A firm has a simple capital structure if it has no potentially dilutive securities outstanding. These are securities that are not yet common stock, but might become common stock if exercised or converted. Thus, they could potentially dilute (meaning reduce) earnings per share.

For a firm with a simple capital structure, EPS is simply earnings available to common shareholders divided by the weighted-average number of common shares outstanding.

Question 20-2

There is a fundamental difference between the increase in shares caused by stock dividends and stock splits and an increase from selling new shares. When additional shares are sold, both the assets of the firm and shareholders’ equity are increased by an additional investment by owners. On the other hand, stock dividends or stock splits merely increase the number of shares without affecting the firm’s assets. As a consequence, the same "pie" is divided into more pieces resulting in a larger number of less valuable shares. Shares outstanding prior to a stock dividend or stock split are retroactively restated to reflect the increase in shares, as if the distribution occurred at the beginning of the period. On the other hand, any new shares issued are "time-weighted’ by the fraction of the period they were outstanding and then added to the number of shares outstanding for the entire period.

Question 20-3

The weighted-average number of shares for calculating EPS would be 104,500 determined as follows:

100,000 (1.05) – 1,200 (5/12) = 104,500 shares
shares stock treasury
at Jan. 1 dividend shares
adjustment

The 1,200 shares retired are weighted by (5/12) to reflect the fact they were not outstanding the last five months of the year. Purchases of shares that occur after a stock dividend or split are not affected by the distribution.

Question 20-4

Preferred dividends are deducted from the numerator in the EPS fraction so that "earnings available to common shareholders" will be divided by the weighted-average number of common shares. An exception would be when the preferred stock is noncumulative and no dividends were declared in the reporting period. Another time the deduction is not made is when the preferred stock is convertible and the calculation of EPS assumes the preferred stock had been converted and therefore no dividends would have been paid.

Question 20-5

Basic EPS does not reflect the dilutive effect of potentially dilutive securities. On the other hand, diluted EPS incorporates the dilutive effect of all potentially dilutive securities, if the effect is not antidilutive.

Question 20-6

When calculating diluted EPS, we assume that the shares specified by stock options, warrants, and rights are issued at the exercise price and that the proceeds are used to buy back as treasury stock as many of those shares as could be acquired at the average market price during the reporting period.

Question 20-7

The potentially dilutive effect of convertible bonds is reflected in diluted EPS calculations by assuming the bonds were converted into common stock. The conversion is assumed to have occurred at the beginning of the period, or at the time the convertible bonds were issued, if later. When conversion is assumed, the additional common shares that would have been issued upon conversion are added to the denominator of the EPS fraction. The numerator is increased by the after-tax interest that would have been avoided if the bonds really had not been outstanding. This effect is reflected in diluted EPS calculations only if the effect is dilutive.

Question 20-8

The potentially dilutive effect of convertible preferred stock is reflected in diluted EPS calculations by assuming the preferred stock was converted into common stock, just as is done with convertible bonds. The conversion is assumed to have occurred at the beginning of the period, or at the time the convertible preferred stock was issued, if later.

When conversion is assumed, the additional common shares that would have been issued upon conversion are added to the denominator of the EPS fraction. Since EPS are calculated as if the preferred shares had been converted into common shares, there would be no dividends on the preferred stock; so, earnings available to common shareholders are increased in the calculation by the dividends that otherwise would have been distributed to preferred shareholders. This is similar to the way after-tax interest would be added back to net income if the securities were convertible bonds. The difference is that dividends have no tax effect to consider. This effect is reflected in diluted EPS calculations only if the effect is dilutive.

Question 20-9

The order in which convertible securities are included in the dilutive EPS calculation is determined by comparing the incremental effect of their conversion. They should be included in numerical order, beginning with the lowest incremental effect (that is, the most dilutive).

Question 20-10

Contingently issuable shares areconsidered outstanding in the computation of diluted EPS when they will later be issued upon the mere passage of time or because of conditions that currently are met. If this year’s operating income was $2.2 million, the additional shares would be considered outstanding in the computation of diluted EPS by simply adding 50,000 additional shares to the denominator of the EPS fraction:

Contingently issuable shares:

no numerator adjustment
———————————
+ 50,000
additional
shares

If conditions specified for issuance are not yet met, the additional shares are ignored in the calculation. This would be the case if this year’s operating income had been $2 million.

