
4/12
5/12

Shares
Outstanding
200,000
260,000
160,000

Weighted-Average
Shares
50,000
86,667
66,667
203,334

PRACTICE 18–2 SHARES OUTSTANDING: STOCK DIVIDENDS AND STOCK SPLITS
Period
Jan. 1–Mar. 1
Mar. 1–June 1
June 1–Sept. 1
Sept. 1–Dec. 31

Total

Fraction of
the Year
2/12
3/12
3/12
4/12

Shares
Adjustment
Outstanding
Factor
150,000
2.0 1.20
300,000
1.20
345,000
1.20
414,000
1.00

Weighted-Average
Shares
60,000
90,000
103,500
138,000
391,500


PRACTICE 18–3 IMPACT OF PREFERRED STOCK ON BASIC EPS
1.

When the preferred stock is not cumulative, an adjustment is made to basic EPS
only for preferred dividends declared during the year.
Basic EPS = $220,000/100,000 common shares = $2.20 per share

2.

When the preferred stock is cumulative, an adjustment is made to basic EPS for
all preferred dividends whether they are declared during the year or not.
Preferred dividends = 30,000 shares

$100 par

5% = $150,000

Basic EPS = ($220,000 – $150,000)/100,000 common shares = $0.70 per share
PRACTICE 18–4 COMPUTATION OF BASIC EPS
Computation of weighted-average number of common shares outstanding:
Period
Jan. 1–Apr. 1
Apr. 1–Aug. 1
Aug. 1–Dec. 31
Total

Fraction of
the Year
3/12
4/12

5/12

Shares
Adjustment
Outstanding
Factor
200,000
2.0
260,000
2.0
520,000
1.0

Preferred dividends = 20,000 shares

$50 par

Weighted-Average
Shares
100,000
173,333
216,667
490,000

8% = $80,000

Basic EPS = ($300,000 – $80,000)/490,000 common shares = $0.45 per share


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Chapter 18

PRACTICE 18–5 TWO-CLASS METHOD
Participating dividends per share: $1.40 per share [$1.00 + 0.80($1.00 – $0.50)]
Participating preferred dividends paid for the year: $1.40 per share making a
total of $140,000 ($1.40 per share × 100,000 shares)
Common dividends paid for the year: $1.00 per share making a total of
$320,000 ($1.00 per share × 320,000 shares)
The excess dividends paid so far have been $160,000 for common shares
[$320,000 total common dividends less $160,000 ($0.50 per share × 320,000
shares) baseline common dividends] and $40,000 for participating preferred
shares [$140,000 total preferred dividends less $100,000 ($1.00 per share ×
100,000 shares) baseline preferred dividends]. Thus, 80% of the excess dividends [$160,000 ÷ ($160,000 + $40,000)] have gone to common shareholders
and 20% have gone to participating preferred shareholders.
The undistributed earnings of $540,000 ($1,000,000 – $320,000 – $140,000) are allocated as follows:
Preferred
Common
Stock
Stock
Total undistributed earnings ........................................... $ 540,000
$540,000
Allocation percentage ...................................................... ×
0.20
×
0.80
Allocation of undistributed earnings .............................. $ 108,000
$432,000
Number of shares ............................................................. ÷ 100,000

÷320,000
Undistributed earnings per share ................................... $
1.08
$
1.35
The basic earnings per share amounts are computed and reported as follows:
Participating
Preferred
Common
Stock
Stock
Distributed earnings .........................................................
$1.40
$1.00
Undistributed earnings ....................................................
1.08
1.35
Basic earnings per share .................................................
$2.48
$2.35
PRACTICE 18–6 DILUTED EPS AND STOCK OPTIONS
1.

Hypothetical proceeds from the exercise of the options (50,000

$10) = $500,000

Number of shares that could be repurchased with hypothetical proceeds:
$500,000/$16 = 31,250 shares
Net increase in shares outstanding if options had been exercised and proceeds

used to repurchase shares:
50,000 shares issued – 31,250 shares repurchased = 18,750 shares
Diluted EPS = $400,000/(200,000 + 18,750) = $1.83


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Chapter 18

809

PRACTICE 18–6 (Concluded)
2.

Hypothetical proceeds from the exercise of the options (50,000

$10) = $500,000

Number of shares that could be repurchased with hypothetical proceeds:
$500,000/$8 = 62,500 shares
Net decrease in shares outstanding if options had been exercised and proceeds
used to repurchase shares:
50,000 shares issued – 62,500 shares repurchased = 12,500 shares
These options are antidilutive. In addition, it is unlikely that they will be exercised soon because the average stock price is less than the option exercise
price. These options are ignored in the computation of diluted EPS.
Diluted EPS = $400,000/200,000 = $2.00
PRACTICE 18–7 STOCK OPTIONS ISSUED DURING THE YEAR
1.

Hypothetical proceeds from the exercise of the options (50,000


$10) = $500,000

Number of shares that could be repurchased with hypothetical proceeds:
$500,000/$5 = 100,000 shares
Net decrease in shares outstanding if options had been exercised and proceeds
used to repurchase shares:
50,000 shares issued – 100,000 shares repurchased = 50,000 shares
These options are antidilutive. In addition, it is unlikely that they will be exercised soon because the average stock price is less than the option exercise
price. These options are ignored in the computation of diluted EPS.
Diluted EPS = $400,000/200,000 = $2.00
2.

