Chapter 19, Problem 19.10BYP

To determine

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 preferred stock, and stock options, reduce the EPS by increasing the common shares.

Use the following formula to determine EPS:

$\begin{array}{c}\begin{array}{l}\text{Earnings }\\ \text{per share}\end{array}\}\text{ = }\frac{\text{Earnings available to common shareholders}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{Net income –Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\end{array}$

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.

$\begin{array}{c}\text{Preferred dividends}=\left\{\begin{array}{l}\text{Preferred stock }\times \\ \text{Par value per preference share }\times \\ \text{Preferred dividend percentage}\end{array}\right\}\\ =20,000\text{,000 shares×\$10×8\%}\\ \text{=\$16,000,000}\end{array}$ (1)

Step 2: Compute basic EPS for 2016.

$\begin{array}{c}\text{Basic EPS= }\frac{\text{Net income –Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$145,000,000 – \$16,000,000}}{\text{60,000,000 shares}}\\ \text{= \$2}\text{.15 per share}\end{array}$

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.

$\begin{array}{c}\text{Interest on bonds = Bond value × Interest rate}\\ \text{= \$50,000,000 × 10\%}\\ \text{= \$5,000,000}\end{array}$ (2)

Step 2: Compute after-tax interest savings due to conversion of outstanding bonds.

$\begin{array}{c}\begin{array}{l}\text{After-tax savings }\\ \text{on interest}\end{array}|\text{ = }\left\{\begin{array}{l}\text{Interest on bonds – }\\ \left(\text{Interest on bonds × Tax rate}\right)\end{array}\right\}\\ \text{= \$5,000,000–}\left(\text{\$5,000,000×40\%}\right)\\ \text{= \$5,000,000–\$2,000,000}\\ \text{= \$3,000,000}\end{array}$ (3)

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.

$\begin{array}{c}\text{Diluted EPS = }\frac{\text{Net income –Preferred dividends+After-tax interest savings}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$145,000,000 – \$16,000,000+\$3,000,000}}{\text{69,000,000 shares}}\\ \text{= \$1}\text{.91 per share}\end{array}$

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.

$\begin{array}{c}\begin{array}{l}\text{Preferred dividends for }\\ \text{the whole year for }\\ \text{10,000,000 preferred shares}\end{array}\}=\left\{\begin{array}{l}\frac{\text{Preferred stock}}{2}\times \\ \text{Par value per preferred share }\times \\ \text{Preferred dividend percentage}\end{array}\right\}\\ =\frac{20,000\text{,000 shares}}{2}\text{×\$10×8\%}\\ \text{=\$8,000,000}\end{array}$ (4)

Step 2: Compute the amount of preferred dividends for the half year for 10,000,000 preferred shareholders.

$\begin{array}{c}\begin{array}{l}\text{Preferred dividends for }\\ \text{the half year for }\\ \text{10,000,000 preference shares}\end{array}\}=\left\{\begin{array}{l}\frac{\text{Preference stock}}{2}\times \\ \text{Par value per preference share }\times \\ \text{Preference dividend percentage}\end{array}\right\}\times \frac{1}{2}\\ =\frac{20,000\text{,000 shares}}{2}\text{×\$10×8\%}\times \frac{1}{2}\\ \text{=\$4,000,000}\end{array}$ (5)

Step 3: Compute weighted average common shares which were retired since March 1, 2017 to December 31, 2017 (10 months).

$\begin{array}{c}\begin{array}{l}\text{Weighted average }\\ \text{of shares }\end{array}\}\text{= Number of shares retired }\times \text{ Time period}\\ \text{= 12,000,000 shares × }\frac{10}{\text{12}}\\ \text{= 10,000,000 shares}\end{array}$ (6)

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.

$\begin{array}{c}\text{Basic EPS= }\frac{\text{Net income –Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$134,000,000 – \$8,000,000–\$4,000,000}}{\text{50,000,000 shares}}\\ \text{= \$2}\text{.44 per share}\end{array}$

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.

$\begin{array}{c}\text{Diluted EPS = }\frac{\text{Net income –Preferred dividends+After-tax interest savings}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$134,000,000 – \$12,000,000+\$3,000,000}}{\text{59,000,000 shares}}\\ \text{= \$2}\text{.12 per share}\end{array}$

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.

$\begin{array}{c}\text{Basic EPS= }\frac{\text{Net income –Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$95,000,000 – \$0}}{\text{38,000,000 shares}}\\ \text{= \$2}\text{.50 per share}\end{array}$

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.

$\begin{array}{c}\text{Diluted EPS= }\frac{\text{Net income –Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$95,000,000 – \$0}}{\text{38,000,000 shares}}\\ \text{= \$2}\text{.50 per share}\end{array}$

Note: Refer to Table (4) for value and computation of weighted average number of common shares outstanding.