Calculate diluted earnings per share accounting for stock options, convertible bonds, and warrants using the treasury stock method.
Diluted EPS estimates earnings per common share after accounting for securities that could become common shares. Enter earnings attributable to common shareholders, weighted-average common shares, and the relevant terms for options, warrants, or convertible bonds. Options and warrants affect the denominator through assumed exercise and share repurchase, while convertibles can affect both earnings and shares. The common surprise is that outstanding options are not simply added to the share count: assumed exercise proceeds offset part of their dilution, and antidilutive instruments should be excluded.
A concrete input and expected output from the current implementation.
Input
Net income: $110,000 Preferred dividends: $0 Weighted-average common shares: 10,000 Options outstanding: 2,000 Average exercise price: $5.00 Average market price: $10.00 Convertible bonds: none Warrants: none
Expected output
Incremental option shares: 1,000 Diluted weighted-average shares: 11,000 Basic EPS: $11.00 Diluted EPS: $10.00
Assumed exercise raises $10,000, enough to repurchase 1,000 shares at the $10 average market price, leaving 1,000 incremental shares. Dividing $110,000 by 11,000 diluted shares gives diluted EPS of $10.00.
For an option or warrant, incremental shares equal the instruments assumed exercised minus the shares hypothetically repurchased with the exercise proceeds at the average market price. With N instruments, exercise price X, and average market price M, the treasury stock calculation is N - (N x X / M). An instrument with X at least equal to M produces no dilution.
Convertible debt uses an if-converted adjustment rather than the treasury stock formula. The calculation adds back interest expense that would have been avoided, net of its tax effect, and adds the common shares issuable upon conversion. Diluted EPS is the adjusted earnings numerator divided by the adjusted weighted-average share denominator, using period-consistent amounts.
A properly screened diluted EPS normally cannot be higher than basic EPS, because potential common shares are included only when they reduce EPS or increase loss per share. If the result is higher, inspect negative incremental-share amounts, the convertible interest addback, the tax rate, and whether an instrument should have been excluded as antidilutive.
No. For the treasury stock method, use the average market price for the reporting period represented by the EPS calculation. A closing price can materially misstate the assumed number of shares repurchased. If calculating one quarter, the market price and weighted-average share inputs should both correspond to that quarter.
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