You have recently discovered a new strain of grain that is higher in protein than quinoa (a grain that is very high in protein). Although you like the taste of this grain, it has a slightly bitter taste that you are not sure everyone will like. You think that if it is cooked properly (with an appropriate combination of spices and herbs) many people will actually like its bitterness. However, you are not sure whether there will be a large enough market for this grain to justify the cost of land and production. In fact, you have done some analysis on the cost and revenue that a 100 acre farm could generate in order to determine whether this 100 acre farm would be a positive NPV project. You have determined that the start-up cost of such a farm would be $1.2 MM (the cost of the land and the equipment) and that, at a risk-adjusted discount rate of 15%, the present value of the net cash flows (revenue minus operating costs) would only be $.7 MM. Thus, it appears to have an NPV of -.5MM.
However, your analysis has not considered the option to expand. You estimate that it may take 5 years before you will know whether enough people will have a taste for this grain. If they do, then you can expand production to 2100 acres. If you expand, the cost of adding the extra acreage will remain at its current level of $1.2MM per 100 acres. You also estimate that the net cash flows from the production and sale of the grain will on average remain at $.7 MM per 100 acres -- but that it will vary by 20% per year. The risk-free rate on 5 year treasury securities corresponds to a stated 3% continuously compounded annual rate.
What is the value of the option to expand with this grain? Does it make sense to invest in the first 100 acres? Why or why not?