Hypothetical proceeds from the exercise of the options (50,000

$10) = $500,000

Number of shares that could be repurchased with hypothetical proceeds:
$500,000/$14 = 35,714 shares
Net increase in shares outstanding if options had been exercised and proceeds
used to repurchase shares:
50,000 shares issued – 35,714 shares repurchased = 14,286 shares
Weighted-average number of additional shares from options: 14,286
4,762
Diluted EPS = $400,000/(200,000 + 4,762) = $1.95

(4/12) =


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PRACTICE 18–8 DILUTED EPS AND CONVERTIBLE PREFERRED STOCK
Preferred dividends = 10,000 shares
Basic EPS = ($400,000
1.

$100 par

5% = $50,000

$50,000)/100,000 common shares = $3.50 per share

If the preferred shares had been converted at the beginning of the year:
40,000 additional common shares (10,000 4) would have been outstanding.
The $50,000 in preferred dividends would have been available to all common
stockholders.
Preliminary diluted EPS calculation: $400,000/(100,000 + 40,000) = $2.86 per
share
Conversion of these preferred shares would decrease earnings per share ($2.86
< $3.50). Thus, they are dilutive and are included in the calculation of diluted
EPS. In addition, it is likely that the preferred shareholders would give up their
preferred dividends of $5.00 ($100 0.05) per share to join the common stockholders and earn $14.00 per share (basic EPS of $3.50 4 converted shares).
Diluted EPS = $2.86 per share

2.

If the preferred shares had been converted at the beginning of the year:
10,000 additional common shares (10,000 1) would have been outstanding.

The $50,000 in preferred dividends would have been available to all common
stockholders.
Preliminary diluted EPS calculation: $400,000/(100,000 + 10,000) = $3.64 per
share
Conversion of these preferred shares would increase earnings per share ($3.64
> $3.50). Thus, they are antidilutive and are ignored in the calculation of diluted
EPS. In addition, it is unlikely that the preferred shareholders would give up
their preferred dividends of $5.00 ($100 0.05) per share to get one share and
join the common stockholders who are earning basic EPS of $3.50 per share.
Diluted EPS = Basic EPS = $3.50 per share


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Chapter 18

811

PRACTICE 18–9 CONVERTIBLE PREFERRED STOCK ISSUED DURING THE YEAR
Preferred dividends = 10,000 shares
Basic EPS = ($400,000
1.

$100 par

5% = $50,000

$50,000)/100,000 common shares = $3.50 per share

If the preferred shares had been converted on February 1 when they were issued:
45,833 additional common shares [10,000 5 (11/12)] would have been outstanding.

The $50,000 in preferred dividends would have been available to all common
stockholders.
Preliminary diluted EPS calculation: $400,000/(100,000 + 45,833) = $2.74 per
share
Conversion of these preferred shares would decrease earnings per share ($2.74
< $3.50). Thus, they are dilutive and are included in the calculation of diluted
EPS. In addition, it is likely that the preferred shareholders would give up their
preferred dividends of $5.00 ($100 0.05) per share to join the common stockholders and earn $17.50 per share (basic EPS of $3.50 5 converted shares).
Diluted EPS = $2.74 per share

2.

If the preferred shares had been converted on February 1 when they were issued:
9,167 additional common shares [10,000 1 (11/12)] would have been outstanding.
The $50,000 in preferred dividends would have been available to all common
stockholders.
Preliminary diluted EPS calculation: $400,000/(100,000 + 9,167) = $3.66 per share
Conversion of these preferred shares would increase earnings per share ($3.66
> $3.50). Thus, they are antidilutive and are ignored in the calculation of diluted
EPS. In addition, it is unlikely that the preferred shareholders would give up
their preferred dividends of $5.00 ($100 0.05) per share to get one share and
join the common stockholders who are earning basic EPS of $3.50 per share.
Diluted EPS = Basic EPS = $3.50 per share


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PRACTICE 18–10 DILUTED EPS AND CONVERTIBLE BONDS
Basic EPS = $100,000/50,000 common shares = $2.00 per share
Interest on convertible bonds = 100 bonds $1,000 face value 10% = $10,000
After-tax cost of interest on convertible bonds = $10,000 (1 – 0.30) = $7,000
1.

If the convertible bonds had been converted at the beginning of the year:
5,000 additional common shares (100 50) would have been outstanding.
The $7,000 in after-tax interest would have been available to all common
stockholders.
Preliminary diluted EPS calculation: ($100,000 + $7,000)/(50,000 + 5,000) = $1.95
per share
Conversion of these bonds would decrease earnings per share ($1.95 < $2.00).
Thus, they are dilutive and are included in the calculation of diluted EPS.
Diluted EPS = $1.95 per share

2.

