Calculate Basic And Diluted EPS - CPA Far

1. What is the company's diluted earnings per share for the year?
   Answer: $2.43 Use the if-converted method for convertible bonds. First check for dilution: Basic EPS = $2,000,000 ÷ 800,000 = $2.50. After-tax interest = $1,000,000 × 6% × (1 - 0.25) = $45,000. Conversion shares = ($1,000,000 ÷ $1,000) × 40 = 40,000 shares. Individual EPS effect = $45,000 ÷ 40,000 = $1.125. Since $1.125 < $2.50, the bonds are dilutive. Adjusted numerator = $2,000,000 + $45,000 = $2,045,000. Diluted WACSO = 800,000 + 40,000 = 840,000. Diluted EPS = $2,045,000 ÷ 840,000 = $2.43. Distractor C is basic EPS.
2. What is the relationship between basic and diluted EPS for this company?
   Answer: Diluted EPS will be equal to basic EPS. When a company has a net loss from continuing operations, any potential common shares (from options, convertible securities, etc.) are considered antidilutive. Including them in the calculation would increase the number of shares in the denominator, which would spread the loss over more shares, resulting in a smaller loss per share. A smaller loss is an improvement, which is antidilutive. Therefore, for any company with a net loss, diluted EPS is reported as the same amount as basic EPS. Distractor A would be the result of a dilutive effect, which doesn't occur with a loss. Distractor B describes the antidilutive effect that is prohibited. Distractor D is incorrect; both basic and diluted EPS must be reported, but they will be the same number.
3. What is the income available to common shareholders for the purpose of calculating basic EPS in Year 2?
   Answer: $840,000 For cumulative preferred stock, the dividend for the current period is deducted from net income to calculate income available to common shareholders, regardless of whether it was declared. Dividends in arrears from prior periods that are paid in the current period do not affect the current period's EPS calculation because they would have already been included in the prior period's EPS calculation (as a reduction to income available to common shareholders). Preferred dividend for Year 2 = 20,000 shares × $100 par × 8% = $160,000. Income available to common shareholders for Year 2 EPS = $1,000,000 (Net Income) - $160,000 (Current year's dividend) = $840,000. Distractor A ($680,000) incorrectly subtracts two years of dividends ($1,000,000 - $320,000). Distractor C ($1,000,000) incorrectly ignores the preferred dividend requirement. Distractor D results from adding the dividend instead of subtracting.
4. Birch Corporation had the following capital structure during the current year: 900,000 common shares outstanding all year, and $3,000,000 of 6% convertible bonds issued at par. Each $1,000 bond converts to 20 common shares. The company also had 75,000 warrants outstanding, each exercisable for one share at $25 per share. Net income was $5,400,000, and the tax rate is 30%. The quarterly average stock prices were: Q1 $35, Q2 $40, Q3 $45, Q4 $50. For diluted EPS purposes, which securities should be included as dilutive?
   Answer: Both convertible bonds and warrants should be included as dilutive instruments in the calculation First, test convertible bonds: Interest savings = $3,000,000 × 6% × (1 - 0.30) = $126,000 after-tax. Additional shares = 3,000 bonds × 20 = 60,000 shares. Basic EPS = $5,400,000 ÷ 900,000 = $6.00. Bond dilution effect = $126,000 ÷ 60,000 = $2.10 per share, which is less than $6.00, so bonds are dilutive. For warrants: Average stock price = ($35 + $40 + $45 + $50) ÷ 4 = $42.50. Since $42.50 > $25 exercise price, warrants are dilutive. Proceeds = 75,000 × $25 = $1,875,000. Shares repurchased = $1,875,000 ÷ $42.50 = 44,118. Net dilutive effect = 75,000 - 44,118 = 30,882 shares. Both securities are dilutive. Choice B incorrectly concludes warrants are antidilutive. Choice C incorrectly fails the bond test. Choice D incorrectly rejects both securities.
5. What is Corbin Corp.'s basic earnings per share (EPS) for the year ended December 31, Year 1?
   Answer: $2.00 Basic EPS = Net Income / Weighted-Average Common Shares Outstanding (WACSO). The 200,000 shares were outstanding for the full 12 months, and the 60,000 shares were outstanding for 9 months (April 1 to December 31). WACSO = (200,000 × 12/12) + (60,000 × 9/12) = 200,000 + 45,000 = 245,000 shares. Basic EPS = $490,000 / 245,000 = $2.00. Distractor A incorrectly uses year-end shares (490,000/260,000). Distractor C incorrectly weights new shares for 3 months instead of 9. Distractor D incorrectly uses beginning shares only.
