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

A company has 10 million shares outstanding and has issued 2 million warrants, each giving the right to buy one new share. The Black-Scholes-Merton value of an otherwise identical regular call, using a stock price that already reflects the market's anticipation of the dilution, is $6.00. Using the standard dilution adjustment, what is the value of each warrant?

Each warrant is worth $5.00. The dilution adjustment multiplies the regular call value by N/(N+M), which is 10/12 here, so 6.00 × 10/12 equals 5.00. The adjustment lowers the value because exercise creates new shares that share in the firm's value.

  1. A$5.00Correct
  2. B$6.00
  3. C$7.20
  4. D$1.00

Explanation

Warrant value = N/(N+M) × c = 10/(10+2) × 6.00 = 5.00. Using (N+M)/N would give 7.20, which wrongly increases the value. Ignoring dilution gives 6.00. M/(N+M) × 6 = 1.00 uses the wrong proportion.

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