If the convertible bonds had been converted at the beginning of the year:
2,000 additional common shares (100 20) would have been outstanding.
The $7,000 in after-tax interest would have been available to all common
stockholders.
Preliminary diluted EPS calculation: ($100,000 + $7,000)/(50,000 + 2,000) = $2.06
per share
Conversion of these bonds would increase earnings per share ($2.06 > $2.00).
Thus, they are antidilutive and are not included in the calculation of diluted EPS.
Diluted EPS = Basic EPS = $2.00 per share

PRACTICE 18–11 CONVERTIBLE BONDS ISSUED DURING THE YEAR
Basic EPS = $100,000/50,000 common shares = $2.00 per share

Interest on convertible bonds = 100 bonds $1,000 face value 10% (3/12) =
$2,500
After-tax cost of interest on convertible bonds = $2,500 (1 – 0.30) = $1,750
1.

If the convertible bonds had been converted on October 1 when they were issued:
2,500 additional common shares [100 100 (3/12)] would have been outstanding.
The $1,750 in after-tax interest would have been available to all common
stockholders.
Preliminary diluted EPS calculation: ($100,000 + $1,750)/(50,000 + 2,500) = $1.94
per share
Conversion of these bonds would decrease earnings per share ($1.94 < $2.00).
Thus, they are dilutive and are included in the calculation of diluted EPS.
Diluted EPS = $1.94 per share


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Chapter 18

813

PRACTICE 18–11 (Concluded)
2.

If the convertible bonds had been converted on October 1 when they were issued:
375 additional common shares [100 15 (3/12)] would have been outstanding.
The $1,750 in after-tax interest would have been available to all common
stockholders.
Preliminary diluted EPS calculation: ($100,000 + $1,750)/(50,000 + 375) = $2.02
per share

Conversion of these bonds would increase earnings per share ($2.02 > $2.00).
Thus, they are antidilutive and are not included in the calculation of diluted EPS.
Diluted EPS = Basic EPS = $2.00 per share

PRACTICE 18–12 SHORTCUT ANTIDILUTION TESTS
1.

Preferred dividends = 10,000 shares $100 par 0.05 = $50,000
Basic EPS = ($300,000 $50,000)/100,000 common shares = $2.50 per share
Incremental impact on EPS:
$50,000 dividends/(10,000 1 new share) = $5.00 per share
Incremental impact is greater than the basic EPS ($5.00 > $2.50), so the convertible preferred shares are antidilutive.

2.

Basic EPS = $300,000/100,000 common shares = $3.00 per share
Interest on convertible bonds = 500 bonds $1,000 face value 0.10 = $50,000
After-tax cost of interest on convertible bonds = $50,000 (1 – 0.30) = $35,000
Incremental impact on EPS:
$35,000 after-tax interest/(500

25 new shares) = $2.80 per share

Incremental impact is less than the basic EPS ($2.80 < $3.00), so the convertible
bonds are dilutive.
3.

Preferred dividends = 20,000 shares $50 par 0.10 = $100,000
Basic EPS = ($300,000 $100,000)/100,000 common shares = $2.00 per share
Incremental impact on EPS:

$100,000 dividends/(20,000 4 new shares) = $1.25 per share
Incremental impact is less than the basic EPS ($1.25 < $2.00), so the convertible
preferred shares are dilutive.

4.

Basic EPS = $300,000/100,000 common shares = $3.00 per share
Interest on convertible bonds = 2,000 bonds $1,000 face value 0.08 = $160,000
After-tax cost of interest on convertible bonds = $160,000 (1 – 0.30) = $112,000
Incremental impact on EPS:
$112,000 after-tax interest/(2,000

15 new shares) = $3.73 per share

Incremental impact is greater than the basic EPS ($3.73 > $3.00), so the convertible bonds are antidilutive.


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Chapter 18

PRACTICE 18–13 BASIC AND DILUTED EPS AND ACTUAL CONVERSION OF STOCK
OPTIONS
1.
Period
Jan. 1–Apr. 1
Apr. 1–Dec. 31
Total


Fraction of
the Year
3/12
9/12

Shares
Outstanding
100,000
140,000

Weighted-Average
Shares
25,000
105,000
130,000

Basic EPS: $200,000/130,000 shares = $1.54
2.

Hypothetical proceeds from the exercise of the options on January 1 (40,000
$10) = $400,000
Number of shares that could be repurchased with hypothetical proceeds:
$400,000/$15 (use stock price on actual exercise date) = 26,667 shares
Net increase in shares outstanding on January 1 if options had been exercised
and proceeds used to repurchase shares:
40,000 shares issued – 26,667 shares repurchased = 13,333 shares
Weighted-average increase in shares: 13,333

(3/12) = 3,333


Diluted EPS = $200,000/(130,000 + 3,333) = $1.50
PRACTICE 18–14 BASIC AND DILUTED EPS AND ACTUAL CONVERSION OF CONVERTIBLE PREFERRED
1.
Period
Jan. 1–Sept. 1
Sept. 1–Dec. 31
Total

Fraction of
the Year
8/12
4/12

Preferred dividends = 5,000 shares
Basic EPS: ($300,000
2.

