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FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model

A firm grants 1,000,000 employee stock options with a four-year cliff vesting period. The grant-date fair value from a BSM-based model is $4.00 per option, and the firm expects 10% of the options to be forfeited before vesting. Assuming straight-line recognition, what annual compensation expense does the firm record during the vesting period?

The annual expense is $900,000. Expected vesting options are 900,000 after the 10% forfeiture, times $4.00 fair value gives $3.6 million, and straight-line recognition over four years gives $900,000 per year. Ignoring forfeitures or the vesting period produces the wrong figures.

  1. A$900,000Correct
  2. B$1,000,000
  3. C$810,000
  4. D$4,000,000

Explanation

Expected vesting options = 1,000,000 × 0.90 = 900,000. Total cost = 900,000 × 4.00 = $3,600,000. Spread over 4 years this gives $900,000 per year. $1,000,000 ignores forfeitures, $810,000 applies the forfeiture twice, and $4,000,000 ignores both forfeitures and spreading over the vesting period.

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