代写ACCT 3230 – Corporate Financial Reporting II Earnings Per Share调试Haskell程序

日期：2024-04-03 11:47

ACCT 3230 – Corporate Financial Reporting II

Earnings Per Share

? EPS Introduction

? Basic EPS

? Diluted EPS

Earnings Per Share (EPS) Calculation

Why do firms compute EPS and present it on the income statement?

? EPS = Portion of the company’s earnings that accrue to an owner of an individual share of common stock.

? This is relevant for analysts and investors valuing the stock and projecting future performance.

Several issues complicate a seemingly simple ratio:

? Preferred shareholders: Preferred dividends are distributions of net income that common shareholders do not receive – they must be adjusted for.

? Change in shares outstanding: Common shares outstanding can change drastically throughout the year, complicating the denominator of EPS.

? Dilutive securities: Convertible securities, options, warrants, and restricted stock can quickly dilute earnings per share – investors want to know how low EPS will go if these securities become common shares.

Given its potential usefulness for valuing the firm, EPS is presented as a summary number on the face of the income statement:

Basic EPS

Net Income ? PTefeTTed Dividends

weighted AveTage # of commonshaTes outstanding

? Preferred dividends: Subtract dividends that are declared or owed to preferred shareholders. For cumulative preferred shares, subtract 1 year of dividends even if not declared or paid (or the portion of the annual dividend if the security is issued during the year). This is a consistent application and avoids manipulation when paying dividends in arrears. For non-cumulative preferred shares, only subtract dividends if they are declared during the year.

? Denominator: We use weighted average shares outstanding to account for treasury stock (which is no longer outstanding), actual conversions of bonds and exercises of options/warrants, and stock dividends/splits. The basic idea is that the resources made available by these shares were only available for part of the period.

? WAvg Shares utstanding = Beginning shares outstanding + Shares issued * Portion of year remaining – Shares reacquired * Portion of year outstanding

Note: Stock splits and stock dividends do not generate or use capital; we want EPS to reflect the new amount of outstanding shares, but we do not want to “weight” a change that does not alter a firm’s capital structure. The result: stock splits and stock dividends are applied retroactively, as if they occurred at the beginning of the period (to include all periods presented).

Also: If the firm has any “mandatorily convertible securities”, the number of these shares would be ADDED to the weighted average # of common shares outstanding in the EPS calculation. The intuition is that since these must be converted into common stock at some point, we treat these as though they are already part of the number of common stock shares.

Basic EPS example

Firm A began 2019 with 100,000 common shares outstanding. Net income for the year was $200,000. The firm has 1,000 shares of $5 par, 10% cumulative preferred stock outstanding, and 500 shares of $4 par, 8% noncumulative preferred stock outstanding. Assume that the firm does not declare or pay any dividends during the year. A timeline of events in 2019 affecting the firm’s equity is:

- 3/1: Repurchased 10,000 common shares to hold in treasury at a cost of $8 per share.

- 5/1: Issued 5,000 new shares of common stock.

- 7/1: Declared a 2:1 stock split.

- 11/1: Issued 20,000 new shares of common stock.

Required: Given the above information, calculate basic EPS.

Basic EPS: Numerator

? No preferred dividends were declared in 2019. Therefore, noncumulative preferred stock is not an issue since those shareholders are not owed a dividend. Cumulative preferred stockholders, however, are entitled to a dividend regardless of whether it was declared, so we should subtract one year of cumulative preferred dividends from net income.

o Cumulative preferred dividend = 1,000 shares * $5 par * 10% = $500

Numerator = net income – preferred dividends = 200,000 – 500 = 199,500

Basic EPS: Denominator

? The table below shows the calculation of W/A common shares outstanding. Each stock split/dividend requires new columns for the retroactive application, so check for those before setting up a table like this.

Basic EPS = Numerator / Denominator = 199,500 / 193,333 = $1.03 per share

Diluted EPS: Firms with complex capital structures

A “complex” capital structure occurs when a firm issues securities that are convertible into common stock (or allow for the purchase of common stock) under specified conditions.

This includes: Warrants, Convertible bonds, and Employee Stock

Options (among others)

Companies issue these securities as they are attractive to some investors (i.e., bond investors with a greater risk appetite) or to employees.

However, these securities present an issue for EXISTING holders of common stock: Potential dilution

? Dilution: If a holder of a convertible bond (for example) converts the bond into common equity, now the bond-holder will also share in all future common stock dividends. As a result, the existing common stock-holder receives a smaller portion of all future dividends (and a lower % claim to the firm’s earnings).

? Basic EPS ignores this potential dilution.

Intuitively: Diluted EPS is a worst-case scenario that includes the potential effects of all dilutive securities, while omitting potential effects of all anti-dilutive securities. Further, if the firm records a net loss from continuing operations, we set Basic EPS = Diluted EPS (to avoid recording a smaller net loss per share for diluted EPS).

