Chapter 19, Problem 19.19P

EPS; options; restricted stock; additional components for “proceeds” in treasury stock method

• LO19–1, LO19–2, LO19–4, LO19–8, LO19–11

Witter House is a calendar-year firm with 300 million common shares outstanding throughout 2018 and 2019. As part of its executive compensation plan, at January 1, 2017, the company had issued 30 million executive stock options permitting executives to buy 30 million shares of stock for $10 within the next eight years, but not prior to January 1, 2020. The fair value of the options was estimated on the grant date to be $3 per option.

In 2018, Witter House began granting employees stock awards rather than stock options as part of its equity compensation plans and granted 15 million restricted common shares to senior executives at January 1, 2018. The shares vest four years later. The fair value of the stock was $12 per share on the grant date. The average price of the common shares was $12 and $15 during 2018 and 2019, respectively.

The stock options qualify for tax purposes as an incentive plan. The restricted stock does not. The company’s net income was $150 million and $160 million in 2018 and 2019, respectively. Its income tax rate is 40%.

Required:

1. Determine basic and diluted earnings per share for Witter House in 2018.

2. Determine basic and diluted earnings per share for Witter House in 2019.

To determine

The basic and diluted earnings per share of W House for the year 2018

Explanation of Solution

Determine basic EPS of W House for the year 2018.

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

Determine diluted EPS of W House for the year 2018.

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 2018.

$\begin{array}{c}\text{Hypothetical proceeds = }\left\{\begin{array}{l}\text{Exercisable options + }\\ \text{Un-expensed compensation }\\ \text{expense for 2018}\end{array}\right\}\\ \text{=\$300,000,000+\$30,000,000}\\ \text{=\$330,000,000}\end{array}$ (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 2018.

$\begin{array}{c}\begin{array}{l}\text{Hypothetical }\\ \text{proceeds}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Cash proceeds +Un-expensed compensation }\\ \text{expense for 2019, 2020, and 2021}\end{array}\right\}\\ \text{=\$0+}\left(\text{\$45,000,000}\times \text{3 years}\right)\\ \text{=\$135,000,000}\end{array}$ (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 2018	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 2018.

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

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

To determine

The basic and diluted earnings per share of W House for the year 2019

Explanation of Solution

Determine basic EPS of W House for the year 2019.

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

Determine diluted EPS of W House for the year 2019.

Step 1: Compute the hypothetical proceeds in 2019.

$\begin{array}{c}\begin{array}{l}\text{Hypothetical }\\ \text{proceeds}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Exercisable options + }\\ \text{Un-expensed compensation expense for 2019}\end{array}\right\}\\ \text{=\$300,000,000+\$0}\\ \text{=\$300,000,000}\end{array}$ (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, 2019.

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 2019.

$\begin{array}{c}\begin{array}{l}\text{Hypothetical }\\ \text{proceeds}\end{array}\}\text{ = }\left\{\begin{array}{l}\text{Cash proceeds +Un-expensed compensation }\\ \text{expense for 2018 and 2019}\end{array}\right\}\\ \text{=\$0+}\left(\text{\$45,000,000}\times 2\text{ years}\right)\\ \text{=\$90,000,000}\end{array}$ (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 2019.

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

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