Shares
Outstanding
200,000
225,000
$100 par

Weighted-Average
Shares
133,333
75,000
208,333

0.05 = $25,000


$25,000)/208,333 shares = $1.32

If the preferred shares had been converted on January 1:
16,667 additional weighted-average common shares [5,000 5 (8/12)] would
have been outstanding.
The $25,000 in preferred dividends would have been available to all common
stockholders.
Preliminary diluted EPS calculation: $300,000/(208,333 + 16,667) = $1.33 per share
Hypothetical conversion of these preferred shares would increase earnings per
share ($1.33 > $1.32). Thus, they are antidilutive and are not included in the calculation of diluted EPS.
Diluted EPS = $1.32 per share
Note that in this case, if the preferred dividends had not been paid before the
conversion, both basic EPS and diluted EPS would have been different.
Basic EPS: $300,000/208,333 shares = $1.44
Diluted EPS: $300,000/(208,333 + 16,667) = $1.33


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815

PRACTICE 18–15 BASIC AND DILUTED EPS AND ACTUAL CONVERSION OF CONVERTIBLE BONDS
1.
Period
Jan. 1–Aug. 1
Aug. 1–Dec. 31
Total


Fraction of
the Year
7/12
5/12

Shares
Outstanding
100,000
120,000

Weighted-Average
Shares
58,333
50,000
108,333

Basic EPS: $400,000/108,333 shares = $3.69
2.

Preconversion interest on convertible bonds = 500 bonds $1,000 face value
0.10 (7/12) = $29,167
After-tax cost of interest on convertible bonds = $29,167 (1 – 0.40) = $17,500
If the convertible bonds had been converted on January 1:
11,667 additional weighted-average common shares [500 40 (7/12)] would
have been outstanding.
The $17,500 in after-tax interest would have been available to all common
stockholders.
Preliminary diluted EPS calculation: ($400,000 + $17,500)/(108,333 + 11,667) =
$3.48 per share
Conversion of these bonds would decrease earnings per share ($3.48 < $3.69).

Thus, they are dilutive and are included in the calculation of diluted EPS.
Diluted EPS = $3.48 per share

PRACTICE 18–16 DILUTED EPS AND A LOSS
1a. Preferred dividends = 10,000 shares $100 par 0.05 = $50,000
Basic EPS: (–$300,000 – $50,000)/100,000 shares = $(3.50) per share
2a. If the preferred shares had been converted at the beginning of the year:
30,000 additional common shares (10,000 3) would have been outstanding.
The $50,000 in preferred dividends would have been available to all common
stockholders.
Preliminary diluted EPS calculation: –$300,000/(100,000 + 30,000) = $(2.31) per
share
Conversion of these preferred shares would increase earnings per share (–$2.31
> –$3.50). Thus, they are antidilutive and are not included in the calculation of
diluted EPS. When the company reports a net loss, all potentially dilutive convertible securities are antidilutive.
Diluted EPS = $(3.50) per share


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PRACTICE 18–16 (Concluded)
1b. Basic EPS = –$300,000/100,000 common shares = $(3.00) per share
2b. Interest on convertible bonds = 500 bonds $1,000 face value 0.10 = $50,000
After-tax cost of interest on convertible bonds = $50,000 (1 – 0.30) = $35,000
If the convertible bonds had been converted at the beginning of the year:
12,500 additional common shares (500 25) would have been outstanding.
The $35,000 in after-tax interest would have been available to all common

stockholders.
Preliminary diluted EPS calculation: (–$300,000 + $35,000)/(100,000 + 12,500) =
$(2.36) per share
Conversion of these bonds would increase earnings per share (–$2.36 > –$3.00).
Thus, they are antidilutive and are not included in the calculation of diluted EPS.
When the company reports a net loss, all potentially dilutive convertible securities are antidilutive.
Diluted EPS = $(3.00) per share
1c. Basic EPS = –$300,000/100,000 common shares = $(3.00) per share
2c. Hypothetical proceeds from the exercise of the options (40,000

$10) = $400,000

Number of shares that could be repurchased with hypothetical proceeds:
$400,000/$16 = 25,000 shares
Net increase in shares outstanding if options had been exercised and proceeds
used to repurchase shares:
40,000 shares issued – 25,000 shares repurchased = 15,000 shares
Diluted EPS = –$300,000/(100,000 + 15,000) = $(2.61) per share
Exercise of these options would increase earnings per share (–$2.61 > –$3.00).
Thus, they are antidilutive and are not included in the calculation of diluted EPS.
In addition, cases in which the net number of shares outstanding would be reduced by the exercise of the options (i.e., when the exercise price is greater than
the average market price) are always ignored (whether a company has net income or a net loss) in computing diluted EPS.
Diluted EPS = $(3.00) per share


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PRACTICE 18–17 MULTIPLE POTENTIALLY DILUTIVE SECURITIES
1.

Preferred dividends = 10,000 shares $100 par 0.05 = $50,000
Basic EPS: ($300,000 – $50,000)/100,000 shares = $2.50 per share

2.