Diluted EPS: Accounting treatment of potentially dilutive securities

Convertible bonds: Use the if-converted method and treat the bonds as if they were converted at the date of issuance (or the beginning of the period if they were issued in a prior period). EPS adjustments from assuming conversion come from after-tax interest expense (numerator) and new shares issued (denominator).

Convertible preferred stock: Use the if-converted method and treat the shares as if they were converted at the date of issuance (or the beginning of the period if they were issued in a prior period). EPS adjustments from assuming conversion come from preferred dividends (numerator) and new shares issued (denominator).

Stock options and warrants: Options and warrants increase the denominator but also generate cash from the strike price that can be used to repurchase treasury shares and offset the dilution. Use the treasury stock method and treat the securities as if they were exercised at the date of issuance (or the beginning of the period if they were issued in a prior period). EPS adjustments from assuming exercise come from new shares issued (denominator increase) and treasury shares purchased at the average market price (denominator decrease).

Diluted EPS with multiple securities

EPS changes with each additional dilutive security added. To ensure that anti-dilutive securities are not being included, take the following steps:

? Calculate the incremental EPS effect of each individual security.

? Rank the securities from lowest to highest incremental EPS.

? Add the numerator and denominator effects to basic EPS one by one until a security increases EPS. That security and any remaining security are anti-dilutive and should not be included.

Diluted EPS example

Firm A began 2019 with 100,000 common shares outstanding. Net income for the year was $200,000. The firm has 1,000 shares of $5 par, 10% cumulative preferred stock outstanding, and 500 shares of $4 par, 8% noncumulative preferred stock outstanding. Assume that the firm does not declare or pay any dividends during the year. A timeline of events in 2019 affecting the firm’s equity is:

? 3/1: Repurchased 10,000 common shares to hold in treasury at a cost of $8 per share.

? 5/1: Issued 5,000 new shares of common stock.

? 7/1: Declared a 2:1 stock split.

? 11/1: Issued 20,000 new shares of common stock.

Additional information:

? Each cumulative preferred share is convertible into one share of (post-split adjusted) common stock. The convertible preferred stock was issued on November 1st, 2017.

? Convertible bonds with a par value of $1,000,000 were issued on March 1st , 2019. The interest rate on the bonds is 17%. The bonds can be converted into 100,000 (post-split adjusted) common shares. The tax rate is 40%.

? There are 10,000 (post-split adjusted) stock options outstanding with a strike price of $10. The average market price of the stock was $20 in 2019. The options were granted in 2018.

Required: Use the information above to calculate diluted EPS.

Basic EPS

For basic EPS, this is the same problem as before. The numerator is 199,500, the denominator is 193,333, and basic EPS is $1.03 per share.

Potentially dilutive securities

Convertible preferred:

? Numerator: The cumulative preferred dividend was $500. Assuming they were converted at the beginning of the year, we would not owe this dividend. Therefore, the numerator effect should be +$500.

? Denominator: The 1,000 preferred shares are convertible into 1,000 shares of common stock. Therefore, the denominator effect should be +1,000

? Earnings per incremental share effect = 500/1,000 = $0.50

Diluted EPS, Example continued…

Convertible bonds:

? Numerator: The numerator effect would be the net-of-tax interest avoided if these bonds were converted at the date of issuance. Therefore, the numerator effect should be ($1,000,000 * 17% * 10/12) * (1 – 40%) = +$85,000

? Denominator: The shares can be converted into 100,000 common shares. The earliest date possible is the date of issuance, March 1st, so they would not be outstanding the entire year. Therefore, the denominator effect is 100,000 * 10/12 = +83,333

? Earnings per incremental share effect = 85,000/83,333 = $1.02

Stock options:

? Numerator: No numerator effect

? Denominator - issuance: Assuming the options are exercised at the beginning of the year, the first denominator effect is +10,000 from the issuance of new shares.

? Denominator – treasury: Proceeds from 10,000 options exercised at a strike price of $10 are 10,000 * $10 = $100,000. The second denominator effect is the amount of shares that can be repurchased at the market price of $20 using the $100,000 proceeds. Therefore, the second denominator effect is -$100,000/$20 = -5,000

? The total denominator effect is 10,000 – 5,000 = 5,000

? Earnings per incremental share effect = $0/5,000 = $0

Rank securities in order of Earnings Per Marginal Share effect:

1. $0         Stock options

2. $0.50     Cumulative preferred

3. $1.02     Convertible bonds

Anti-dilution test and diluted EPS calculation

Note: The convertible bonds are anti-dilutive, despite the EPS effect of $1.02, being lower than basic EPS of $1.03. This illustrates the need for ranking the securities in order of EPS effect.

Summary of accounting treatment for securities underlying diluted EPS:

Source: Gordon, Raedy, and Sanella (Pearson, 2nd Edition)