Entities with a capital structure that includes common stock and either (1) participating securities or (2) common stock with a different dividend rate are required to use the two-class method in calculating basic and diluted EPS.
See Q&A 6-10 for guidance on the definition of a participating security.
Question
Under the two-class method, how do entities calculate basic and diluted EPS?
Answer
Entities use the following three-step process to calculate basic and diluted EPS:
Step 1 — Use the two-class method to compute basic EPS. As indicated in ASC 260-10-45-60, “[t]he two-class method is an earnings allocation formula that treats a participating security as having rights to earnings that otherwise would have been available to common shareholders.” See Example 6 in ASC 260-10-55-62 for an illustration of the calculation of basic EPS using the two-class method.
Step 2 — Use the total earnings allocated to the common stock in step 1 to determine diluted EPS. If the participating security is also a potential common share, separately perform steps 2a and 2b to determine the dilutive effect.
Step 2a — Assume that the participating security has been exercised, converted, or issued; that is, apply the treasury stock method, the if-converted method, or the contingently issuable share method.
Step 2b — Add back the undistributed earnings allocated to the participating security (or securities) in arriving at basic EPS, and assume that all other dilutive potential common shares have been exercised, converted, or issued in order of antidilution. Next, reallocate the undistributed earnings, including any additional income that would result from the exercise, conversion, or issuance of potential common shares, to the (1) common shares and potential common shares and (2) participating security (or securities).
Step 3 — Determine which step — 2a or 2b — results in the more dilutive effect.
Examples 1–4 below illustrate (1) the calculation of basic and diluted EPS under the two-class method and (2) the use of this three-step process to determine diluted EPS.
Example 1 — Participating Convertible Preferred Stock
Assume that Entity A has 1 million weighted-average shares of common stock outstanding for the fiscal year ended December 31, 20X1; a current-period net income of $5 million; and an effective tax rate of 40 percent.
On January 1, 20X1, A issued 100,000 convertible preferred securities. Each preferred share is convertible into two shares of A’s common stock. The preferred shareholders are entitled to a noncumulative annual dividend of
$5 per share before any dividend is paid to the common shareholders. After the common shareholders are paid a dividend of $2 per share, the preferred shareholders participate in any remaining undistributed earnings on a 40:60 per-share basis with the common shareholders. Accordingly, the preferred securities are participating securities for which A must use the two-class method in calculating basic and diluted EPS. In fiscal year 20X1, A declared and paid $2.5 million in dividends (or a $5 dividend for preferred shareholders and a $2 dividend for common shareholders).
Step 1 — Use the two-class method to determine basic EPS.
Net income $ 5,000,000
Less dividends to preferred shareholders 500,000a Net income available to common shareholders 4,500,000 Less dividends to common shareholders 2,000,000a
Undistributed 20X1 earnings $ 2,500,000
a The dividends would be based on the number of common stock and preferred stock outstanding as of the declaration date. For simplicity, the weighted average and the shares outstanding are assumed to be consistent.
Allocation of undistributed earnings:
To participating convertible preferred shares:
{(0.4 × 100,000 preferred shares1) ÷ [(0.4 × 100,000 preferred shares2) + (0.6 × 1,000,000 common shares3)]} × 2,500,000 undistributed earnings4 = $156,250
$156,250 ÷ 100,000 preferred shares5 = $1.56 per share To common shares:
{(0.6 × 1,000,000 common shares6) ÷ [(0.4 × 100,000 preferred shares7) + (0.6 × 1,000,000 common shares8)]} × 2,500,000 undistributed earnings9 = $2,343,750
$2,343,750 ÷ 1,000,000 common shares10 = $2.34 per share Basic EPS amounts:
Common Shares
Participating Convertible Preferred Shares
Distributed earnings $ 2.00 $ 5.00
Undistributed earnings 2.34 1.56
Total $ 4.34 $ 6.56
Step 2 — Determine diluted EPS.
Step 2a — Use the treasury stock method, the if-converted method, or the contingently issuable share method to determine diluted EPS.
Determine the antidilution sequencing:
Since there are no potential common shares other than the participating convertible preferred shares, antidilution sequencing is not required.
