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
Transcript
Module 18Earnings 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:
PeriodA
Actual Shares Outstanding
B
Fraction of Year Outstanding
CEquivalent Whole Units
D = B x C1/1 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) = 2,750Total 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.
ExampleGarcia 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 publicJuly 1 2-for-1 stock splitOctober 1 Purchased 3,000 shares as treasury stockDecember 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:
PeriodA
Actual Shares Outstanding
B
Multiplication Factor
C
Fraction of Year Outstanding
D
Equivalent Whole Units
E = B x C x D1/1 to 3/31 10,000 1.2 x 2 = 2.4 3/12 6,0004/1 to 6/30 12,000 1.2 x 2 = 2.4 3/12 7,2007/1 to 9/30 24,000 1.2 3/12 7,200
10/1 to 11/30 21,000 1.2 2/12 4,20012/1 to 12/31 25,200 1 1/12 2,100
Total 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.
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. ExampleSmith 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 = $40,000Number of treasury shares that can be bought back = $40,000/$25 = 1,600Thus, Number of new shares issued = 2,000Number of new treasury shares purchased back = 1,600Hence, 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.
NoteA 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).
ExampleHunter 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:
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. 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 _______.
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 1Trevino Company
Trevino Company had 10,000 shares outstanding as of January 1, 2002. The following transactions took place during 2002:Date EventFebruary 1 2-for-1 stock splitApril 1 5,000 new shares issuedJuly 1 20% stock dividend issuedOctober 1 Purchased 2,000 shares of treasury stock
Solution to Demonstration Problem 1, Trevino Company
Period
Actual Shares
OutstandingAssumed Shares
OutstandingFraction of
YearEquivalent
Shares1/1 to 1/31 10,000 10,000 x 2 x 1.2 =
24,0001/12 2,000
2/1 to 3/31 20,000 20,000 x 1.2 = 24,000 2/12 4,0004/1 to 6/30 25,000 25,000 x 1.2 = 30,000 3/12 7,5007/1 to 9/30 30,000 30,000 3/12 7,500
10/1 to 12/31 28,000 28,000 3/12 7,000Total 28,000
Demonstration Problem 2Williams 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 EventApril 1 7,000 new shares issuedJuly 1 2-for-1 stock splitOctober 1 Purchased 2,000 shares of treasury stockThe 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.
PeriodActual Shares Outstanding
Assumed Shares Outstanding
Fraction of Year
Equivalent Shares
1/1 to 3/31 20,000 20,000 x 2 = 40,000 3/12 10,0004/1 to 9/30 27,000 27,000 x 2 = 54,000 6/12 27,000
10/1 to 12/31 52,000 52,000 3/12 13,000Total 50,000
Step 2. Calculate net income available for common stockholders.Preferred dividends = 1,000 x 0.06 x $100 = $6,000Net 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 = $1.88Extraordinary gain per share = $20,000/50,000 = $0.40Net income per share = $2.28
Demonstration Problem 3Parker 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 stockNumerator effect (dividends that need not be paid) = $100 x 0.04 x 2,000 = $8,000Denominator effect (to be issued upon conversion) = 4,000 shares
b. Convertible bondsInterest that need not be paid if conversion is assumed = $1,000 x 0.09 x 500 = $45,000Numerator 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. OptionsDenominator effect for options:Proceeds from exercising options = $160,000 ($16 x 10,000)Number of treasury shares assumed to be purchased = $160,000/$20 = 8,000Thus, increase in number of shares = 2,000
ItemNumerator
Effect
Denominator Effect
(no. of shares) Ratio RankConvertible
preferred stock $ 8,000 4,000 $2.00 2
Convertible bond 36,000 10,000 3.60 3
Options 0 2,000 0 1Thus, 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)
Woods Company had 20,000 shares outstanding as of January 1, 2002. The following transactions took place during 2002:Date EventApril 1 4,000 new shares issuedMay 1 10% stock dividend issuedJuly 1 2-for-1 stock splitNovember 1 Purchased 1,800 shares of treasury stock
Solution to Practice Problem 1, Woods Company
Period
Actual Shares
OutstandingAssumed Shares
OutstandingFraction of
YearEquivalent
Shares1/1 to 3/31 20,000 20,000 x 1.1 x 2 =
44,0003/12 11,000
4/1 to 4/30 24,000 24,000 x 1.1 x 2 = 52,800
1/12 4,400
5/1 to 6/30 26,400 26,400 x 2 = 52,800 3/12 13,2007/1 to 10/31 52,800 52,800 3/12 13,200
11/1 to 12/31 51,000 51,000 2/12 8,500Total 50,300
Practice Problem 2Lewis 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 EventMay 1 20% stock dividend issuedJuly 1 6,000 new shares issuedNovember 1 Purchased 3,600 shares of treasury stockThe 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.
