Chapter 19, Problem 19.19P

(1)

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 determine: The basic and diluted earnings per share of W House for the year 2016

Explanation of Solution

Determine basic EPS of W House for the year 2016.

$\begin{array}{c}\text{Basic EPS = }\frac{\text{Net income–Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$150,000,000 – \$0}}{\text{300,000,000 shares}}\\ \text{= \$0}\text{.50 per share}\end{array}$

Determine diluted EPS of W House for the year 2016.

Step 1: Compute the total compensation cost of stock options to W House.

$\begin{array}{c}\begin{array}{l}\text{Total compensation }\\ \text{cost of stock options}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Estimated fair market value of the option × }\\ \text{Number of options granted}\end{array}\right\}\\ \text{= \$3 × 30,000,000 shares}\\ \text{= \$90,000,000}\end{array}$ (1)

Step 2: Compute the compensation expense allocated each year.

$\begin{array}{c}\begin{array}{l}\text{Expense allocated }\\ \text{each year}\end{array}\}\text{ =}\frac{\text{ Total compensation cost of stock options}}{\text{Vesting period}}\\ \text{=}\frac{\text{\$90,000,000}}{\text{3 years}}\\ \text{= \$30,000,000}\end{array}$ (2)

Note: Refer to Equation (1) for the value and computation of compensation cost.

Step 3: Compute the value of exercisable options.

$\begin{array}{c}\text{Exercisable options value = Number of shares × Exercise price}\\ \text{= 30,000,000 shares × \$10}\\ \text{= \$300,000,000}\end{array}$ (3)

Step 4: Compute the hypothetical proceeds of options in 2016.

$\begin{array}{c}\text{Hypothetical proceeds = }\left\{\begin{array}{l}\text{Exercisable options + }\\ \text{Un-expensed compensation }\\ \text{expense for 2016}\end{array}\right\}\\ \text{=\$300,000,000+\$30,000,000}\\ \text{=\$330,000,000}\end{array}$ (4)

Note: Refer to Equations (3) and (2) for the value and computation of exercisable options and compensation expense.

Step 5: Compute the number of shares assumed to be reacquired.

$\begin{array}{c}\begin{array}{l}\text{Number of shares }\\ \text{assumed reacquired}\end{array}\}\text{ = }\frac{\text{Hypothetical proceeds of options}}{\text{Average market price per share}}\\ \text{= }\frac{\text{\$330,000,000}}{\text{\$12}}\\ \text{= 27,500,000 shares }\end{array}$ (5)

Note: Refer to Equation (4) for the value and computation of hypothetical proceeds of options.

Step 6: Compute the total compensation cost of stock awards to W House.

$\begin{array}{c}\begin{array}{l}\text{Total compensation }\\ \text{cost of stock awards}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Estimated fair market value of the award × }\\ \text{Number of awards granted}\end{array}\right\}\\ \text{= \$12 × 15,000,000 shares}\\ \text{= \$180,000,000}\end{array}$ (6)

Step 7: Compute the compensation expense allocated each year.

$\begin{array}{c}\begin{array}{l}\text{Expense allocated }\\ \text{each year}\end{array}\}\text{ =}\frac{\text{ Total compensation cost of stock awards}}{\text{Vesting period}}\\ \text{=}\frac{\text{\$180,000,000}}{\text{4 years}}\\ \text{= \$45,000,000}\end{array}$ (7)

Note: Refer to Equation (6) for the value and computation of compensation cost.

Step 8: Compute the hypothetical proceeds of awards in 2016.

$\begin{array}{c}\begin{array}{l}\text{Hypothetical }\\ \text{proceeds}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Cash proceeds +Un-expensed compensation }\\ \text{expense for 2017, 2018, and 2019}\end{array}\right\}\\ \text{=\$0+}\left(\text{\$45,000,000}\times \text{3 years}\right)\\ \text{=\$135,000,000}\end{array}$ (8)

Note: There are no cash proceeds until the completion of the vesting years. Refer to Equation (7) for the value and computation of compensation expense for one year.

Step 9: Compute the number of shares assumed reacquired.

$\begin{array}{c}\begin{array}{l}\text{Number of shares }\\ \text{assumed reacquired}\end{array}\}\text{ = }\frac{\text{Hypothetical proceeds of options}}{\text{Average market price per share}}\\ \text{= }\frac{\text{\$135,000,000}}{\text{\$12}}\\ \text{= 11,250,000 shares }\end{array}$ (9)

Note: Refer to Equation (8) for the value and computation of hypothetical proceeds of awards.

Step 10: Compute the total weighted average number of common shares.