Determination of whether each potentially dilutive security is dilutive:
a. Hypothetical proceeds from the exercise of the options (30,000
$300,000

$10) =

Number of shares that could be repurchased with hypothetical proceeds:
$300,000/$18 = 16,667 shares
Net increase in shares outstanding if options had been exercised and
proceeds used to repurchase shares:
30,000 shares issued – 16,667 shares repurchased = 13,333 shares
Because the average stock price is greater than the exercise price, these
stock options are dilutive.
Intermediate diluted EPS: ($300,000 $50,000)/(100,000 + 13,333) = $2.21 per
share
This is the new benchmark to determine whether a security is dilutive or not.
b. If the preferred shares had been converted at the beginning of the year:
40,000 additional common shares (10,000 4) would have been outstanding.
The $50,000 in preferred dividends would have been available to all common stockholders.
Incremental EPS of convertible preferred shares: $50,000/40,000 shares =
$1.25 per share
c. Interest on convertible bonds = 500 bonds

$1,000 face value
0.10 =
$50,000
After-tax cost of interest on convertible bonds = $50,000 (1 – 0.40) = $30,000
If the convertible bonds had been converted at the beginning of the year:
20,000 additional common shares (500 40) would have been outstanding.
The $30,000 in after-tax interest would have been available to all common
stockholders.
Incremental EPS of bonds: $30,000/20,000 shares = $1.50 per share
Include the potentially dilutive security with the smallest incremental EPS
first.


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818

Chapter 18

PRACTICE 18–17 (Concluded)
Convertible preferred shares ($1.25 incremental EPS):
Intermediate diluted EPS:
Income: ($300,000 – $50,000 + $50,000)
Shares: (100,000 + 13,333 + 40,000)
= $1.96 per share
The incremental contribution of the convertible bonds is still lower than this
intermediate diluted EPS number ($1.50 < $1.96), so the convertible bonds
are also included.
Convertible bonds ($1.50 incremental EPS):
Diluted EPS:
Income: ($300,000 – $50,000 + $50,000 + $30,000)

Shares: (100,000 + 13,333 + 40,000 + 20,000)
= $1.90 per share
PRACTICE 18–18 MULTIPLE POTENTIALLY DILUTIVE SECURITIES
1.

Preferred dividends = 5,000 shares $100 par 0.05 = $25,000
Basic EPS: ($430,000 $25,000)/120,000 shares = $3.38 per share

2.

Determination of whether each potentially dilutive security is dilutive:
a. Hypothetical proceeds from the exercise of the options (20,000
$200,000

$10) =

Number of shares that could be repurchased with hypothetical proceeds:
$200,000/$8 = 25,000 shares
Net decrease in shares outstanding if options had been exercised and
proceeds used to repurchase shares:
20,000 shares issued – 25,000 shares repurchased = 5,000 shares
Because the average stock price is less than the exercise price, these stock
options are antidilutive.
b. If the preferred shares had been converted at the beginning of the year:
25,000 additional common shares (5,000 5) would have been outstanding.
The $25,000 in preferred dividends would have been available to all common stockholders.
Incremental EPS of convertible preferred shares: $25,000/25,000 shares =
$1.00 per share



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Chapter 18

819

PRACTICE 18–18 (Concluded)
c. Interest on convertible bonds = 1,000 bonds
$1,000 face value
0.10 =
$100,000
After-tax cost of interest on convertible bonds = $100,000
(1 – 0.30) =
$70,000
If the convertible bonds had been converted at the beginning of the year:
22,000 additional common shares (1,000 22) would have been outstanding.
The $70,000 in after-tax interest would have been available to all common
stockholders.
Incremental EPS of bonds: $70,000/22,000 shares = $3.18 per share
Include the potentially dilutive security with the smallest incremental EPS
first.
Convertible preferred shares ($1.00 incremental EPS):
Intermediate diluted EPS:
Income: ($430,000)
Shares: (120,000 + 25,000)
= $2.97 per share
The incremental contribution of the convertible bonds is not lower than this
intermediate diluted EPS number ($3.18 > $2.97), so the convertible bonds
are antidilutive. This exercise demonstrates the importance of doing the dilution comparisons in the correct order. If the $3.18 incremental EPS contribution of the convertible bonds shares had been compared to the $3.38 basic
EPS, they would have incorrectly been included.
Diluted EPS = $2.97 per share



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820

Chapter 18

PRACTICE 18–19 EPS AND FINANCIAL STATEMENT PRESENTATION
Number of shares used in the basic EPS calculations: 100,000
Number of shares used in the diluted EPS calculations:
Hypothetical proceeds from the exercise of the options (50,000 $10) = $500,000
Number of shares that could be repurchased with hypothetical proceeds:
$500,000/$14 = 35,714 shares
Net increase in shares outstanding if options had been exercised and proceeds
used to repurchase shares:
50,000 shares issued – 35,714 shares repurchased = 14,286 shares
Shares used for diluted EPS calculations = 100,000 + 14,286 = 114,286
Income from continuing operations
Extraordinary loss (net of taxes)
Discontinued operations (net of taxes)
Net income

Basic EPS
$ 1.92
(0.50)
(0.35)
$ 1.07

Diluted EPS
$ 1.68

(0.44)
(0.31)
$ 0.94*

*Diluted EPS numbers do not sum to the total because of rounding.
‡

PRACTICE 18–20 COMPREHENSIVE CALCULATION OF DILUTED EPS
1.

