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

A company has 4 million shares outstanding and has issued 1 million warrants, each exercisable into one new share at $30. Just before exercise, the stock trades at $50 and the market value of equity is $200 million. All warrants are exercised, and the firm's value changes only through the cash received. What is the payoff to each warrant holder, measured as the post-exercise share price minus the strike price?

Each warrant pays $16. Equity rises to $230 million after the $30 million strike proceeds, spread over 5 million shares, which gives a $46 share price. Subtracting the $30 strike leaves $16, which is the $20 regular call payoff scaled by 4/5.

  1. A$16Correct
  2. B$20
  3. C$10
  4. D$46

Explanation

Equity after exercise = 200 + 1 × 30 = $230 million, over 5 million shares, so the price is $46. Payoff = 46 − 30 = $16. This equals 20 × N/(N+M) = 20 × 4/5. A payoff of $20 ignores dilution. $10 comes from dividing 200 by 5 and omitting the proceeds. $46 is the share price, not the payoff.

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