9781118041581

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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