1 Weighted-average number of participating convertible preferred shares outstanding.
2 See footnote 1.
3 Weighted-average number of common shares outstanding.
4 Total undistributed earnings for the period.
5 See footnote 1.
6 See footnote 3.
7 See footnote 1.
8 See footnote 3.
9 See footnote 4.
10 See footnote 3.
Calculation of diluted EPS for the common shares in which the use of the if-converted method for the participating convertible preferred shares is assumed:
Distributed/
Undistributed Earnings (Numerator)
Weighted-Average Number of Common Shares
(Denominator) EPS
As reported, basic $ 4,343,750a 1,000,000 $ 4.34
Convertible preferred 656,250b 200,000c —
Diluted EPS $ 5,000,000 1,200,000 $ 4.16
a Amount represents the aggregate of the distributed ($2,000,000) and undistributed earnings ($2,343,750) allocated to the common shareholders.
b Amount represents the aggregate of the distributed ($500,000) and undistributed earnings ($156,250) allocated to the participating convertible preferred shares.
c Number of common shares that would be issued upon conversion of the participating convertible preferred shares.
Step 2b — Use the two-class method to determine diluted EPS.
Because A’s capital structure only includes common shares and participating convertible preferred shares (i.e., there are no other potential common shares), basic and diluted EPS under the two-class method would be the same ($4.34).
Step 3 — Determine which step — 2a or 2b — results in the more dilutive effect.
In this example, A would disclose an amount of diluted EPS per common share that would result from applying the if-converted method ($4.16) because that amount is more dilutive than the amount that would result from applying the two-class method ($4.34). In accordance with ASC 260-10-45-60, A would be permitted, but not required, to present basic and diluted EPS for the participating convertible preferred shares on the face of the income statement.
Example 2 — Participating Convertible Preferred Stock With Convertible Debt and Warrants Assume all the same facts as in Example 1. In addition, assume the following:
• On January 1, 20X1, Entity A issued warrants to purchase 100,000 shares of its common stock at $50 per share for a period of five years. The average market price of A’s stock price for 20X1 was $60 per share.
• On January 1, 20X1, A issued 10,000 units of convertible bonds with an aggregate par value of $1 million.
Each bond is convertible into 10 shares of A’s common stock and bears an interest rate of 3 percent.
Step 1 — Use the two-class method to determine basic EPS.
Entity A’s basic EPS would remain unchanged at $4.34 since the warrants and convertible debt would not affect the computation of basic EPS.
Step 2 — Determine diluted EPS.
Step 2a — Use the treasury stock method, the if-converted method, or the contingently issuable share method to determine diluted EPS.
Determine the antidilution sequencing:
Increase in Earnings Available to Common
Shareholders Increase in Number
of Common Shares Earnings per Incremental Share
Warrants $ — 16,667a $ —
Convertible bonds 18,000b 100,000b 0.18
Participating convertible preferred shares
$ 656,250c 200,000d $ 3.28
a Amount represents the incremental number of common shares for the assumed exercise of the warrants [($60 average market price – $50 exercise price) × 100,000 warrants] ÷ $60 average market price = 16,667.
b Assumed conversion of the convertible bonds would result in 100,000 incremental common shares and the add-back of
$18,000 [$1,000,000 × 3% interest rate × (1 – 40% tax rate)] in after-tax interest expense to undistributed earnings for the period.
c Amount represents the aggregate of the distributed ($500,000) and undistributed earnings ($156,250) allocated to the participating convertible preferred shares.
d Number of common shares that would be issued upon conversion of the participating convertible preferred shares.
Calculation of diluted EPS for the common shares in which the use of the if-converted method for the participating convertible preferred shares is assumed:
Distributed/
Undistributed Earnings (Numerator)
Weighted-Average Number of Common
Shares (Denominator) EPS
As reported, basic $ 4,343,750 1,000,000 $ 4.34
Warrants — 16,667a —
$ 4,343,750 1,016,667 4.27
Convertible bonds 18,000b 100,000b —
$ 4,361,750 1,116,667 $ 3.91
Participating convertible preferred 656,250c 200,000d —
Diluted EPS $ 5,018,000 1,316,667 $ 3.81
a Amount represents the incremental number of common shares for the assumed exercise of the warrants [($60 average market price – $50 exercise price) × 100,000] ÷ $60 average market price = 16,667.
b Assumed conversion of the convertible bonds would result in 100,000 incremental common shares and the add-back of
$18,000 [$1,000,000 × 3% interest rate × (1 – 40% tax rate)] in after-tax interest expense to undistributed earnings for the period.
c Amount represents the aggregate of the distributed ($500,000) and undistributed earnings ($156,250) allocated to the participating convertible preferred shares.
d Number of common shares that would be issued upon conversion of the participating convertible preferred shares.
