How do I apply Black-Scholes specifically for employee stock option valuation?

Question

AcadiFi · Accepted Answer

Black-Scholes for employee stock options uses the same equation but with modified inputs per FASB ASC 718 and IFRS 2:

c = S·e^(-q·T)·N(d1) − K·e^(-r·T)·N(d2)

The six inputs and their adjustments:

1. S (SPOT PRICE): Current share price at grant date. For private companies, use an independent 409A valuation.

2. K (STRIKE): Contractual exercise price, usually grant-date fair market value.

3. T (EXPECTED TERM): NOT contractual life. Use historical exercise data or the SEC simplified method: (vesting + contractual)/2.

4. r (RISK-FREE RATE): US Treasury yield matching T. For a 6-year expected term in 2026, use the 6-year Treasury yield.

5. σ (VOLATILITY): Expected volatility over T. Use historical volatility of weekly/monthly returns, implied volatility of traded options, or industry peers for young companies. Many firms average historical and implied.

6. q (DIVIDEND YIELD): Expected continuous dividend yield over T.

Concrete example: Hesperia Retail Grp. Spot $58, strike $58, expected term 6 years, rf 4.0%, vol 38%, div yield 2.1%.
d1 = [ln(58/58) + (0.04 − 0.021 + 0.38²/2)(6)] / (0.38·√6) = [0 + (0.0912)(6)] / 0.9308 = 0.5876
d2 = 0.5876 − 0.9308 = −0.3432
N(d1) ≈ 0.7217, N(d2) ≈ 0.3659
c = 58·e^(-0.021·6)·0.7217 − 58·e^(-0.04·6)·0.3659 ≈ 58·0.8819·0.7217 − 58·0.7866·0.3659 ≈ $36.92 − $16.70 ≈ $20.22

That $20.22 per option × total grant = total SBC expense to recognize over vesting.

How do I apply Black-Scholes specifically for employee stock option valuation?

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