Let’s say that a company had 100,000 shares outstanding at the beginning of the year and issued 30,000 more shares on May 1. The 100,000 shares would…

The weighted average number of shares outstanding is calculated by time-weighting the number of shares outstanding for each period within the year. The initial 100,000 shares were outstanding for 4 months (January 1 - April 30), and the subsequent 130,000 shares (100,000 + 30,000) were outstanding for the remaining 8 months (May 1 - December 31).

The calculation is as follows:

(100,000 shares × 4/12 months) + (130,000 shares × 8/12 months)

= 33,333.33 + 86,666.67

= 120,000 shares.

This calculation is fundamental for determining metrics like Earnings Per Share (EPS).

A. 100,000: This represents the number of shares at the beginning of the year, failing to account for the new shares issued.

C. 140,000: This is a mathematically incorrect calculation and does not reflect the proper time-weighting of the shares outstanding.

D. 180,000: This is a mathematically incorrect calculation and does not reflect the proper time-weighting of the shares outstanding.

References:

1. Financial Accounting Standards Board (FASB). Accounting Standards Codification (ASC) Topic 260, Earnings Per Share. Specifically, ASC 260-10-55, "Implementation Guidance and Illustrations," provides examples for computing weighted-average shares. The principle requires weighting shares by the portion of the period they are outstanding.

2. Kieso, D. E., Weygandt, J. J., & Warfield, T. D. (2019). Intermediate Accounting (17th ed.). Wiley. Chapter 16, "Dilutive Securities and Earnings per Share," explains that "companies must weight the shares issued or purchased during the period by the fraction of the period they are outstanding."

3. MIT OpenCourseWare. (2004). 15.511 Financial Accounting, Fall 2004. Lecture Notes, Lecture 12: Earnings per share; Accounting for income taxes. Section 1.1, "Simple Capital Structure," outlines the computation of weighted average common shares outstanding, demonstrating the time-weighting methodology for share issuances during a period. Available at: https://ocw.mit.edu/courses/15-511-financial-accounting-fall-2004/resources/lec12/

4. Pratt, S. P., & Grabowski, R. J. (2010). Cost of Capital: Applications and Examples (4th ed.). Wiley. While focused on the cost of capital, Chapter 4, "Developing the Cost of Equity Capital," discusses the components of market value, including shares outstanding, which implicitly relies on the weighted-average concept for per-share metrics used in valuation models. This text is a foundational resource in the NACVA body of knowledge.