Question 20-11

The calculation of diluted EPS assumes convertible bonds had been converted at the beginning of the year (unless they actually were issued later). If they actually had been converted, the actual conversion would cause an actual increase in shares at the conversion date. These additional shares would be time-weighted for the remainder of the year. The numerator would be higher because net income actually would be increased by the after-tax interest saved on the bonds for that period. But the calculation also would assume conversion for the period before the actual conversion date because they were potentially dilutive during that period. The shares assumed outstanding would be time-weighted for the fraction of the year before the conversion, and the numerator would be increased by the after-tax interest assumed saved on the bonds for the same period.

Question 20-12

EPS data (both basic and diluted for a complex capital structure) must be reported on the face of the income statement for income from continuing operations and net income. Per share numbers for discontinued operations, extraordinary items, and the cumulative effect of a change in accounting principle also should be reported either on the face of the income statement or in related disclosure notes when these components of net income are present.

Question 20-13

Disclosure notes should include (a) a summary description of the rights and privileges of the company’s various securities and (b) supplemental EPS data for transactions that occur after the balance sheet date that result in a material change to the number of shares outstanding at the balance sheet date, and (c) a reconciliation of the numerator and denominator used in the basic EPS computations to the numerator and the denominator used in the diluted EPS computations.

Exercises

Exercise 20-1

(amounts in millions, except per share amount)

net Earnings
income Per Share

$741 $741

——————————————————————— = —— = $1.30

544 + 36 (10/12) – 6 (8/12) 570
shares new shares
at Jan. 1 shares retired

Exercise 20-2

(amounts in thousands, except per share amount)

net Earnings
income Per Share

$655 $655

———————————————————————— = —— = $.64

900 (1.05) + 60 (8/12) (1.05) + 72 (7/12) 1,029
shares new new
at Jan. 1 shares shares
­___ stock dividend ___­

adjustment

Exercise 20-3

(amounts in millions, except per share amount)

net preferred
income dividends Earnings
$426 – $16 $410 Per Share

—————————————————— = —— = $.50

820 820

common
shares

Since the preferred stock is cumulative, the dividends (8% x $200 million = $16 million) are deducted even though no dividends were declared. There are no potentially dilutive securities, so a single calculation of EPS is appropriate.

Exercise 20-4

(amounts in thousands, except per share amount)

net preferred Earnings
income dividends Per Share

$2,000 – $50 $1,950

————————————————— = ———— = $1.95

800 (1.25) 1,000
shares stock dividend
at Jan. 1 adjustment
 
 

Exercise 20-5

(amounts in thousands, except per share amount)

net preferred Net Loss
loss dividends Per Share
– $114 – $761 - $190

—————————————————————— = —— = ($.50)

373 + 12 (7/12) 380
shares new
at Jan. 1 shares

(amounts in millions, except per share amount)

net preferred Earnings
income dividends Per Share
$150 – $27¹ $123

—————————————————————— = ——— = $.65

200 (1.05) – 24 (10/12) (1.05) + 4 (3/12) 190
shares treasury new
at Jan. 1 shares shares
­___ stock dividend ___­

adjustment

19% x $300 = $27
 

Exercise 20-8

(amounts in millions, except per share amount)

Basic EPS

net preferred
income dividends

$150 – $27 $123

—————————————————————————— = —— = $.65

200 (1.05) – 24 (10/12) (1.05) + 4 (3/12) 190
shares treasury new
at Jan. 1 shares shares
­___ stock dividend ___­

adjustment
 
 

Diluted EPS

net preferred
income dividends

$150 – $27 $123

—————————————————————————— = —— = $.63

200 (1.05) – 24 (10/12) (1.05) + 4 (3/12) + (30 – 24*) 196
shares treasury new assumed exercise
at Jan. 1 shares shares of options
­___ stock dividend ___­

adjustment

Exercise 20-14

(amounts in millions, except per share amounts)

Basic EPS

net
income
$250 $250

—————————————————————————— = ——— = $4.72

50 + 12 (3/12) 53
shares new
at Jan. 1 shares
 
 

Diluted EPS

net after-tax
income interest savings
$250 +$40* – 40% ($40*) $274

—————————————————————————— = ——— = $4.35

50 + 12 (3/12) + 10 63
shares new conversion
at Jan. 1 shares of bonds

* $400 x 10%
 
 
 
 

Exercise 20-15

Basic EPS

net
income
$900 $900

————————————————————————= ——— = $4.57

191 + 9 (8/12) 197
shares new
at Jan. 1 shares
 
 