PeriodActual Shares Outstanding
Assumed Shares Outstanding
Fraction of Year
Equivalent Shares
1/1 to 6/30 10,500 10,500 x 1.2 = 12,600 6/12 6,3007/1 to 10/31 18,600 18,600 4/12 6,20011/1 to 12/31 15,000 15,000 2/12 2,500
Total 15,000
Step 2. Calculate net income available for common stockholders.Preferred dividends = 500 x 0.08 x $100 = $4,000Net 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 = $4.00Extraordinary gain per share = $15,000/15,000 = $1.00Net income per share = $45,000/15,000 = $3.00
Practice Problem 3Charles 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 stockNumerator effect (dividends that need not be paid) = $100 x 0.05 x 1,000 = $5,000Denominator effect (to be issued upon conversion) = 1,000 shares
b. Convertible bondsInterest that need not be paid, if conversion is assumed = $1,000 x 0.12 x 100 = $12,000Numerator 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. OptionsDenominator effect for options:Proceeds from exercising options = $100,000 ($20 x 5,000)Number of treasury shares assumed to be purchased = $100,000/$25 = 4,000Thus, increase in number of shares = 1,000
ItemNumerator
Effect
Denominator Effect
(no. of shares) Ratio RankConvertible
preferred stock $5,000 1,000 $5.00 3
Convertible bond 8,400 2,000 4.20 2
Options 0 1,000 0 1Thus, 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 isa. 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 isa. 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 isa. $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 isa. 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 isa. 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 willa. 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 area. 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 1Geiger Company
Geiger Company had 30,000 shares outstanding as of January 1, 2002. The following transactions took place during 2002:Date EventMarch 1 6,000 new shares issuedJune 1 15 % stock dividend issuedSeptember 1 Purchased 2,400 shares of treasury stockDecember 1 2-for-1 stock split
Solution to Homework Problem 1, Geiger Company
Period
Actual Shares
OutstandingAssumed Shares
OutstandingFraction of
YearEquivalent
Shares1/1 to 2/28 30,000 30,000 x 1.15 x 2 = 69,000 2/12 11,5003/1 to 5/31 36,000 36,000 x 1.15 x 2 = 82,800 3/12 20,7006/1 to 8/31 41,400 41,400 x 2 = 82,800 3/12 20,7009/1 to 11/30 39,000 39,000 x 2 = 78,000 3/12 19,500
12/1 to 12/31 78,000 78,000 1/12 6,500Total 78,900
Homework Problem 2Harman 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 EventApril 1 Issued 8,000 new sharesOctober 1 Purchased 12,000 new shares as treasury stockDecember 1 2-for-1 stock splitThe 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.
PeriodActual Shares Outstanding
Assumed Shares Outstanding
Fraction of Year
Equivalent Shares
1/1 to 3/31 40,000 40,000 x 2 = 80,000 3/12 20,0004/1 to 9/30 48,000 48,000 x 2 = 96,000 6/12 48,000
11/1 to 12/31 36,000 36,000 x 2 = 72,000 3/12 18,000Total 86,000
Step 2. Calculate net income available for common stockholders.Preferred dividends = 1,000 x 0.07 x $100 = $7,000Net 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 = $1.70Extraordinary gain per share = $17,200/86,000 = $0.20Net income per share = $129,000/86,000 = $1.50
Homework Problem 3Bowles 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 stockNumerator effect (dividends that need not be paid) = $100 x 0.05 x 400 = $2,000Denominator effect (to be issued upon conversion) =1,250 shares
b. Convertible bondsInterest that need not be paid, if conversion is assumed = $1,000 x 0.10 x 200 = $20,000Numerator 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. OptionsDenominator effect for options:Proceeds from exercising options = $36,000 ($9 x 4,000)Number of treasury shares assumed to be purchased = $36,000/$12 = 3,000Thus, increase in number of shares = 1,000
ItemNumerator
Effect
Denominator Effect
(no. of shares) Ratio RankConvertible
preferred stock $ 2,000 1,250 $1.60 2
Convertible bond 15,000 3,000 5.00 3
Options 0 1,000 0.00 1Thus, 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)
1. The denominator of EPS isa. 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 isa. 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 isa. $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 isa. Interest expense.b. Interest expense, net of tax.c. Preferred dividends.d. Cash interest paid, net of tax.
6. Options are considered dilutive ifa. 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 willa. 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 area. 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.