Weighted-average number of shares outstanding for the year:

Period
Jan. 1–June 1
June 1–Dec. 1
Dec. 1–Dec. 31
Total

Fraction of
the Year
5/12
6/12
1/12

Shares
Adjustment
Outstanding
Factor
100,000
2.0

125,000
2.0
250,000
1.0

Weighted-Average
Shares
83,333
125,000
20,833
229,166

Preferred dividends = 10,000 shares $100 par 0.05 = $50,000
Basic EPS: ($300,000 – $50,000)/229,166 shares = $1.09 per share

‡

Relates to Expanded Material.


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Chapter 18

821

‡

PRACTICE 18–20 (Continued)
2.


Determination of whether each potentially dilutive security is dilutive:
a. Hypothetical proceeds from the exercise of the options [30,000
($10/2)] = $300,000

2.0

Number of shares that could be repurchased with hypothetical proceeds:
$300,000/($18/2) = 33,333 shares
Net increase in shares outstanding if options had been exercised and
proceeds used to repurchase shares:
60,000 post-split shares issued – 33,333 post-split shares repurchased =
26,667 shares
Because the average stock price is greater than the exercise price, these
stock options are dilutive.
Intermediate diluted EPS: ($300,000
share

$50,000)/(229,166 + 26,667) = $0.98 per

This is the new benchmark to determine whether a security is dilutive or not.
b. If the preferred shares had been converted at the beginning of the year:
80,000 additional post-split common shares (10,000 4 2) would have
been outstanding.
The $50,000 in preferred dividends would have been available to all common stockholders.
Incremental EPS of convertible preferred shares: $50,000/80,000 shares =
$0.63 per share
c. Interest on convertible bonds = 500 bonds
$1,000 face value
0.10 =
$50,000

After-tax cost of interest on convertible bonds = $50,000
(1 – 0.40) =
$30,000
If the convertible bonds had been converted at the beginning of the year:
40,000 additional post-split common shares (500
40
2) would have
been outstanding.
The $30,000 in after-tax interest would have been available to all common
stockholders.
Incremental EPS of bonds: $30,000/40,000 shares = $0.75 per share
Include the potentially dilutive security with the smallest incremental EPS
first.

‡

Relates to Expanded Material.


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822

Chapter 18

‡

PRACTICE 18–20 (Concluded)
Convertible preferred shares ($0.63 incremental EPS):
Intermediate diluted EPS:
Income: ($300,000 $50,000 + $50,000)

Shares: (229,166 + 26,667 + 80,000)
= $0.89 per share
The incremental contribution of the convertible bonds is still lower than this
intermediate diluted EPS number ($0.75 < $0.89), so the convertible bonds
are also included.
Convertible bonds ($0.75 incremental EPS):
Diluted EPS:
Income: ($300,000 $50,000 + $50,000 + $30,000)
Shares: (229,166 + 26,667 + 80,000 + 40,000)
= $0.88 per share

‡

Relates to Expanded Material.


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Chapter 18

823

EXERCISES
18–21.

Jan. 1 to Feb. 1
76,000 1/12 3*
1.20† =
Feb. 1 to May 1
124,000 3/12 3
1.20 =

May 1 to Aug. 1
104,000 3/12 3
1.20 =
Aug. 1 to Sept. 1 124,800 1/12 3
=
Sept. 1 to Nov. 1 139,800 2/12 3
=
Nov. 1 to Dec. 31 419,400 2/12
=
Weighted-average number of shares
outstanding .........................................................
*3-for-1 stock split
†
20% stock dividend

18–22.

22,800
111,600
93,600
31,200
69,900
69,900

Increase/Decrease
in No. of Shares
(76,000 + 48,000)
(124,000 – 20,000)
(104,000 1.20)
(124,800 + 15,000)

(139,800 2)

399,000

Weighted-average number of shares outstanding, 2013:
Jan. 1 to Apr. 1—200,000 1.1 2.0 3/12 .................................
Apr. 1 to Oct. 1—200,000 + (50 2,500) = 325,000;
325,000 1.1 2.0 6/12 ..............................................................
Oct. 1 to Dec. 31—325,000 1.1 = 357,500;
357,500 + 7,000 = 364,500; 364,500 2.0 3/12...........................
Weighted-average number of common shares ...........................
Weighted-average number of shares outstanding, 2014:
Jan. 1 to Oct. 1—364,500 2.0 = 729,000; 729,000 9/12 ...........
Oct. 1 to Dec. 31—(729,000 + 170,000) 3/12 ..............................
Weighted-average number of common shares ...........................

18–23.

110,000
357,500
182,250
649,750
546,750
224,750
771,500

Computation of shares outstanding (working backward):
Oct. 1 to Dec. 31 .........................................................
581,900*
July 1 to Oct. 1 ...........................................................

529,000†
May 1 to July 1 ...........................................................
514,000**
Apr. 1 to May 1 ...........................................................
257,000§
Feb. 1 to Apr. 1 ...........................................................
260,000#
Jan. 1 to Feb. 1 ...........................................................
220,000***
COMPUTATIONS:
*Total dividends divided by dividend per share at Dec. 31 ($407,330/$0.70)
†
Shares outstanding before 10% stock dividend at Oct. 1 (581,900/1.10)
** Shares outstanding before July 1 stock sale (529,000 – 15,000)
§
Shares outstanding before 2-for-1 stock split on May 1 (514,000/2)
#
Shares outstanding before purchase of treasury stock on Apr. 1
(257,000 + 3,000)
*** Shares outstanding before Feb. 1 stock sale (260,000 – 40,000)


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824

18–23.

