You are the senior assistant to the Chairman of the Board of Hi-Teck Inc. In order to attract the chief operating officer of his choice from another firm, the Chairman offers the following incentive supplement to her base salary package:
- 2% of any price appreciation in the price of the stock up to $60 per share;
- 3% of any price appreciation above $60 but less than $75 per share;
- 4% of any price appreciation above $75 per share;
The price appreciation is to be computed with respect to the share price exactly 3 years from now, and there is no early payment of the supplement. The aggregate value of the supplement is based on the price appreciation of 10 million shares. The annual (not continuously compounded) risk free rate is 10% and the stock volatility is 50% annualized. The current price of the stock is $55.
Use the Black Scholes formula to value the supplement. Should you be concerned in your calculations that the new chief operating officer might increase the expected rate of price appreciation by wise actions?