Earnings per share (EPS): The amount of earnings made available to each common share is referred to as earnings per share. Dilutive securities like convertible bonds, convertible
Use the following formula to determine EPS:
To demonstrate: The paradox of increase in EPS while profit decreased with supporting calculations
Explanation of Solution
The following are the main reasons for the paradox of increase in EPS while profit decreased:
- EPS has increased because all the preferred shares ware retired in 2017. Preferred dividends decrease numerator of EPS. Since preferred stock is retired, preferred dividends does not exist to deduct from the numerator, which eventually increases EPS.
- EPS has increased because $50,000,000 convertible debt is retired in 2018. The convertible debt increases the denominator of EPS due to increase in number of shares. Since number of convertible shares is decreased, denominator decreases, which eventually increases EPS.
Supporting computations:
Determine basic EPS of Company DC for the year 2016.
Step 1: Compute the amount of preferred dividends.
Step 2: Compute basic EPS for 2016.
Note: Refer to Equation (1) for value and computation of preferred dividend amount.
Determine diluted EPS of Company DC for the year 2016.
Step 1: Compute interest on bonds.
Step 2: Compute after-tax interest savings due to conversion of outstanding bonds.
Note: Refer to Equation (2) for value and computation of interest on bonds.
Step 3: Compute the total weighted average number of common shares.
Details | Number of Shares |
Weighted average number of shares held on December 31, 2015 | 60,000,000 |
Number of new shares due to bond conversion | 9,000,000 |
Total weighted average number of shares | 69,000,000 shares |
Table (1)
Step 4: Compute diluted EPS for 2016.
Note: Refer to Equation (1) for value and computation of preferred dividends, Equation (3) for value and computation of after-tax interest savings, and Table (1) for value and computation of weighted average number of common shares outstanding.
Determine basic EPS of Company DC for the year 2017.
Step 1: Compute the amount of preferred dividends for the whole year for 10,000,000 preferred shareholders.
Step 2: Compute the amount of preferred dividends for the half year for 10,000,000 preferred shareholders.
Step 3: Compute weighted average common shares which were retired since March 1, 2017 to December 31, 2017 (10 months).
Step 4: Compute the total weighted average number of common shares.
Details | Number of Shares |
Weighted average number of shares held on December 31, 2016 | 60,000,000 |
Weighted average number of shares retired | (10,000,000) |
Total weighted average number of shares | 50,000,000 shares |
Table (2)
Note: Refer to Equation (6) for value and computation of weighted average number of shares retired.
Step 5: Compute basic EPS for 2017.
Note: Refer to Equations (4) and (5) for value and computation of preferred dividend amounts, and Table (2) for value and computation of weighted average number of common shares outstanding.
Determine diluted EPS of Company DC for the year 2017.
Step 1: Compute the total weighted average number of common shares.
Details | Number of Shares |
Weighted average number of shares held on December 31, 2016 | 60,000,000 |
Weighted average number of shares retired | (10,000,000) |
Number of new shares due to bond conversion | 9,000,000 |
Total weighted average number of shares | 59,000,000 shares |
Table (3)
Note: Refer to Equation (6) for value and computation of weighted average number of shares retired.
Step 2: Compute diluted EPS for 2017.
Note: Refer to Equations (4) and (5) for value and computation of preferred dividend amounts, Equation (3) for value and computation of after-tax interest savings, and Table (3) for value and computation of weighted average number of common shares outstanding.
Determine basic EPS of Company DC for the year 2018.
Step 1: Compute the total weighted average number of common shares.
Details | Number of Shares |
Weighted average number of shares held on December 31, 2017 | 60,000,000 |
Weighted average number of shares retired | (10,000,000) |
Number of shares retired | (12,000,000) |
Total weighted average number of shares | 38,000,000 shares |
Table (4)
Note: Refer to Equation (6) for value and computation of weighted average number of shares retired.
Step 2: Compute basic EPS for 2018.
Note: Refer to Table (4) for value and computation of weighted average number of common shares outstanding.
Determine diluted EPS of Company DC for the year 2018.
Note: Refer to Table (4) for value and computation of weighted average number of common shares outstanding.
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Chapter 19 Solutions
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