18–24.

Chapter 18


(Concluded)
Computation of weighted-average shares:
Jan. 1 to Feb. 1 220,000 2 (stock split) 1.10 (stock
dividend) 1/12...............................................
Feb. 1 to Apr. 1 260,000 2 (stock split) 1.10 (stock
dividend) 2/12...............................................
Apr. 1 to July 1 257,000 2 (stock split) 1.10 (stock
dividend) 3/12...............................................
July 1 to Dec. 31 (514,000 + 15,000) 1.10 (stock
dividend) 6/12...............................................
Weighted-average shares 2013..........................................................
*Rounded.
2013
Computation of earnings:
Income before income taxes ........................................................
Less: Income taxes (30%) ............................................................
Net income ....................................................................................
Less: Preferred dividend ..............................................................
Net income identified with common stock ..................................

40,333*
95,333*
141,350
290,950
567,966

$ 636,400
190,920
$ 445,480

70,000
$ 375,480

Computation of weighted-average number of shares:
60,000 9/12 = 45,000
100,000 3/12 = 25,000
70,000
Basic EPS: $375,480/70,000 .........................................................
2014
Computation of earnings:
Income before income taxes
($461,000 – $42,000) .................................................
Less: Income taxes (30%) ..........................................
Income before extraordinary items............................
Less: Dividend requirement on cumulative
10% preferred ...........................................................
Income before extraordinary items identified with
common stock..........................................................
Extraordinary gain ......................................................
Less: Income taxes (30%) ..........................................
Extraordinary gain net of taxes ..................................
Net income identified with common stock ................

$

5.36

$ 419,000
125,700
$ 293,300

70,000
$ 223,300
$ 42,000
12,600
29,400
$ 252,700


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Chapter 18

825

18–24. (Concluded)
Computation of weighted-average number of shares:
100,000 4/12 = 33,333
120,000 8/12 = 80,000
113,333
Basic EPS:
Income before extraordinary items ($223,300/113,333)
Extraordinary gain ($29,400/113,333) .......................
Net income ($252,700/113,333)..................................

$1.97
0.26
$2.23

18–25. Basic EPS:
Income from continuing operations ........................
Loss from disposal of segment ($4,200/20,000) .....

Net income ...............................................................

a
$ 1.05*
(0.21)
$ 0.84

b
$ 0.75†
(0.21)
$ 0.54

*$21,000/20,000 = $1.05
†
Income from continuing operations ...................................................
Dividend requirement on cumulative preferred ($75,000 0.08) ......
Income from continuing operations identified with common
stock ...................................................................................................
Earnings per share: $15,000/20,000 = $0.75
**Income from continuing operations less dividend requirement on 8% cumulative preferred stock ..........................................
Dividends declared on 7% noncumulative preferred ........................
Income from continuing operations identified with common
stock ...................................................................................................
Earnings per share: $12,000/20,000 = $0.60

18–26.

a. After-tax interest:
$500,000 0.075 = $37,500; $37,500
Contribution per share:

$24,375/12,500 shares (500 bonds

c
$ 0.60**
(0.21)
$ 0.39
$21,000
6,000
$15,000

$15,000
3,000
$12,000

0.65* = $24,375
25 shares per bond) = $1.95

The contribution is greater than the $1.54 basic EPS; therefore, the bond
conversion is antidilutive.
*The after-tax rate: 100% – 35% tax rate = 65%
b. Contribution per share:
30,000 shares $6 per share = $180,000; $180,000/90,000 shares
(30,000 preferred shares 3 shares of common for each preferred
share) = $2.00
The contribution is greater than the $1.54 basic EPS; the security is antidilutive.


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826


Chapter 18

18–26. (Concluded)
c. The average market price exceeds the exercise price; assumed conversion
is dilutive.
d. After-tax interest:
$800,000 0.11 = $88,000; $88,000
Contribution per share:
$57,200/20,000 shares (800 bonds

0.65 = $57,200
25 shares per bond) = $2.86

The contribution is greater than the $1.54 basic EPS; the convertible bonds
are antidilutive.
e. Contribution per share:
$1,000,000 0.07 = $70,000; $70,000/50,000 shares (10,000

5) = $1.40

The contribution is less than the $1.54 basic EPS; the security is dilutive.

18–27.

18–28.

Number of shares to be used in computing diluted EPS:
Actual number of shares outstanding
during entire year ....................................................
Incremental shares:

On assumed exercise of options ........................
Less: Assumed repurchase of shares
with proceeds from exercise of options
(12,000 $6)/$8 ..................................................

55,000
12,000

9,000

Application of proceeds from assumed exercise of options
outstanding to purchase treasury stock:
Proceeds from assumed exercise of options, 40,000 $14 .......
Number of outstanding shares that could be repurchased
with proceeds from options, $560,000/$20 ...............................
Number of incremental shares to be used in computing
diluted EPS:
Incremental shares:
On assumed exercise of options......................................
Less: Maximum assumed repurchase of shares
from proceeds of options ..............................................
Total incremental shares for diluted EPS ........................

