4 – 10
Chapter 4
Decision Analysis
Case Problem 1: Property Purchase Strategy
The decision tree for the Oceanview decision problem is shown below. Note that the final outcome of
whether the zoning change is approved or rejected by the voters occurs after Oceanview decides to bid and
then wins the bid. Otherwise, the outcome of the vote on the zoning change does not enter into the
problem.
Zoning
Approved
10
7
Bid
Do Not Bid
Not Highest Bid
Highest Bid
Zoning
Approved
Zoning
Rejected
4
2
1
Market
Research
Predicts
Rejection
Payoff*
1,985,000
1,985,000
-515,000
-15,000
-15,000
Decision Analysis
4 – 11
The decision tree with branch probabilities and expected values is as follows:
If the market research is not conducted, Oceanview should go ahead and bid. The expected value of this
action is $50,000 as shown at node 8 of the decision tree. However, the analysis shows that the
recommended strategy is to conduct the market research first. the value of the market research exceeds its
cost. The optimal strategy is as follows:
9
Highest Bid
Approved
.6585
Rejected
.3415
10
7
Bid
Not Highest Bid
Highest Bid
Approved
.0508
Rejected
.9492
8
2
5
1
Market
Research
No Market
Research
Predicts
Bid
Do Not Bid
Not Highest Bid
.7
1,985,000
-515,000
-15,000
1,985,000
-515,000
-15,000
-500,000
0
0
EV = 78,993
.2
.2
EV = 50,000
.8
EV = 1,131,250
EV = -388,000
EV = -89,600
Chapter 4
4 – 12
Case Problem 2: Lawsuit Defense Strategy
1. Decision Tree
To find the optimal decision strategy, we must fold the tree back computing expected values at the chance
nodes and choosing the least cost alternative at the decision nodes. Shown below are the values computed
at each node.
Node
Value
1
670
2
670
3
825
4
600
5
825
1
Allied Accepts John’s
Offer of $750,000
0.3
$750
John Accepts
Allied’s Counteroffer
$400
Allied Wins
No Damages
0.10
0.4 0.5
0.2
Allied Accepts
0.5
5
Allied Rejects
John‘s Counteroffer
0.3
Allied Loses Damages
of $750,000
0.5
0.20
$0
$750
Decision Analysis
4 – 13
Shown below is the decision tree with all nonoptimal branches eliminated.
3. If John accepts Allied’s counteroffer of $400,000, no further action is required. If John rejects
Allied’s counteroffer and elects to have a jury decide the settlement amount, Allied must prepare for
a trial. If John counteroffers with $600,000, Allied should accept John’s counteroffer.
4. To develop the risk profile for the optimal strategy, we simply multiple the branch probabilities on
all paths to the end points of the decision tree. The risk profile is given below in tabular form.
Probability
0.08
1
0.3
John Accepts
Allied’s Counteroffer
$400
Allied Loses
Damages of $1,500,000
Allied Wins
No Damages
0.10
0.4 0.5
0.2
Allied Accepts
0.5
$1500
$0