Cosmogonic Petroleum's Chairman, Yukon Cornelius, has been attempting to increase the efficiency of his firm's oil exploration process. Currently, the firm classifies areas as 'promising' and 'not promising'. The firm has exploration rights in 300 'promising' areas and 100 'not promising' areas. The firm begins exploring an area by sending out a grizzled prospector to sniff around the area (at a cost of $250,000). Depending on the prospector's report, the firm reclassifies the area as 'highly likely' or 'highly unlikely'. The probability of the prospector classifying an area as 'highly likely' is 0.9 if the area was earlier classified as promising and 0.5 if it was earlier classified as 'not promising'. If the firm goes on to dig a well (at a cost of $1,000,000), oil is found in a 'highly likely' area with probability 0.8, and in a 'highly unlikely' area with probability 0.1. If oil is found, an average well contributes a profit of $500,000 a year and has a life of 6 years (assume these cash flows occur at the end of the year). If oil is not found, the company is left with a million-dollar hole in the ground in the middle of the desert. This asset is worth zero. The required rate of return is 20% for the oil exploration business.

(i) Show that the probability that there is actually oil in a promising area is 0.73, and 0.45 for the not promising area. If you fail in this step, continue on and use these figures for the parts (ii) and (iii).

(ii) Assuming that prospecting and drilling take no time, what is the optimal oil exploration strategy for the firm (that is, where should it prospect, and when should it drill)?

(iii) The firm now has the option of investing $20 million in developing a new seismic test which will increase the informativeness of the prospecting. The new test will determine for certain if an area has oil or no oil. While the new test will cost only $100,000, it will render the grizzled prospector obsolete. The $50 million in training costs invested in the old prospector (after all, it takes a lot to grizzle a prospector) will now be lost. Also the new technology will require a special laboratory, which, because of space constraints, will have to be built on the executive parking lot. An air-conditioned tramway from the worker's parking lot will have to be arranged for the executives which will necessitate an expenditure of $ 10 million. Should the firm develop the new test (assume that the test will be available a year from now if the project is given the go ahead, and all areas can be tested simultaneously with either test)?