Optimal date of development

Consider the market for oil. Assume that owners of oil reserves have the choice of when and how rapidly to extract their oil reserves. In particular, owners must make an investment in order to begin extracting their oil. Assume that it requires an initial capital investment of $100,000,000 (made at the time at which extraction begins) to develop the field after which the field will produce 1,200 barrels per day for 10 years. After 10 years the usable reserves will be exhausted. Assume the annual costs of the labor and other inputs required to extract the oil are $3,000,000 per year. Assume the current price of oil is $50.00.

A. Assume oil prices are expected to rise at a constant rate of 2% per year above inflation, inflation on both capital costs and other costs is 1.5% per year, and the nominal interest rate is 6%. When and at what price of oil will it be worthwhile to develop the field?

B. Will the field be developed as soon as it is profitable to do so? Why or why not?

Please answer problems C-G as independent experiments (i.e. each starts from the base case described above).

C. How will the date of development change if capital costs were decreasing at 1% per year rather than rising at 1.5% per year? Why?

D. How would the optimal date of development change if production started at 1200 barrels per day but declined over the life of the field rather than remained constant for 10 years? Why?

E. How would the date of development change if "secondary recovery" is introduced which allows additional oil to be extracted after the 10 years is up with the investment of additional dollars? Would secondary recovery be done right away or might it pay to wait? Why?

F. How would an increase in the current price of oil affect the time of development if the rate of price increase in the future remains at 2%?

G. How would changing the rate of increase in oil prices above inflation to 2.5% affect the date of extraction (holding the current price fixed at $50.00)? Why?