6. What is the company's basic earnings per share for Year 1?
   Answer: $2.00 Stock splits are applied retroactively to all shares outstanding before the split. Beginning shares adjusted for split: 300,000 × 2 = 600,000 shares (treated as outstanding from January 1). Treasury stock purchase: 40,000 shares held for 3 months (October 1 to December 31). Weighted reduction = 40,000 × 3/12 = 10,000 shares. WACSO = 600,000 - 10,000 = 590,000 shares. Basic EPS = $1,180,000 / 590,000 = $2.00. Distractor B would result from using $1,140,000 net income. Distractor D ignores the stock split's effect on the denominator.
7. What is the company's basic earnings per share for the year?
   Answer: $3.00 To calculate weighted-average common shares outstanding (WACSO), stock dividends are treated as if they occurred at the beginning of the period. The beginning shares and any shares issued before the dividend are multiplied by (1 + dividend percentage). 1. Restate beginning shares for the dividend: 100,000 shares × 1.10 = 110,000 shares. These are outstanding for the full year. 2. Calculate weighted shares for the new issuance (which occurred after the dividend and is not affected by it): 30,000 shares × 2/12 = 5,000 shares. 3. Total WACSO = 110,000 + 5,000 = 115,000 shares. 4. Basic EPS = Net Income / WACSO = $345,000 / 115,000 = $3.00. Distractor A ($2.76) results from applying the dividend only from October 1 and not retroactively. Distractor B ($2.82) results from incorrectly applying the dividend to the shares issued on Nov 1. Distractor D ($3.14) results from ignoring the new issuance on Nov 1.
8. What is the correct order to include these securities when calculating diluted EPS?
   Answer: The options first, then the preferred stock. When a company has multiple potentially dilutive securities, they must be ranked and included in the diluted EPS calculation from most dilutive to least dilutive. The dilutiveness is measured by the individual EPS effect of each security. 1. Stock Options: The numerator effect is always $0. The denominator effect is positive (incremental shares). Therefore, options (if dilutive) are always the most dilutive security and are considered first. 2. Convertible Preferred Stock: Individual EPS effect = (Dividends saved) / (Shares from conversion) = (10,000 $100 5%) / (10,000 * 4) = $50,000 / 40,000 = $1.25. Since options have an EPS effect of $0, they are more dilutive than the preferred stock with an effect of $1.25. Therefore, the options are included first. Distractor B reverses the correct order. Distractor C is incorrect because the order matters; including an antidilutive security after a dilutive one could incorrectly increase the EPS. Distractor D describes an incorrect rule.
9. Pine Corporation had 800,000 common shares outstanding at the beginning of the year and net income of $4,000,000. The company has two potentially dilutive securities: (1) 50,000 stock options with an exercise price of $20 per share, and (2) $2,400,000 of 5% convertible bonds, each $1,000 bond convertible into 15 shares. The tax rate is 30%. The average stock price during the year was $35 per share. When applying the if-converted method and treasury stock method in the correct sequence for diluted EPS, what is the proper order of inclusion and the resulting diluted EPS?
   Answer: Test dilution independently, include most dilutive first; diluted EPS of $4.35 Under ASC 260, potentially dilutive securities should be tested for dilution independently, then included in order from most dilutive to least dilutive. Basic EPS = $4,000,000 ÷ 800,000 = $5.00. Test stock options: Proceeds = 50,000 × $20 = $1,000,000. Shares repurchased = $1,000,000 ÷ $35 = 28,571. Net dilution = 50,000 - 28,571 = 21,429 shares. Test convertible bonds: Interest savings = $2,400,000 × 5% × (1 - 0.30) = $84,000. Additional shares = 2,400 bonds × 15 = 36,000. Dilution per share = $84,000 ÷ 36,000 = $2.33. Since $2.33 < $5.00, bonds are more dilutive than options. Include bonds first: ($4,000,000 + $84,000) ÷ (800,000 + 36,000) = $4.88. Then test options against new base: Since options add shares with no earnings, they're still dilutive. Final diluted EPS = $4,084,000 ÷ (836,000 + 21,429) ≈ $4.35. Choice D correctly identifies the sequencing requirement and approximate result.