Step 2b — Use the two-class method to determine diluted EPS.
Distributed/
Undistributed Earnings (Numerator)
Weighted-Average Number of Common Shares
(Denominator) EPS
As reported, basic $ 4,343,750 1,000,000 $ 4.34
Add back: undistributed earnings allocated to the participating
convertible preferred shares 156,250 — —
Warrants — 16,667a —
Less: undistributed earnings reallocated to participating
convertible preferred shares (153,846)b —
Subtotal $ 4,346,154 1,016,667 $ 4.28
Add back: undistributed earnings allocated to the participating
convertible preferred shares 153,846b —
Convertible bonds 18,000c 100,000c
Less: undistributed earnings reallocated to participating
convertible preferred shares (141,859)d —
Diluted EPS for common stock $ 4,376,141 1,116,667 $ 3.92
a Amount represents the incremental number of common shares for the assumed exercise of the warrants [($60 average market price – $50 exercise price) × 100,000 warrants] ÷ $60 average market price = 16,667.
b {0.4 × 100,000 preferred shares ÷ [(0.4 × 100,000 preferred shares) + (0.6 × (1,000,000 common shares + 16,667 incremental shares from warrants))]} × $2,500,000 undistributed earnings = $153,846.
c Assumed conversion of the convertible bonds would result in 100,000 incremental common shares and the add-back of
$18,000 [$1,000,000 × 3% interest rate × (1 – 40% tax rate)] in after-tax interest expense to undistributed earnings for the period.
d {0.4 × 100,000 preferred shares ÷ [(0.4 × 100,000 preferred shares) + (0.6 × (1,000,000 common shares + 16,667 incremental shares from warrants + 100,000 incremental shares from the convertible bonds))]} × ($2,500,000 undistributed earnings + $18,000 interest add-back) = $141,859.
Step 3 — Determine which step — 2a or 2b — results in the more dilutive effect.
In this example, A would disclose an amount of diluted EPS per common share that would result from applying the if-converted method ($3.81) because that amount is more dilutive than the amount that would result from applying the two-class method ($3.92). In accordance with ASC 260-10-45-60, A would be permitted, but not required, to present basic and diluted EPS for the participating convertible preferred shares on the face of the income statement.
Example 3 — Participating Nonvested Share-Based Payment Awards
Assume that Entity A has 1 million weighted-average shares of common stock outstanding for the fiscal year ended December 31, 20X1; a current-period net income of $5 million; and an effective tax rate of 40 percent.
On January 1, 20X1, A issued 250,000 nonvested share-based payment awards to its employees. The nonvested shares had a grant-date fair-value-based measure of $50 per share and vest at the end of the fourth year of service (i.e., cliff vesting). The average market price of A’s stock price for 20X1 was $60 per share.
Holders of nonvested shares have a nonforfeitable right to receive cash dividends on a 1:1 per-share basis with the common shareholders. Accordingly, the nonvested shares are participating securities for which A must use the two-class method in calculating basic and diluted EPS. In fiscal year 20X1, A declared and paid $2.5 million in dividends for both the common shares and the nonvested shares.
Step 1 — Use the two-class method to determine basic EPS.
Net income $ 5,000,000
Less dividends paid
Nonvested shareholders 500,000
Common shareholders 2,000,000 $ 2,500,000
Undistributed 20X1 earnings $ 2,500,000
Allocation of undistributed earnings:
To nonvested shares:
[250,000 nonvested shares11 ÷ (250,000 nonvested shares12 + 1,000,000 common shares13)] × $2,500,000 undistributed earnings14 = $500,000
$500,000 ÷ 250,000 nonvested shares15 = $2.00 per share To common shares:
[1,000,000 common shares16 ÷ (250,000 nonvested shares17 + 1,000,000 common shares18] × $2,500,000 undistributed earnings19 = $2,000,000
$2,000,000 ÷ 1,000,000 common shares20 = $2.00 per share Basic EPS amounts:
Common Shares Participating Nonvested Shares
Distributed earnings $ 2.00 $ 2.00
Undistributed earnings 2.00 2.00
Total $ 4.00 $ 4.00
Step 2 — Determine diluted EPS.
Step 2a — Use the treasury stock method, the if-converted method, or the contingently issuable share method to determine diluted EPS.
Determine the antidilution sequencing:
Because there are no potential common shares other than the participating nonvested shares, antidilution sequencing is not required.