Diluted EPS

net
income
$900 $900

————————————————————————= ——— = $4.48

191 + 9 (8/12) + (48 – 44*) 201
shares new exercise
at Jan. 1 shares of options

Exercise 20-19

List A List B

_ e_ 1. Subtract preferred dividends.                 a. Options exercised.
_m_ 2. Time-weighted by 5/12.                          b. Simple capital structure.
_ a_ 3. Time-weighted shares assumed issued    c. Basic EPS.
           plus time-weighted-actual shares.           d. Convertible preferred stock.
__i_ 4. Mid-year event treated as if it occurred  e. Earnings available to common shareholders
           at the beginning of the reporting period. f. Antidilutive.
__l_ 5. Preferred dividends do not reduce         g. Increased marketability.
           earnings.                                             h. Extraordinary items.
_ b_ 6. Single EPS presentation.                       i. Stock dividend.
_ g_ 7. Stock split.                                           j. Add after-tax interest to numerator.
 _d_ 8. Potentially dilutive security.                  k. Diluted EPS.
__f_ 9. Exercise price exceeds market price.     l. Noncumulative, undeclared.
__c_ 10. No dilution assumed. preferred dividends.
__j_ 11. Convertible bonds. m. Common shares retired in August.

_n_ 12. Contingently issuable shares. n. Include in diluted EPS when

_k_ 13. Maximum potential dilution. conditions for issuance are met.

_h_ 14. Per share amounts for net income and

for income from continuing operations.
 

Problems

Problem 20-7

Basic EPS:

Basic EPS

net preferred
income dividends
750,000 – $30,000 $720,000
——————————————————————————————————————— = ——— = $2.31
300,000 + 36,000 (4/12) 312,000
shares new
at Jan. 1 shares

Diluted EPS

net preferred after-tax
income dividends Interest savings
750,000 – $30,000 + $80,000 - 40% ($80,000) $768,000
——————————————————————————————————————— = ——— = $2.11
300,000 + 36,000 (4/12) + (30,000–18,750) + 40,000 363,250
shares new exercise conversion
at Jan. 1 shares of options of bonds

1. Schedule to Compute Shares for Basic EPS

300,000     Outstanding Jan. 1
  12,000     Shares issued (36,000 x 4/12)
312,000

2. Schedule to Compute Basic EPS

$750,000     Net income
  (30,000)    Preferred dividends ($3 x 10,000)
$720,000     Income available to common
÷312,000     (See Sch. 1)
$    2.31

3. Schedule to Compute Shares for Diluted EPS*

  11,250     Options (30,000 - 18,750) [See Schedule 1A]
  40,000     Conversion of bonds
312,000     (See Sch. 1)
363,250

4. Schedule to Compute Diluted EPS

$ 750,000     Net income
  (30,000)     Preferred dividends ($3 x 10,000)
   48,000      After-tax savings on bonds ($80,000 - (80,000 x .40))
$768,000      Income available to common
÷363,250     (See Sch. 3)
$    2.11

Schedule 1A - Computation of Treasury Shares

    30,000     shares
x  $22.50     exercise price
$675,000     proceeds
    ÷  $36     average share price
   18,750     treasury shares

Real World Case 20-9

Requirement 1

Yes and no. The income statement sometimes reports items that require separate presentation within the statement, including one or more of the following:

Requirement 2

The price-earnings ratio is simply the market price per share divided by the earnings per share. For Kellogg’s most recent 12 months, the ratio is:

It purports to measure the market's perception of the "quality" of a company’s earnings by indicating the price multiple the securities market is willing to pay for the company’s earnings. The P/E ratio reflects analysts’ perceptions of the company’s growth potential, stability, and relative risk by relating these performance measures with the external judgment of the marketplace in regard to the value of the company.

Care is needed when evaluating price-earnings ratios. Like other ratios, it is best evaluated in context of P/E ratios of earlier periods and other, similar companies. For example, although Kellogg’s results are down from last year, the P/E ratio of General Mills, Kellogg’s prime competitor was 27.3 at the same time. Both are high relative to the average P/E ratio for all companies at the time, which was approximately 17.

Requirement 3

The dividend payout ratio expresses the percentage of earnings that is distributed to shareholders as dividends. The ratio is calculated by dividing dividends per common share by the earnings per share. For Kellogg’s most recent 12 months, the ratio is:

$.92 ÷ ($.08 + 1.12) = 77%