10. What is the impact of these stock options on the calculation of diluted EPS?
    Answer: They are antidilutive and are excluded from the calculation. Stock options are considered antidilutive and are excluded from the diluted EPS calculation if their exercise price is greater than the average market price of the stock. In this case, the exercise price ($40) is greater than the average market price ($35). If exercised, the options would be 'out of the money,' and the treasury stock method would result in repurchasing more shares than were issued, which would decrease the share count and improperly increase EPS. Therefore, they are antidilutive and ignored. Distractor A is incorrect because the options are antidilutive. Distractor C is incorrect because potential dilution is calculated whether or not the options are exercised. Distractor D is incorrect because the treasury stock method uses the average market price, not the year-end price.
11. Which of the following best describes the primary objective of reporting diluted earnings per share?
    Answer: To measure the performance of an entity over the reporting period by showing the potential dilution of earnings per share from all potential common shares that were outstanding during the period. The objective of diluted EPS is to measure an entity's performance for the reporting period while giving effect to all dilutive potential common shares that were outstanding during that period. It shows the 'worst-case' scenario of dilution based on the capital structure that existed during the year. Distractor A is too narrow; it focuses only on exercise and not conversion. Distractor C uses the term 'worst-case scenario' but this is a means to an end; the primary objective is performance measurement, not just being conservative. Distractor D is incorrect; EPS is a measure of past performance, not a prediction of future performance.
12. What is Apex's basic earnings per share for Year 1?
    Answer: $4.00 Basic EPS is calculated as (Net Income - Preferred Dividends) / Weighted-Average Common Shares Outstanding. For non-cumulative preferred stock, dividends are subtracted from net income only if they are declared in the period. Since Apex's board did not declare any dividends, there is no deduction for preferred dividends in the EPS calculation for Year 1. Income available to common shareholders = $800,000 - $0 = $800,000. Weighted-average common shares = 200,000. Basic EPS = $800,000 / 200,000 = $4.00. Distractor A ($2.50) incorrectly subtracts the potential preferred dividend ($800,000 - (50,000 $100 0.06)) / 200,000 = $500,000 / 200,000 = $2.50. This would be the correct treatment for cumulative preferred stock. Distractors B and D are incorrect calculations.
13. Under FASB ASC 260, Bravo Inc. reported net income of $5,000,000 for the year ended December 31, 20X5. Bravo has 100,000 shares of $100 par, 8% noncumulative preferred stock outstanding, and preferred dividends of $800,000 were declared for 20X5. Weighted-average common shares outstanding were 2,000,000. Calculate the basic EPS for 20X5.
    Answer: $2.10 FASB ASC 260 requires basic EPS to be calculated using income available to common stockholders divided by weighted-average common shares outstanding. The key data includes net income of $5,000,000, declared noncumulative preferred dividends of $800,000, and 2,000,000 weighted-average common shares. The correct answer of $2.10 properly calculates income available to common as $5,000,000 - $800,000 = $4,200,000, then divides by 2,000,000 shares to get $2.10. Answer B ($2.50) incorrectly ignores the preferred dividends, Answer C ($2.60) uses an incorrect calculation, and Answer D ($2.00) appears to overstate the preferred dividend deduction. For noncumulative preferred stock, only declared dividends are deducted from net income, unlike cumulative preferred where dividends accrue regardless of declaration. This framework ensures that EPS reflects only the earnings attributable to common stockholders after satisfying preferred dividend obligations.
14. What is the company's basic earnings per share?
    Answer: $2.71 Basic EPS includes the actual weighted-average shares outstanding during the period. When convertible bonds are converted during the year, the newly issued shares must be included in the WACSO calculation. 1. WACSO before conversion = 180,000 shares 2. Shares issued upon conversion: ($1,000,000 ÷ $1,000) × 20 shares/bond = 20,000 shares 3. These 20,000 shares were outstanding for 3 months (October 1 to December 31) 4. Weighted contribution = 20,000 × (3/12) = 5,000 shares 5. Total WACSO for basic EPS = 180,000 + 5,000 = 185,000 shares 6. Basic EPS = $501,350 ÷ 185,000 = $2.71 Distractor A ($2.50) incorrectly uses 200,000 total shares without weighting. Distractor B is a calculation error. Distractor D ($2.78) incorrectly uses only the pre-conversion WACSO of 180,000 shares.
15. What is the company's diluted earnings per share for the year?
    Answer: $1.89 Use the treasury stock method for stock options. Proceeds from exercise = 10,000 options × $20 = $200,000. Shares assumed repurchased = $200,000 ÷ $25 average market price = 8,000 shares. Incremental shares = 10,000 options exercised - 8,000 repurchased = 2,000 shares. Diluted WACSO = 500,000 + 2,000 = 502,000 shares. Diluted EPS = $950,000 ÷ 502,000 = $1.89. Distractor A is a calculation error. Distractor C ($1.90) is basic EPS. Distractor D is a calculation error.