3,000
58,000

$ 560,000
28,000

40,000

28,000
12,000


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Chapter 18

18–29.

827

Basic EPS:
Net income ..............................................................
Number of common shares outstanding ...............
Basic EPS ................................................................
Diluted EPS:
Net income ..............................................................
Add interest on convertible bonds, net
of taxes:
Interest, $45,000 0.09 .....................................
Less: Income taxes of 30% ...............................
Adjusted net income ...............................................

18–30.

$ 75,000
÷ 10,000
$ 7.50
$ 75,000


$4,050
1,215

2,835
$ 77,835

Actual number of shares outstanding ...................
Additional shares issued on assumed
conversion of bonds ............................................

10,000

Adjusted number of shares ....................................

14,000

Diluted EPS, $77,835/14,000 ...................................

$5.56

4,000

Basic EPS:
Income before extraordinary gain
($199,800/100,000) ..............................................
Extraordinary gain ($43,520/100,000)...................
Net income ............................................................
*Rounded down.
Diluted EPS:
Income before extraordinary gain ..........................

Add interest on convertible bonds, net
of taxes:
Interest ($800,000 0.05) ..................................
Less: Income taxes (30%) .................................
Adjusted income before extraordinary gain
Actual number of shares outstanding ...................
Additional shares assumed issued on
conversion (50 800) ...........................................
Total shares for computing diluted EPS ...............
Diluted EPS:
Income before extraordinary gain
($227,800/140,000) ...........................................
Extraordinary gain ($43,520/140,000) ................
Net income ..........................................................

$2.00
0.43*
$2.43

$ 199,800

$ 40,000
12,000

28,000
$ 227,800
100,000
40,000
140,000


$1.63
0.31
$1.94


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828

18–31.

Chapter 18

1. Because the preferred stock is noncumulative and no preferred dividends
were declared or paid, no adjustment to income for preferred dividends is
required.
Per
Totals
Share
Basic loss per share:
Loss from operations ............................................ $ (200,000)
Actual number of common shares
outstanding .........................................................
180,000
Basic loss per share
($200,000/180,000) ..............................................
$ (1.11)
Diluted loss per share:
Because Cougar had an operating loss, no adjustment for the assumed
conversion of the preferred stock is required. If the preferred stock were
converted, the number of shares would be increased by 80,000 shares.

The new computation, therefore, would be –$200,000/260,000 = $(0.77)
per share. This figure is antidilutive because it is a lower loss per share
than the basic loss per share.
2. Because the preferred stock is cumulative, an income adjustment is necessary for preferred dividends.
Per
Totals
Share
Basic loss per share:
Loss from operations ............................................ $(200,000)
Less: Preferred dividends .....................................
(80,000)
Loss identified with common stock ..................... $(280,000)
Actual number of common shares
outstanding .........................................................
Basic loss per share
($280,000/180,000) ..............................................

÷ 180,000
$(1.56)

Again, the conversion of the preferred stock is antidilutive because of the
operating loss.


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Chapter 18

18–32.

829


Basic EPS:
Net income ....................................................................................

$950,000

Weighted-average number of shares:
Jan. 1 to May 1
800,000
4/12 ...........................................
May 1—Issue
50,000
May 1 to Aug. 1
850,000
3/12 ...........................................
Aug. 1—Purchase 100,000
Aug. 1 to Oct. 1
750,000
2/12 ...........................................
Conversion
160,000
Oct. 1 to Dec. 31
910,000
3/12 ...........................................
Total weighted-average shares .................................................

266,667*
212,500
125,000
227,500

831,667

Basic EPS: $950,000/831,667 = $1.14
*Rounded.
Diluted EPS:
Test convertible bonds for dilution:
($1,000 0.11 0.70)/80 = $0.96. Since $0.96 is less than $1.14, the bonds
are dilutive and will be considered in computing diluted EPS.
Income:
Income and number of shares are adjusted on the basis that conversion
occurred at the beginning of the year. This requires two computations: the
effect of the assumed conversion of the converted bonds for the period
January 1 to October 1 and the effect of the assumed conversion of the
nonconverted bonds for the entire year.
$950,000 + ($2,000,000 0.11 9/12 0.70) + ($3,000,000 0.11 0.70) =
$950,000 + $115,500 + $231,000 = $1,296,500
Alternatively, the computation could be made by computing the effect on
income and number of shares assuming no conversion and deducting the
effect of the conversion.
$950,000 + ($5,000,000 0.11 0.70) – ($2,000,000 0.11 0.70 3/12) =
$950,000 + $385,000 – $38,500 = $1,296,500
Shares:
Weighted- average number of shares—basic .............................
Additional shares for converted bonds assuming conversion
at January 1 rather than October 1 (2,000 80 9/12) ............
Additional shares assuming $3,000,000 bonds not converted
were converted at January 1 (3,000 80) .................................
Weighted-average number of shares ..........................................

831,667

120,000
240,000
1,191,667*

Diluted EPS ($1,296,500/1,191,667) ..............................................
*Alternatively, the number of shares can be computed as follows:
831,667 + (5,000 80) – (2,000 80 3/12) =
831,667 + 400,000 – 40,000 = 1,191,667

$1.09