11 Weighted-average number of participating nonvested shares.
12 See footnote 11.
13 See footnote 3.
14 See footnote 4.
15 See footnote11.
16 See footnote 3.
17 See footnote 11.
18 See footnote 3.
19 See footnote 4.
20 See footnote 3.
Calculation of diluted EPS for the common shares in which the use of the treasury stock method for the participating nonvested shares is assumed:
Distributed/
Undistributed Earnings (Numerator)
Weighted-Average Number of Common Shares
(Denominator) EPS
As reported, basic $ 4,000,000a 1,000,000 $ 4.00
Participating nonvested shares 1,000,000b 51,042c —
Diluted EPS $ 5,000,000 1,051,042 $ 4.76
a Amount represents the aggregate of the distributed earnings ($2,000,000) and undistributed earnings ($2,000,000) allocated to the common shareholders.
b Amount represents the aggregate of the distributed earnings ($500,000) and undistributed earnings ($500,000) allocated to the participating nonvested shares.
c Incremental number of shares for assumed conversion of nonvested shares:
• Exercise price = 0.
• Average unrecognized compensation cost = $10,937,500.
o $12,500,000 – [(250,000 shares × $50) ÷ 4 years] = $9,375,000.
o ($12,500,000 + $9,375,000) ÷ 2 = $10,937,500.
• Excess tax benefit of $1,000,000 = [($60 – $50) × 250,000 shares] × 40% tax rate.
• Assumed proceeds of $11,937,500 = $1,000,000 excess tax benefit + $10,937,500 average unrecognized compensation cost.
• Shares repurchased = 198,958 = $11,937,500 assumed proceeds ÷ $60 average share price.
• Incremental shares = 51,042 = 250,000 shares – 198,958 shares repurchased.
Step 2b — Use the two-class method to determine diluted EPS.
Because A’s capital structure only includes common shares and the participating nonvested shares (i.e., there are no other potential common shares), basic and diluted EPS under the two-class method would be the same ($4.00).
Step 3 — Determine which step — 2a or 2b — results in the more dilutive effect.
In this example, A would disclose an amount of diluted EPS per common share that would result from applying the two-class method ($4.00) because that amount is more dilutive than the amount that would result from applying the treasury stock method ($4.76). In accordance with ASC 260-10-45-60, A would be permitted, but not required, to present basic and diluted EPS for the participating nonvested shares on the face of the income statement.
Example 4 — Participating Nonvested Share-Based Payment Awards With Convertible Debt and Warrants
Assume all the same facts as in Example 3. In addition, assume the following:
• On January 1, 20X1, Entity A issued warrants to purchase 100,000 shares of its common stock at $40 per share for a period of five years.
• On January 1, 20X1, A issued 10,000 units of convertible bonds with an aggregate par value of $1 million.
Each bond is convertible into 10 shares of A’s common stock and bears an interest rate of 3 percent.
Step 1 — Use the two-class method to determine basic EPS.
Entity A’s basic EPS would remain unchanged at $4.00 because the warrants and convertible debt would not affect the computation of basic EPS.
Step 2 — Determine diluted EPS.
Step 2a — Use the treasury stock method, the if-converted method, or the contingently issuable share method to determine diluted EPS.
Determine the antidilution sequencing:
Increase in Earnings Available to Common
Shareholders Increase in Number
of Common Shares Earnings per Incremental Share
Warrants $ — 33,333a $ —
Convertible bonds 18,000b 100,000b 0.18
Participating nonvested shares $ 1,000,000c 51,042d $ 19.59
a Amount represents the incremental number of common shares for the assumed exercise of the warrants [($60 average market price – $40 exercise price) × 100,000 warrants] ÷ $60 average market price = 33,333.
b Assumed conversion of the convertible bonds would result in 100,000 incremental common shares and the add-back of
$18,000 [$1,000,000 × 3% interest rate × (1 – 40% tax rate)] in after-tax interest expense to undistributed earnings for the period.
c Amount represents the aggregate of the distributed earnings ($500,000) and undistributed earnings ($500,000) allocated to the participating nonvested shares.
d Incremental number of shares for assumed conversion of nonvested shares:
• Exercise price = 0.
• Average unrecognized compensation cost = $10,937,500.
o $12,500,000 – [(250,000 shares × $50) ÷ 4 years] = $9,375,000.
o ($12,500,000 + $9,375,000) ÷ 2 = $10,937,500.