16. Spruce Inc. reported net income of $5,100,000 for the current year. The company had 900,000 common shares outstanding throughout the year. There are two potentially dilutive securities: (1) 80,000 employee stock options with a $25 exercise price, and (2) $3,600,000 face value of 4% convertible bonds issued at par, with each $1,000 bond convertible into 18 common shares. The company's tax rate is 25%. During the year, the quarterly average market prices were $40, $45, $50, and $55 respectively. However, in the fourth quarter, the market price dropped significantly, and the year-end price was $30. For diluted EPS calculations, what market price should be used for the treasury stock method?
    Answer: The annual average market price of $47.50 should be used for consistency with the if-converted method Under ASC 260, the treasury stock method requires using the average market price during the period, not the ending price or quarterly testing. The annual average = ($40 + $45 + $50 + $55) ÷ 4 = $47.50. Since $47.50 > $25 exercise price, the options are dilutive. This approach ensures consistency and prevents manipulation through period-end price fluctuations. The year-end price of $30 (Choice A) would make options antidilutive, but GAAP requires average pricing. Choice C incorrectly suggests using the highest price, which isn't required. Choice D incorrectly suggests quarterly testing, which isn't the standard approach for annual EPS calculations. The correct approach uses the $47.50 average for treasury stock method calculations.
17. What is the company's diluted earnings per share for the year?
    Answer: $2.40 Use the if-converted method for convertible preferred stock. First calculate basic EPS: Preferred dividends = 50,000 × $100 × 4% = $200,000. Income available to common = $1,200,000 - $200,000 = $1,000,000. Basic EPS = $1,000,000 ÷ 400,000 = $2.50. Check for dilution: Individual EPS effect = $200,000 ÷ (50,000 × 2) = $200,000 ÷ 100,000 = $2.00. Since $2.00 < $2.50, the preferred is dilutive. Diluted numerator = $1,200,000 (add back preferred dividends). Diluted WACSO = 400,000 + 100,000 = 500,000. Diluted EPS = $1,200,000 ÷ 500,000 = $2.40. Distractor B is basic EPS.
18. What is Triton's basic earnings per share for Year 1?
    Answer: $2.20 Basic EPS is calculated as (Net Income - Preferred Dividends) / Weighted-Average Common Shares Outstanding. Because the preferred stock is cumulative, the preferred dividends must be subtracted from net income regardless of whether they were declared. Preferred Dividend Amount = 100,000 shares × $50 par × 8% = $400,000. Income available to common shareholders = $1,500,000 - $400,000 = $1,100,000. Weighted-average common shares = 500,000 (since it was constant). Basic EPS = $1,100,000 / 500,000 = $2.20. Distractor B ($2.33) is incorrect. Distractor C ($3.00) incorrectly ignores the preferred stock dividends ($1,500,000 / 500,000). Distractor D ($3.80) is incorrect and may result from a calculation error.
19. What is the company's basic loss per share for Year 1?
    Answer: $(3.00) When calculating EPS with a net loss, the preferred dividend requirement is still added to the loss to determine the net loss attributable to common shareholders. Preferred Dividend Amount = 20,000 shares × $100 par × 5% = $100,000. Since the preferred stock is cumulative, this dividend is required for the period. Net loss available to common shareholders = Net Loss - Preferred Dividends = $(200,000) - $100,000 = $(300,000). Weighted-average common shares = 100,000. Basic Loss per Share = $(300,000) / 100,000 = $(3.00). Distractor A ($1.00) incorrectly subtracts the preferred dividend amount from the loss. Distractor B ($2.00) ignores the effect of the preferred dividends. Distractor D ($4.00) is a calculation error.
20. What is the company's basic earnings per share for the year?
    Answer: $1.70 To calculate basic EPS, determine the weighted-average common shares outstanding (WACSO). The 500,000 shares were outstanding for the full year before the treasury purchase. The 60,000 treasury shares were not outstanding for 8 months (May 1 to December 31). Weighted reduction = 60,000 × 8/12 = 40,000 shares. WACSO = 500,000 - 40,000 = 460,000 shares. Basic EPS = $782,000 / 460,000 = $1.70. Distractor A incorrectly uses beginning share count. Distractor B would result from using $750,000 net income. Distractor D incorrectly weights treasury shares for 4 months.

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