Petrol Inc. is negotiating to acquire a proven but not yet develop oil field from Commercial Oil Inc. (CO) to broaden its reserves base. Based on its production and price projections for the prospect, the present value of the future expected cash flows, before investment and development costs, equals $80 million if they buy the field and begin production immediately. The cost of development will equal $40 million, giving an NPV of $40. If they pay more than $40 million to CO for the field and begin production immediately the deal would, net of the price paid to CO, be a negative NPV for Petrol. However, CO is insisting on a price of $45 million. By buying the field, Petrol is buying an option to expand production.

Petrol believes that oil prices will be highly variable in coming years resulting in the potential for a large payoff. Based upon the past behavior of oil prices the annual standard deviation of projected cash flows is expected to be 50%. Assume for purposes of this analysis that this is a European option that will mature in exactly 4 years. Assume the cost of development at the end of year 4 will equal $40 million, and the PV today of the expected cash flows beginning at the end of year 5, equals $80 million. There are no cash distributions over the life of the option (i.e. like a non-dividend paying stock). The current continuously compounded implied annual Treasury bond rate (corresponding to the expected term of the option) is 1%. Is the value of the option to expand, expressed as a European call option, sufficient to justify paying COs asking price of $45 million?