Details	Number of Shares
Weighted average number of shares held in 2016	300,000,000
Number of exercisable options granted as shares	30,000,000
Number of shares assumed reacquired as treasury stock	(27,500,000)
Number of exercisable awards granted as shares	15,000,000
Number of shares assumed reacquired as treasury stock	(11,250,000)
Total weighted average number of shares	306,250,000 shares

Table (1)

Note: Refer to Equation (5) for the value and computation of number of options assumed reacquired as treasury stock, and Equation (9) for number of awards assumed reacquired as treasury stock.

Step 11: Compute diluted EPS of W House for the year 2016.

$\begin{array}{c}\text{Diluted EPS = }\frac{\text{Net income –Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$150,000,000 – \$0}}{\text{306,250,000 shares}}\\ \text{= \$0}\text{.49 per share}\end{array}$

Note: Refer to Table (1) for value and computation of weighted average number of common shares outstanding.

(2)

To determine

The basic and diluted earnings per share of W House for the year 2017

Explanation of Solution

Determine basic EPS of W House for the year 2017.

$\begin{array}{c}\text{Basic EPS = }\frac{\text{Net income–Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$160,000,000 – \$0}}{\text{300,000,000 shares}}\\ \text{= \$0}\text{.53 per share}\end{array}$

Determine diluted EPS of W House for the year 2017.

Step 1: Compute the hypothetical proceeds in 2017.

$\begin{array}{c}\begin{array}{l}\text{Hypothetical }\\ \text{proceeds}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Exercisable options + }\\ \text{Un-expensed compensation expense for 2017}\end{array}\right\}\\ \text{=\$300,000,000+\$0}\\ \text{=\$300,000,000}\end{array}$ (10)

Note: Refer to Equation (3) for the value and computation of exercisable options value. Do not add any compensation expense because options could be exercised after December 31, 2017.

Step 2: Compute the number of shares assumed to be reacquired.

$\begin{array}{c}\begin{array}{l}\text{Number of shares }\\ \text{assumed reacquired}\end{array}\}\text{ = }\frac{\text{Hypothetical proceeds of options}}{\text{Average market price per share}}\\ \text{= }\frac{\text{\$300,000,000}}{\text{\$15}}\\ \text{= 20,000,000 shares }\end{array}$ (11)

Note: Refer to Equation (10) for the value and computation of hypothetical proceeds of options.

Step 3: Compute the hypothetical proceeds of awards in 2017.

$\begin{array}{c}\begin{array}{l}\text{Hypothetical }\\ \text{proceeds}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Cash proceeds +Un-expensed compensation }\\ \text{expense for 2016 and 2017}\end{array}\right\}\\ \text{=\$0+}\left(\text{\$45,000,000}\times 2\text{ years}\right)\\ \text{=\$90,000,000}\end{array}$ (12)

Note: Since the vesting period is 4 years, there are no cash proceeds. Refer to Equation (7) for the value and computation of compensation expense for one year.

Step 4: Compute excess tax benefit per share.

$\begin{array}{c}\text{Excess tax benefit = }\left\{\begin{array}{l}\left(\begin{array}{l}\left(\text{Market price – Fair market value}\right)\text{ × }\\ \text{Number of stock awards}\end{array}\right)\text{ × }\\ \text{Tax rate}\end{array}\right\}\\ \text{=}\left(\text{\$15–\$12}\right)\text{×15,000,000 shares ×40\%}\\ \text{=\$18,000,000}\end{array}$ (13)

Step 5: Compute the number of shares assumed to be reacquired.

$\begin{array}{c}\begin{array}{l}\text{Number of shares }\\ \text{assumed reacquired}\end{array}\}\text{ = }\frac{\text{Hypothetical proceeds + Excess tax benefit}}{\text{Average market price per share}}\\ \text{= }\frac{\text{\$90,000,000+\$18,000,000}}{\text{\$15}}\\ \text{= 7,200,000 shares }\end{array}$ (14)

Note: Refer to Equations (12) and (13) for the value and computation of hypothetical proceeds and excess tax benefit.

Step 6: Compute the total weighted average number of common shares.

Details	Number of Shares
Weighted average number of shares held in 2016	300,000,000
Number of exercisable options granted as shares	30,000,000
Number of shares assumed reacquired as treasury stock	(20,000,000)
Number of exercisable awards granted as shares	15,000,000
Number of shares assumed reacquired as treasury stock	(7,200,000)
Total weighted average number of shares	317,800,000 shares

Table (2)

Note: Refer to Equation (11) for the values and computation of number of options assumed reacquired as treasury stock, and Equation (14) for number of awards assumed reacquired as treasury stock.

Step 7: Compute diluted EPS of W House for the year 2017.

$\begin{array}{c}\text{Diluted EPS = }\frac{\text{Net income –Preferred dividends}}{\text{Weighted average number of common shares outstanding}}\\ \text{= }\frac{\text{\$160,000,000 – \$0}}{\text{317,800,000 shares}}\\ \text{= \$0}\text{.50 per share}\end{array}$

Note: Refer to Table (2) for value and computation of weighted average number of common shares outstanding.