Share-based payment and earnings per share

Many companies pay part of their employees' compensation in shares or share options rather than cash. Options align employees' interests with shareholders', conserve cash for young companies and help retain staff who would lose unvested awards by leaving. For decades, however, most companies recorded no expense for options granted at the market price, because the options had no 'intrinsic value' on the grant date. After years of debate, both boards concluded that options are valuable compensation and must be expensed at fair value: the IASB in IFRS 2 (2004) and the FASB in what is now ASC 718 (2004). This lesson explains how, and then turns to earnings per share, where options, convertible debt and preferred shares all affect the number that investors watch most closely.

Measuring equity-settled share-based payment

ASC 718, Compensation – Stock Compensation, requires the cost of employee services received in exchange for equity-classified awards, such as stock options and restricted stock units settled in shares, to be measured at the grant-date fair value of the award. Fair value is not remeasured later for equity-classified awards. For options, fair value is estimated with an option-pricing model, such as Black–Scholes–Merton or a lattice model, using the share price, exercise price, expected term, expected volatility, expected dividends and the risk-free rate. Non-public companies may use a calculated value based on an industry index's volatility, or the intrinsic value for some liability awards. FIN-301 lesson 11 derives the Black–Scholes formula.

The cost is recognized over the vesting period, the period during which employees must work to earn the award. Service conditions, such as remaining employed for four years, and non-market performance conditions, such as reaching a revenue target, affect how many awards are expected to vest, not their fair value per unit; the entity estimates the number expected to vest and trues up to the actual number at the end. Market conditions, such as a target share price, are built into the grant-date fair value and are not trued up: the cost is recognized even if the market condition is never met, as long as the service condition is.

# Black-Scholes value of an employee option and the cost recognized each year
from math import log, sqrt, exp, erf
N = lambda x: 0.5 * (1 + erf(x / sqrt(2)))
S, K, T, sigma, r, q = 24.0, 24.0, 5.0, 0.30, 0.035, 0.01
d1 = (log(S / K) + (r - q + sigma ** 2 / 2) * T) / (sigma * sqrt(T))
d2 = d1 - sigma * sqrt(T)
value = S * exp(-q * T) * N(d1) - K * exp(-r * T) * N(d2)
print(f"Fair value per option: {value:.2f}")

options, vest_years = 100_000, 4
expected_rate = [0.92, 0.88, 0.88, 0.86]       # estimate at the end of each year
cum_prev = 0
for y, rate in enumerate(expected_rate, start=1):
    cum = options * rate * round(value, 2) * y / vest_years
    print(f"Year {y}: expected vesting {rate:.0%}, cumulative cost {cum:,.0f}, expense {cum - cum_prev:,.0f}")
    cum_prev = cum

Fair value per option: 7.08
Year 1: expected vesting 92%, cumulative cost 162,840, expense 162,840
Year 2: expected vesting 88%, cumulative cost 311,520, expense 148,680
Year 3: expected vesting 88%, cumulative cost 467,280, expense 155,760
Year 4: expected vesting 86%, cumulative cost 608,880, expense 141,600

Graded vesting, forfeitures and modifications

Many awards vest in installments, for example 25 percent at the end of each of four years (graded vesting). For awards with only service conditions, ASC 718 allows a policy choice: recognize cost straight-line over the whole vesting period, as long as cumulative cost at least equals the portion vested, or treat each tranche separately as IFRS 2 requires. Most US companies choose straight-line. Since ASU 2016-09, companies may also elect to account for forfeitures when they occur rather than estimating them. Modifications such as repricings require recognition of incremental fair value over the remaining service period.

Cash-settled awards and tax effects

Liability-classified awards, such as stock appreciation rights settled in cash, are remeasured at fair value each reporting date until settlement, with changes recognized in compensation cost. In the United States, the employer receives a tax deduction for nonqualified stock options equal to the intrinsic value at exercise. A deferred tax asset is recognized as compensation cost is booked, and since ASU 2016-09 the difference between the deduction and the recognized cost (an excess tax benefit or shortfall) is recognized in income tax expense, which can make the effective tax rate swing with the share price. Incentive stock options generally produce no deduction for the employer.

