Final answer:
The value of an American put option on ENRON stock with a strike price of $82.5 that matures in 7 months, assuming the stock price goes to zero and the continuously compounded risk-free rate is 8%, is the present value of the strike price, which is about $78.738.
Step-by-step explanation:
If the price of ENRON stock goes to zero, the value of the American put option with a strike price of $82.5 and matures in 7.0 months can be calculated by considering the put option's intrinsic value. Since the stock is worthless, the put option allows the holder to sell the stock for $82.5. However, we also need to discount this amount back to its present value because of the time value of money.
Using the continuously compounded risk-free rate of 8.0 percent per year, we can calculate the present value of the strike price as follows:
PV = Strike Price / e
(rate * time)
where:
- PV = Present Value of the strike price
- Strike Price = $82.5
- e = base of the natural logarithm
- rate = yearly risk-free rate (expressed as 0.08 for 8%)
- time = time until expiration (expressed as 7/12 years)
So the calculation will be:
PV = $82.5 / e(0.08 * 7/12)
Upon calculating this, we find that the present value of the put option is about $78.738. Therefore, the correct answer is C. 78.738.