Diluted EPS Calculations: Treasury Stock and If-Converted Methods for the CPA Exam

Basic vs. Diluted EPS

Earnings per share (EPS) is one of the most important financial metrics and is heavily tested on the CPA FAR exam. Basic EPS is calculated as net income available to common shareholders divided by the weighted-average number of common shares outstanding. Diluted EPS adjusts both the numerator and denominator to reflect the potential dilution from convertible securities, stock options, warrants, and other potentially dilutive instruments. Under ASC 260, both basic and diluted EPS must be presented on the face of the income statement.

Basic EPS Calculation

The numerator for basic EPS starts with net income and subtracts preferred dividends (declared dividends for noncumulative preferred stock, or the annual dividend requirement for cumulative preferred stock, whether or not declared). The denominator is the weighted-average number of common shares outstanding during the period, adjusted for stock splits and stock dividends retroactively.

Example

A company has net income of $500,000, cumulative preferred stock with an annual dividend requirement of $40,000 (none declared), and 100,000 common shares outstanding all year.

Basic EPS: ($500,000 - $40,000) / 100,000 = $4.60

Treasury Stock Method for Options and Warrants

Stock options and warrants are included in diluted EPS using the treasury stock method. This method assumes the options are exercised at the beginning of the period (or date of issuance, if later), and the proceeds received are used to buy back shares at the average market price during the period. Only in-the-money options (exercise price below average market price) are potentially dilutive.

Treasury Stock Method Example

Given: 20,000 stock options with an exercise price of $30, average market price of $50 during the year.

• Shares issued upon assumed exercise: 20,000
• Proceeds: 20,000 x $30 = $600,000
• Shares repurchased at average price: $600,000 / $50 = 12,000
• Net incremental shares: 20,000 - 12,000 = 8,000

These 8,000 incremental shares are added to the denominator of diluted EPS. The numerator is unchanged because no income adjustment is needed for options.

If the exercise price exceeds the average market price (out-of-the-money options), the treasury stock method produces a net reduction in shares, which would be antidilutive. These options are excluded from diluted EPS.

If-Converted Method for Convertible Bonds

Convertible bonds are included in diluted EPS using the if-converted method. This assumes the bonds are converted at the beginning of the period (or date of issuance, if later). The numerator adds back the after-tax interest expense on the bonds, and the denominator adds the shares that would be issued upon conversion.

If-Converted Example: Bonds

Given: $1,000,000 of 6% convertible bonds, convertible into 25,000 common shares. Tax rate: 25%. Net income: $500,000. Weighted-average shares: 100,000.

• Interest expense: $1,000,000 x 6% = $60,000
• Tax savings lost if converted: $60,000 x 25% = $15,000
• After-tax interest added back: $60,000 - $15,000 = $45,000
• Numerator adjustment: +$45,000
• Denominator adjustment: +25,000 shares

Diluted EPS test: ($500,000 + $45,000) / (100,000 + 25,000) = $545,000 / 125,000 = $4.36

Basic EPS was $5.00 ($500,000 / 100,000). Since diluted EPS ($4.36) is lower than basic EPS, the bonds are dilutive and are included.

If-Converted Method for Convertible Preferred Stock

Convertible preferred stock is also handled with the if-converted method. The numerator adds back the preferred dividends that were subtracted in basic EPS, and the denominator adds the shares that would be issued upon conversion.

Example

Given: Cumulative preferred stock with $40,000 annual dividend, convertible into 15,000 common shares. Net income: $500,000. Common shares: 100,000.

• Basic EPS: ($500,000 - $40,000) / 100,000 = $4.60
• Diluted EPS numerator: $500,000 (add back the $40,000 dividend subtraction)
• Diluted EPS denominator: 100,000 + 15,000 = 115,000
• Diluted EPS: $500,000 / 115,000 = $4.35

Since $4.35 is less than $4.60 (basic EPS), the preferred stock is dilutive.

Antidilution Testing

A security is antidilutive if including it in the diluted EPS calculation would increase EPS or decrease a loss per share. Antidilutive securities must be excluded from diluted EPS. To determine the order of inclusion, potentially dilutive securities are ranked from most dilutive to least dilutive. Options and warrants, which affect only the denominator, are always considered first. Convertible securities are ranked by their incremental EPS effect (numerator adjustment / denominator adjustment), from lowest to highest.

Ranking Example

Security A: adds $45,000 to numerator, 25,000 to denominator. Incremental EPS: $1.80

Security B: adds $30,000 to numerator, 10,000 to denominator. Incremental EPS: $3.00

Security A is more dilutive ($1.80 vs. $3.00) and is included first. After including A, if adding B would increase the running diluted EPS, B is antidilutive and excluded.

Key Exam Tips

• Options and warrants use the treasury stock method; convertible securities use the if-converted method.
• Out-of-the-money options are always antidilutive and excluded.
• The numerator is unchanged for options but adjusted for convertible securities (add back after-tax interest or preferred dividends).
• Always test each security for antidilution: if including it increases EPS, exclude it.
• Rank convertible securities by their incremental EPS effect from most to least dilutive.