Question

Charles Austin of the controller’s office of Cheyenne Corporation was given the assignment of determining the basic and diluted earnings per share values for the year ending December 31, 2018. Austin has compiled the information listed below.

1.		The company is authorized to issue 7,720,000 shares of $10 par value common stock. As of December 31, 2017, 1,930,000 shares had been issued and were outstanding.
2.		The per share market prices of the common stock on selected dates were as follows. Price per Share July 1, 2017 $20.00 January 1, 2018 21.00 April 1, 2018 25.00 July 1, 2018 11.00 August 1, 2018 10.50 November 1, 2018 9.00 December 31, 2018 10.00 3. A total of 691,200 shares of an authorized 1,224,000 shares of convertible preferred stock had been issued on July 1, 2017. The stock was issued at its par value of $25.00, and it has a cumulative dividend of $3 per share. The stock is convertible into common stock at the rate of one share of convertible preferred for one share of common. The rate of conversion is to be automatically adjusted for stock splits and stock dividends. Dividends are paid quarterly on September 30, December 31, March 31, and June 30. 4. Cheyenne Corporation is subject to a 40% income tax rate. 5. The after-tax net income for the year ended December 31, 2018, was $10,980,000. The following specific activities took place during 2018. 1. January 1—A 5% common stock dividend was issued. The dividend had been declared on December 1, 2017, to all stockholders of record on December 29, 2017. 2. April 1—A total of 398,400 shares of the $3 convertible preferred stock was converted into common stock. The company issued new common stock and retired the preferred stock. This was the only conversion of the preferred stock during 2018. 3. July 1—A 2-for-1 split of the common stock became effective on this date. The board of directors had authorized the split on June 1. 4. August 1—A total of 289,200 shares of common stock were issued to acquire a factory building. 5. November 1—A total of 22,800 shares of common stock were purchased on the open market at $9.00 per share. These shares were to be held as treasury stock and were still in the treasury as of December 31, 2018. 6. Common stock cash dividends—Cash dividends to common stockholders were declared and paid as follows.         April 15—$0.30 per share         October 15—$0.20 per share 7. Preferred stock cash dividends—Cash dividends to preferred stockholders were declared and paid as scheduled. (a) Determine the number of shares used to compute basic earnings per share for the year ended December 31, 2018 (b) Determine the number of shares used to compute diluted earnings per share for the year ended December 31, 2018. (c) Compute the adjusted net income to be used as the numerator in the basic earnings per share calculation for the year ended December 31, 2018.

Answer 1

Part 1

The number of shares used to compute basic earnings per share is 4797180 as calculated below

Event	Dates Outstanding	Shares Outstanding	Restatement	Fraction of Year	Weighted Shares
Beginning Balance, including 5% stock dividend	Jan. 1–Apr. 1	2026500 (1930000+(1930000*5%))	2	3/12	1013250
Conversion of preferred stock	Apr. 1–July 1	2444820 2026500+(398400+(398400*5%))	2	3/12	1222410
Stock split	July 1–Aug. 1	4889640 (2444820*2)		1/12	407470
Issued shares for    building	Aug. 1–Nov. 1	5178840 (4889640+289200)		3/12	1294710
Purchase of Treasury stock	Nov. 1–Dec. 31	5156040 (5178840-22800)		2/12	859340
total					4797180

Part 2

The number of shares used to compute basic earnings per share is 5621220, as calculated below

Number of shares to compute basic earnings per                share	4797180
Convertible preferred stock—still outstanding                ((691200-398400) X 2 X 1.05)	614880
Convertible preferred stock—converted                                                     (398400 X 2 X 1.05 X 3/12)	209160
Number of shares to compute diluted earnings                per share	5621220

Part 3

The adjusted net income to be used as the numerator in the basic earnings per share calculation for the year ended December 31, 2018, is $9802800, as computed below.

After-tax net income		10980000
Preferred stock dividends
March 31 (691200 X $0.75)	518400
June 30, September 30, and December 31 ((691200-398400) X $0.75 X 3)	658800	1177200
Adjusted net income		9802800