• Excess tax benefit of $1,000,000 = [($60 – $50) × 250,000 shares] × 40% tax rate.
• Assumed proceeds of $11,937,500 = $1,000,000 excess tax benefit + $10,937,500 average unrecognized compensation cost.
• Shares repurchased = 198,958 = $11,937,500 assumed proceeds ÷ $60 average share price.
• Incremental shares = 51,042 = 250,000 shares – 198,958 shares repurchased.
Calculation of diluted EPS for the common shares in which the use of the treasury stock method for the participating nonvested shares is assumed:
Distributed/
Undistributed Earnings (Numerator)
Weighted-Average Number of Common
Shares (Denominator) EPS
As reported, basic $ 4,000,000 1,000,000 $ 4.00
Warrants — 33,333a
4,000,000 1,033,333 3.87
Convertible bonds 18,000b 100,000b
4,018,000 1,133,333 $ 3.55
Participating nonvested shares 1,000,000c 51,042d
Diluted EPS $ 5,018,000 1,184,375 $ 4.24
a Amount represents the incremental number of common shares for the assumed exercise of the warrants [($60 average market price – $40 exercise price) × 100,000 warrants] ÷ $60 average market price = 33,333.
b Assumed conversion of the convertible bonds would result in 100,000 incremental common shares and the add-back of
$18,000 [$1,000,000 × 3% interest rate × (1 – 40% tax rate)] in after-tax interest expense to undistributed earnings for the period.
c Amount represents the aggregate of the distributed ($500,000) and undistributed earnings ($500,000) allocated to the participating nonvested shares.
d Incremental number of shares for assumed conversion of nonvested shares:
• Exercise price = 0.
• Average unrecognized compensation cost = $10,937,500.
o $12,500,000 – [(250,000 shares × $50) ÷ 4 years] = $9,375,000.
o ($12,500,000 + $9,375,000) ÷ 2 = $10,937,500.
• Excess tax benefit of $1,000,000 = [($60 – $50) × 250,000 shares] × 40% tax rate.
• Assumed proceeds of $11,937,500 = $1,000,000 excess tax benefit + $10,937,500 average unrecognized compensation cost.
• Shares repurchased = 198,958 = $11,937,500 assumed proceeds ÷ $60 average share price.
• Incremental shares = 51,042 = 250,000 shares – 198,958 shares repurchased.
Step 2b — Use the two-class method to determine diluted EPS.
Distributed/
Undistributed Earnings (Numerator)
Weighted-Average Number of Common
Shares (Denominator) EPS
As reported, basic $ 4,000,000 1,000,000 $ 4.00
Add back: undistributed earnings allocated to the participating
nonvested shares 500,000 — —
Warrants — 33,333a —
Less: undistributed earnings reallocated to participating
nonvested shares (487,013)b —
Subtotal $ 4,012,987 1,033,333 $ 3.88
Add back: undistributed earnings allocated to the participating
convertible preferred shares 487,013b —
Convertible bonds 18,000c 100,000c
Less: undistributed earnings reallocated to participating
convertible preferred shares (455,060)d —
Diluted EPS for common stock $ 4,062,940 1,133,333 $ 3.59
a Amount represents the incremental number of common shares for the assumed exercise of the warrants [($60 average market price – $40 exercise price) × 100,000 warrants] ÷ $60 average market price = 33,333.
b [250,000 nonvested shares ÷ (250,000 nonvested shares + 1,000,000 common shares + 33,333 incremental shares from warrants)] × $2,500,000 undistributed earnings = $487,013.
c Assumed conversion of the convertible bonds would result in 100,000 incremental common shares and the add-back of
$18,000 [$1,000,000 × 3% interest rate × (1 – 40% tax rate)] in after-tax interest expense to undistributed earnings for the period.
d [250,000 nonvested shares ÷ (250,000 nonvested shares + 1,000,000 common shares + 33,333 incremental shares from warrants + 100,000 incremental shares from the convertible bonds)] × ($2,500,000 undistributed earnings + $18,000 interest add-back) = $455,060.
Step 3 — Determine which step — 2a or 2b — results in the more dilutive effect.
In this example, A would use the two-class method to disclose diluted EPS per common share ($3.59) because that amount is more dilutive than the amount that would result from applying the if-converted method ($4.24). In accordance with ASC 260-10-45-60, A would be permitted, but not required, to present basic and diluted EPS for the participating nonvested shares on the face of the income statement.