Basic earnings per share

Earnings per share (EPS) is profit attributable to ordinary (common) shareholders divided by the weighted average number of ordinary shares outstanding during the period. ASC 260 requires public entities to present basic and diluted EPS on the face of the income statement. Private companies are not required to present EPS.

The numerator deducts preferred dividends: the current year's dividend on cumulative preferred shares, whether or not declared, and dividends declared on non-cumulative preferred shares. Dividends on preferred shares classified as liabilities are already in interest expense.

The denominator weights each share by the fraction of the year it was outstanding. Shares issued for cash are weighted from the issue date; shares repurchased are removed from the repurchase date. Stock dividends, stock splits and the bonus element of rights issues change the number of shares without changing resources, so they are applied retroactively to all periods presented, as if they had occurred at the start of the earliest period, even if they happen after year end but before the statements are issued.

Diluted earnings per share

Diluted EPS shows what EPS would be if all dilutive potential ordinary shares had been issued: options and warrants, convertible debt and convertible preferred shares, and contingently issuable shares. Each potential share is included only if it is dilutive, that is, if it would reduce EPS (or increase a loss per share). Two methods are used. The treasury stock method applies to options and warrants: assume they are exercised at the start of the year (or the issue date if later), and that the proceeds, including unrecognized compensation cost, are used to buy back shares at the average market price. Only the net incremental shares are added. Options with exercise prices above the average market price are antidilutive and excluded. The if-converted method applies to convertible securities: add back the after-tax interest (or preferred dividends) to the numerator and add the shares that would be issued on conversion to the denominator.

When there are several potential ordinary shares, they are ranked from most to least dilutive by their incremental EPS, the increase in the numerator divided by the increase in shares, and included in that order, stopping when the next one would be antidilutive. Since ASU 2020-06, the if-converted method is required for convertible instruments, and the treasury stock method can no longer be used for them. Because US GAAP records interest close to the cash coupon, the add-back is smaller than under IFRS, so the same bond is more likely to be dilutive.

# Northlake 2027 EPS (US GAAP figures; tax rate 25%)
profit = 4_500_000
pref_div = 250_000                       # cumulative preferred, equity-classified
num = profit - pref_div
# shares: 2,000,000 at 1 Jan; 300,000 issued 1 Jul; 100,000 repurchased 1 Oct; 10% stock dividend 1 Dec
weighted = 2_000_000 + 300_000 * 6/12 - 100_000 * 3/12
weighted *= 1.10                        # stock dividend applied retroactively
basic = num / weighted
print(f"Weighted shares {weighted:,.0f}; basic EPS {basic:.3f}")

# Options: 100,000 at $24 (stock-dividend adjusted to 110,000 at $21.82), average price $30
opts, ex = 110_000, 24 / 1.10
incremental_opts = opts - opts * ex / 30
# Convertible bond: single liability, interest about the 150,000 coupon, converts into 200,000 shares
add_back = 150_000 * (1 - 0.25)
conv_shares = 200_000
print(f"Options add {incremental_opts:,.0f} shares; bond adds {add_back:,.0f} / {conv_shares:,} = {add_back / conv_shares:.3f} per share")
step1 = num / (weighted + incremental_opts)
print(f"After options: {step1:.3f}")
step2 = (num + add_back) / (weighted + incremental_opts + conv_shares)
print(f"After bond: {step2:.3f} -> {'dilutive, include' if step2 < step1 else 'antidilutive, exclude'}")
print(f"Diluted EPS {min(step1, step2):.3f}")

Weighted shares 2,337,500; basic EPS 1.818
Options add 30,000 shares; bond adds 112,500 / 200,000 = 0.562 per share
After options: 1.795
After bond: 1.699 -> dilutive, include
Diluted EPS 1.699

Basic EPS is $1.82: $4,250,000 of earnings available to common stockholders over 2,337,500 weighted shares, after the stock dividend is applied retroactively. The options add 30,000 incremental shares under the treasury stock method. The convertible bond's incremental EPS is about 56 cents a share, well below the $1.80 EPS after options, so it is dilutive and included, giving diluted EPS of $1.70. An IFRS reporter would add back more interest because of the split liability, and report diluted EPS of $1.73.