19.1 Payoff Tables and Decision Trees

TABLE 19.4
Opportunity Loss Table
($) for Two Stocks Under
Four Economic
Conditions
Problems for Section 19.1
LEARNING THE BASICS
19.1 For this problem, use the following payoff table:
a. Construct an opportunity loss table.
b. Construct a decision tree.
19.2 For this problem, use the following payoff table:
a. Construct an opportunity loss table.
b. Construct a decision tree.
APPLYING THE CONCEPTS
ACTION
EVENT A ($) B ($)
1 50 100
2 200 125
ACTION
EVENT A ($) B ($)
1 50 10
2 300 100
3 500 200
19.3 A manufacturer of designer jeans must decide
whether to build a large factory or a small factory in a particular
location. The profit per pair of jeans manufactured is
estimated as $10. A small factory will incur an annual cost
of $200,000, with a production capacity of 50,000 pairs of
jeans per year. A large factory will incur an annual cost
of $400,000, with a production capacity of 100,000 pairs of
jeans per year. Four levels of manufacturing demand are
considered likely: 10,000, 20,000, 50,000, and 100,000 pairs
of jeans per year.
19.1 Payoff Tables and Decision Trees 7
of $30 as compared to a loss of $50 from stock B. In a stable economy, stock A again is better
than stock B because it provides a return of $70 compared to $30 for stock B. However, under
conditions of moderate growth or boom, stock B is superior to stock A. In a moderate growth
period, stock B provides a return of $250 as compared to $100 from stock A, while in boom conditions,
the difference between stocks is even greater, with stock B providing a return of $400 as
compared to $150 for stock A. Table 19.4 summarizes the complete set of opportunity losses.
Event
Optimum
Action
Profit of
Optimum
Action
Alternative Course of Action
A B
Recession A 30 30 - 30 = 0 30 - (-50) = 80
Stable economy A 70 70 - 70 = 0 70 - 30 = 40
Moderate growth B 250 250 - 100 = 150 250 - 250 = 0
Boom B 400 400 - 150 = 250 400 - 400 = 0
a. Determine the payoffs for the possible levels of production
for a small factory.
b. Determine the payoffs for the possible levels of production
for a large factory.
c. Based on the results of (a) and (b), construct a payoff
table, indicating the events and alternative courses of
action.
d. Construct a decision tree.
e. Construct an opportunity loss table.
19.4 An author is trying to choose between two publishing
companies that are competing for the marketing rights to her
new novel. Company A has offered the author $10,000 plus
$2 per book sold. Company B has offered the author $2,000
plus $4 per book sold. The author believes that five levels of
demand for the book are possible: 1,000, 2,000, 5,000,
10,000, and 50,000 books sold.
a. Compute the payoffs for each level of demand for company
A and company B.
b. Construct a payoff table, indicating the events and alternative
courses of action.
c. Construct a decision tree.
d. Construct an opportunity loss table.
19.5 The DellaVecchia Garden Center purchases and sells
Christmas trees during the holiday season. It purchases the
trees for $10 each and sells them for $20 each. Any trees not
sold by Christmas day are sold for $2 each to a company that
makes wood chips. The garden center estimates that four levels
of demand are possible: 100, 200, 500, and 1,000 trees.
a. Compute the payoffs for purchasing 100, 200, 500, or
1,000 trees for each of the four levels of demand.
b. Construct a payoff table, indicating the events and alternative
courses of action.
c. Construct a decision tree.
d. Construct an opportunity loss table.