An oil company contemplates investing 100 million dollars per year (in constant dollars) for five years in exploratory work to confirm the existence of new exploitable reserves. It will then face a potential delay until market conditions justify exploitation, which will require investing 200 million dollars for three years in production facilities, following which delivery of oil can start with a projected net revenue of 100 million dollars per year, essentially ad infinitum.

a. At a real discount rate of 5%/yr what is the longest delay tolerable between the start of exploitation and the start of oil delivery: i.e., how far in advance is it worth proving out reserves?

b. If the real discount rate were 10%/yr, what is the maximum time delay?