Black-Scholes stock option expense: a worked Excel example

How option expense works

For equity-settled awards, the cost is measured once, at the grant date, and not remeasured when the share price moves later. The total grant-date fair value is the value per option times the number of options expected to vest. It is recognized over the service period, normally the vesting period, as compensation expense with the other side in equity (additional paid-in capital).

Step 1: the six Black-Scholes inputs

• Share price S at the grant date: $18.00.
• Exercise price K: $18.00, an at-the-money grant.
• Expected term T: how long employees are expected to hold the option, not the 10-year contractual term. The simplified method, accepted by the US SEC staff for plain options when a company lacks exercise history, uses (vesting + contractual term) ÷ 2 = (4 + 10) ÷ 2 = 7.0 years.
• Expected volatility σ: 45%, from the company's own share price history, implied volatility or, for a young or private company, comparable peers.
• Risk-free rate r: 4.2%, the government zero-coupon yield for the expected term.
• Expected dividend yield q: 0%, as the company pays no dividend.

Step 2: d1, d2 and the option value

d1 = (LN(S/K) + (r − q + σ²/2) × T) ÷ (σ × √T) = 0.8422 and d2 = d1 − σ × √T = −0.3484. In Excel, N(x), the standard normal distribution, is NORM.S.DIST(x,TRUE): N(d1) = 0.8002 and N(d2) = 0.3638.

Value = S × e^(−qT) × N(d1) − K × e^(−rT) × N(d2) = $9.52 per option, 52.9% of the share price. That may look high for an option with no intrinsic value today, but seven years of 45% volatility give the holder a lot of upside.

Worked example: option grant fair value and annual expense

Inputs are yellow. The company, the grant and all figures are fictional.

Worked example: option grant fair value and annual expense

	A	B	Formula in B
1	Option grant, 1 Apr 2026	Value
2	Options granted	120,000
3	Share price at grant date (S)	18.00
4	Exercise price (K)	18.00
5	Vesting period (cliff, years)	4
6	Contractual term (years)	10
7	Expected term T, simplified method	7.0	=(B5+B6)/2
8	Expected volatility σ	45.0%
9	Risk-free rate r	4.2%
10	Expected dividend yield q	0.0%
11	d1	0.8422	=(LN(B3/B4)+(B9-B10+B8^2/2)*B7)/(B8*SQRT(B7))
12	d2 = d1 − σ√T	-0.3484	=B11-B8*SQRT(B7)
13	N(d1)	0.8002	=NORM.S.DIST(B11,TRUE)
14	N(d2)	0.3638	=NORM.S.DIST(B12,TRUE)
15	Fair value per option	9.52	=B3*EXP(-B10*B7)*B13-B4*EXP(-B9*B7)*B14
16	Fair value as % of share price	52.9%	=B15/B3
17	Total grant-date fair value	1,142,747	=B15*B2
18	Expected forfeitures over vesting	10.0%
19	Fair value expected to vest	1,028,472	=B17*(1-B18)
20	Annual expense, years 1–4	257,118	=B19/B5

Educational only, not accounting, tax or investment advice. A simplified summary of ASC 718 (FASB) and IFRS 2 (IASB). Tabellab is not affiliated with either standard setter.

Step 3: from fair value to annual expense

Total grant-date fair value: 120,000 options at $9.52 each, $1,142,747 with the unrounded value. Expense is recognized only for options that vest. With an expected forfeiture rate of 10% over the vesting period, $1,028,472 is expected to vest. With four-year cliff vesting, that is $257,118 a year for four years.

The journal entry each year: debit compensation expense, credit additional paid-in capital, $257,118. If more or fewer employees leave than expected, the cumulative expense is trued up to the options that actually vest. If the share price falls below $18.00, nothing changes: the grant-date value is fixed.

Forfeitures, graded vesting and other details

• Forfeitures: IFRS 2 requires an estimate of the awards expected to vest, trued up as facts change. Under ASC 718, a company may instead make a policy election to account for forfeitures when they occur.
• Graded vesting (for example 25% a year): IFRS 2 expenses each tranche over its own vesting period, which front-loads the expense. ASC 718 allows that or straight-line for awards with only service conditions.
• Market conditions such as a share price or total shareholder return target are built into the fair value, usually with a Monte Carlo simulation rather than Black-Scholes.
• RSUs need no option model: their fair value is the share price at grant, less the present value of expected dividends if holders do not receive them.

Payroll-related entries for cash pay are a different topic, covered in the payroll journal entries guide.

Sensitivity: which input matters most

Volatility and the expected term drive most of the value. A longer expected term or higher volatility raises the fair value, a dividend yield lowers it, and a higher risk-free rate raises it slightly for a call option. Change an input cell in the example and the expense follows. Auditors focus on volatility and the expected term for exactly that reason, so document where each assumption comes from.

Common mistakes

• Using the contractual term as T. Employees often exercise early. Use an expected term, for example the simplified method or company exercise data.
• Remeasuring equity-settled options. The grant-date fair value is fixed. A falling share price does not reduce the expense.
• Expensing all granted options. Recognize expense only for options expected to vest (or, under the ASC 718 election, reverse it when forfeitures occur).
• Mixing up NORM.S.DIST and NORM.DIST. Black-Scholes needs the cumulative standard normal: NORM.S.DIST(x,TRUE). Leaving out TRUE gives the density.
• Using a percentage volatility for the wrong period. σ must be annual, matching T in years. Daily volatility must be scaled by the square root of trading days.
• Expensing graded tranches straight-line under IFRS 2. IFRS 2 requires tranche-by-tranche attribution for graded vesting.