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UTILITY AND DECISION MAKING 581

a. Show the decision tree.
b. Using the following probabilities, what is the optimal decision strategy?
PðFÞ¼ 0:56 Pðs 1 jFÞ¼ 0:57 Pðs 1 jUÞ¼ 0:18 Pðs 1 Þ¼ 0:40
PðFÞ¼ 0:44 Pðs 2 jFÞ¼ 0:43 Pðs 2 jUÞ¼ 0:82 Pðs 2 Þ¼ 0:60
11 Dante Development Corporation is considering bidding on a contract for a new office
building complex. Figure 13.14 shows the decision tree prepared by one of Dante’s
analysts. At node 1, the company must decide whether to bid on the contract. The cost of
preparing the bid is E200 000. The upper branch from node 2 shows that the company has
a 0.8 probability of winning the contract if it submits a bid. If the company wins the bid, it
will have to pay E2 000 000 to become a partner in the project. Node 3 shows that the
company will then consider doing a market research study to forecast demand for the
office units prior to beginning construction. The cost of this study is E150 000. Node 4 is a
chance node showing the possible outcomes of the market research study.
Nodes 5, 6 and 7 are similar in that they are the decision nodes for Dante to either build
the office complex or sell the rights in the project to another developer. The decision to
build the complex will result in an income of E5 000 000 if demand is high and E3 000 000 if
demand is moderate. If Dante chooses to sell its rights in the project to another developer,
income from the sale is estimated to be E3 500 000. The probabilities shown at nodes 4, 8
and 9 are based on the projected outcomes of the market research study.
a. Verify Dante’s profit projections shown at the ending branches of the decision tree by
calculating the payoffs of E2 650 000 and E650 000 for the first two outcomes.
b. Whatis theoptimal decisionstrategy forDante,and whatis theexpected profitforthisproject?
c. What would the cost of the market research study have to be before Dante would
change its decision about the market research study?
d. Develop a risk profile for Dante.

Figure 13.14 Decision Tree for the Dante Development Corporation

Profit (€1000s)
High Demand 2650
Build Complex 0.85
8
Forecast High 5 Moderate Demand 650
0.6 0.15
Sell
1150
Market Research
4 High Demand 2650
Build Complex 0.225
9
Forecast Moderate Moderate Demand 650
6 0.775
Win Contract 0.4 Sell
0.8 3 1150
High Demand 2800
Build Complex 0.6
Bid 10
2 No Market Research Moderate Demand 800
7 0.4
Sell
1300
1 Lose Contract –200
0.2
Do Not Bid
0

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