The Jones Family, Incorporated

The Scene: Early evening in an ordinary family room in Manhattan. Modern furniture, with old copies of The Wall Street Journal and the Financial Times scattered around. Autographed photos of Alan Greenspan and George Soros are prominently displayed. A picture widow reveals a distant view of light on the Hudson River. John Jones sits at a computer terminal, glumly sipping a glass of chardonnay and putting on a carry trade in Japanese yen over the Internet. His wife Marsha enters.

Marsha: John, whats wrong? Have you been selling yen again? Thats been losing trade for weeks.

John: Well, yes. I shouldnt have gone to Goldman Sachs foreign exchange brunch. But Ive got to get out of the house somehow. Im cooped up here all day calculating covariances and efficient risk-return trade-offs while youre out trading commodity futures. You get all the glamour and excitement.

Marsha: Dont worry, dear, it will be over soon. We only recalculate our most efficient common stock portfolio once a quarter. Then you can go back to leveraged leases.

John: You trade, and I do all the worrying. Now theres a rumor that our leasing company is going to get a hostile takeover bid. I knew the debt ratio was too low, and you forgot to put on the poison pill. And youve made a negative-NPV investment!

Marsha: What investment?

John: That wildcat oil well. Another well in that old Sourdough field. Its going to cost $5 million! Is there any oil down there?

Marsha: That Sourdough field has been good to us, John. Where do you think we got the capital for your yen trades? I bet well find oil. Our geologist says theres only a 30% chance of a dry hole.

John: Even if we hit oil, I bet well only get 75 barrels of crude oil per day.

Marsha: Thats 75 barrels day in, day out. There are 365 days in a year, dear.

Johnny and Marshas teenage son Johnny bursts into the room.

Johnny: Hi, Dad! Hi, Mom! Guess what? Ive made the junior varsity derivatives team! That means I can go on the field trip to the Chicago Board Options Exchange. (Pauses.) Whats wrong?

John: Your mother has made another negative-NPV investment. A wildcat oil well, way up on the North Slope of Alaska.

Johnny: Thats O.K, Dad. Mom told me about it. I was going to do an NPV calculation yesterday, but I had to finish calculating the junk-bond default probabilities for my corporate finance homework. (Grabs a financial calculator from his backpack.) Lets see: 75 barrels a day times 365 days per year times $100 per barrel when delivered in Los Angeles thats $2.7 million per year.

John: Thats $2.7 million next year, assuming that we find any oil at all. The production will start declining by 5% every year. And we still have to pay $20 per barrel in pipeline and tanker charges to ship the oil from North Slope to Los Angeles. Weve got some serious operating leverage here.

Marsha: On the other hand, our energy consultants project increasing oil prices. If they increase with inflation, price per barrel should increase by roughly 2.5% per year. The wells ought to be able to keep pumping for at least 15 years.

Johnny: Ill calculate NPV after I finish with the default probabilities. The interest rate is 6%. Is it OK if I work with the beta of .8 and our usual figure of 7% for the market risk premium?

Marsha: I guess so, Johnny. But I am concerned about the fixed shipping costs.

John: (Takes a deep breath and stands up.) Anyway, how about a nice family dinner? Ive reserved our usual table at the Four Seasons.

Everyone exits.

Announcer: Its the wildcat well really negative-NPV? Will John and Marsha have to fight a hostile takeover? Will Johnnys derivatives team use Black-Scholes or the binominal method? Fin out in the next episode of The Johns Family, Incorporated.

Questions:

Calculate the NPV of the wildcat oil well, taking account of the probability of a dry hole, the shipping costs, the decline in production, and the forecasted increase in oil prices. How long does production have to continue for the well to be positive-NPV investment? Ignore taxes and other possible complications.

Hints:

Assume that the risk free interest rate = 6%, production starts today but sold at the end of the year, oil production will start declining by 5% after the first year, the inflation of oil prices and transportation cost start immediately and the life of the oil well is 15 years starting from today (day of investment).