FRM Part I · FRM Exam Part I · The Black-Scholes-Merton Model
A company has 4 million shares outstanding at a price of $50 before it grants 1 million warrants to executives for no cash consideration. Each warrant is exercisable into one new share. A Black-Scholes-Merton call valued with S0 = $50 is worth $8.00. Using the standard dilution adjustment and assuming the market values the warrants fairly, what is the theoretical value per share for the existing shares after the grant?
The theoretical value is $48.40 per share. The adjusted warrant value is 4/5 × $8.00 = $6.40, so total warrants are worth $6.4 million. Subtracting this from the $200 million pre-grant equity leaves $193.6 million, which divided by 4 million shares gives $48.40.
- A$48.00
- B$48.72
- C$48.40Correct
- D$50.00
Explanation
Warrant value = 4/5 × 8.00 = $6.40, so total warrant value is $6.4 million. Pre-grant equity is 4m × $50 = $200m. Equity attributable to the shares is 200 − 6.4 = $193.6m, or $48.40 per share over 4 million shares. The $48.72 option spreads the 6.4m over 5m shares, and $48.00 subtracts the undiluted call value of $8 on the 1m warrants spread over 4m shares.
Did you get it right without looking?
One question tells you little. A timed set on The Black-Scholes-Merton Model shows your real accuracy, how long you take and where you lose marks.
More The Black-Scholes-Merton Model questions
- A stock will pay a single dividend of 2 just before the ex-dividend date in four months. The American call has a strike of 45, expires in si…
- A non-dividend-paying stock has μ = 9% and σ = 30% per annum. Over a 4-year horizon, what is the standard deviation of the continuously comp…
- A trader observes that implied volatilities for equity index options are higher for low strikes than for high strikes of the same maturity. …
- In the Black-Scholes-Merton formula for a European call option on a non-dividend-paying stock, N(d2) is best interpreted as which of the fol…
- A stock has S_0 = 50, μ = 14% and σ = 30% per year under the lognormal model. What is the expected stock price after 2 years, E[S_2]?
- A European call on a non-dividend-paying stock trades at a market price of 6.20. Using a volatility of 20% in the Black-Scholes-Merton model…