9781118041581

(Nancy Kaufman) #1
Decision Trees 509

reserve at a depth of 3,000 feet. The three branches list the profit outcomes for
this field depending on the (uncertain) oil price. The expected profit from such
a field is simply the average of the possible profit outcomes weighted by the
respective probabilities. Thus, the expected profit is (.2)(700) (.5)(350) 
(.3)(150) $360 thousand, listed in chance node D. But what if the field had
yielded 8,000 barrels per year? By an analogous calculation, we find the expected
profit to be $636 thousand in this case, as shown in chance node E. The
expected profits for the chance nodes F through I (corresponding to different-
sized fields at different depths) have also been computed and listed on the tree.
At this point, we have “averaged out” the price uncertainty.
In the next step, we average over the possible quantities of oil found.
Chance node B shows the expected profit if oil is found at 3,000 feet, com-
puted by averaging the expected profits at nodes D through F:

.

Node C lists the expected profit ($353.8 thousand) for a field found at 5,000 feet.
The last step is to compute the overall expected profit of drilling. This is
shown in the initial chance node A and is the average of the expected profits
at B and C and the $400 thousand loss if no oil is found. As always, this expected
value is computed using the branch probabilities as weights. Therefore, the
expected profit from drilling is

.

The wildcatter has solved his decision problem by calculating the expected
profit of drilling in stages. Since this is negative, the wildcatter should choose
not to exercise his option on the site.

(.13)(815.4)(.21)(353.8)(.66)(400)$83.7 thousand

(.15)(360)(.55)(636)(.3)(1,372)$815.4 thousand

CHECK
STATION 2

Suppose the chief executive of an oil company must decide whether to drill a site and,
if so, how deep. It costs $160,000 to drill the first 3,000 feet, and there is a .4 chance of
striking oil. If oil is struck, the profit (net of drilling expenses) is $600,000. If oil is not
struck, the executive can drill 2,000 feet deeper at an additional cost of $90,000. Her
chance of finding oil between 3,000 and 5,000 feet is .2, and her net profit (after all
drilling costs) from a strike at this depth is $400,000. What action should the executive
take to maximize expected profit?

For the last 30 years, globalization of business has been an enduring trend.
Consumers in all parts of the world buy an increasing proportion of foreign goods,
and a growing number of firms operate across national boundaries. The prospects
of rapid growth and high profits from untapped foreign markets are attractive to
large firms. Telecommunication companies vie for shares of the Chinese market,
expecting to quintuple the number of phone lines from 5 per hundred people to
25 (still only about one-third of the U.S. average). Ford has invested $6 billion in

The Perils of
International
Business

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