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```									Use excel adds on – Precision Tree and @ Risk

Problem 3:

A decision maker is working on a problem that requires her to study the uncertainty surrounding
the payoff of an investment. There are three possible levels of payoff -\$1,000, \$5,000, and
\$10,000. As a rough approximation, the decision maker believes that each possible payoff is
equally likely. But she is not fully comfortable with the assessment that each probability is
exactly 1/3, and so would like to conduct a sensitivity analysis. In fact, she believes that each
probability could range from 0 to ½.

1. Show how a Monte Carlo simulation could facilitate a sensitivity analysis of the
probabilities of the payoff
2. Suppose the decision maker is willing to say that each of the three probabilities could be
chosen from a uniform distribution between 0 and 1. Could you incorporate this
information into your simulation? If so, how? If not, explain why not, or what additional
information you would need.

Problem 4

John Campbell, an employee of Manhattan Construction Company claims to have injured his
back as a result of a fall while repairing the roof at one of the Eastview apartment buildings. He
filed a lawsuit against Doug Reynolds, the owner of Eastview Apartments, asking for damage of
\$1,500,000. John claims that the roof had rotten sections and that his fall could have been
prevented if Mr. Reynolds had told Manhattan Construction about the problem. Mr. Reynolds
notified his insurance company, Allied Insurance of the lawsuit. Allied must defend Mr.
Reynolds, and decide what action to take regarding the lawsuit.

Some depositions and a series of discussions took place between both sides. As a result, John
Campbell offered to accept a settlement of \$750,000. Thus one option for Allied to pay John
\$750,000 to settle the claim. Allied is also considering making John a counteroffer of \$400,000
in the hope that he will accept a lesser amount to avoid the time and the cost of going to trial.
Allied’s preliminary investigation shows that John’s case is strong. Allied is concerned that John
may reject their counteroffer and request a jury trial. Allied’s lawyers spent some time exploring
John’s likely reaction if they make a counteroffer of \$400,000.

The lawyers concluded that it is adequate to consider three possible outcomes to represent John’s
possible reaction to a counteroffer of \$400,000. 1. John will accept the counteroffer and the case
will be closed. 2. John will reject the counteroffer and elect to have a jury decide the settlement
amount, or 3. John will make a counteroffer to Allied of \$600,000. If John does make a
counteroffer, Allied decided that they will not make additional counteroffers. They will either
accept John’s counteroffer of \$600,000 or go to trial.

If the case goes to jury trial, Allied considers three outcomes possible: 1. The jury may reject
John’s claim and Allied will not be required to pay any damages; 2. The jury will find in favor of
John and award him \$750,000 in damages or 3. The jury will conclude that John has a strong
case and award him the full amount of \$1,500,000.

Key considerations as Allied develops its strategy for disposing of the case are the probabilities
associated with John’s response to an Allied counteroffer of \$400,000 and the probabilities
associated with the three possible trial outcomes. Allied lawyers believe the probability that John
will accept the counteroffer of \$400,000 is 0.1, that the probability that John will reject the
counteroffer of \$400,000 is 0.4, and the probability that John will, himself, make a counteroffer
to Allied of \$600,000 is 0.5. If the case goes to court, they believe that the probability the jury
will award John damage of \$1,500,000 is 0.3, the probability that the jury will award John
damages of \$750,000 is 0.5, and the probability that the jury will award John nothing is 0.2.

Perform an analysis of the problem facing Allied Insurance and prepare a report that summarizes
your findings and recommendations. Be sure to include: Decision tree, a recommendation
regarding whether Allied should accept John’s initial offer to settle the claim for \$750,000; a
decision strategy that Allied should follow if they decide to make John a counteroffer of
\$400,000 and a risk profile of your recommendation strategy.

Problem 5:

Consider an oil-wildcatting problem. You have mineral rights on a piece of land that you believe
may have oil underground. There is only a 10% chance that you will strike oil if you drill, but the
payoff is \$200,000. It costs \$10,000 to drill. The alternative is not to drill at all, in which case
your profit is zero.

o   Draw a decision tree to represent your problem. Should you drill?
o   Using the decision tree, calculate EVPI.
o   Before you drill, you might consult a geologist who can assess the promise of the
piece of land. She can tell you whether your prospects are “good” or “poor.” But
she is not a perfect predictor. If there is oil, the conditional probability is 0.95 that
she will say prospects are good. If there is no oil, the conditional probability is
0.85 that she will say poor. Draw a decision tree that includes the “Consult
Geologist” alternative. Be careful to calculate the appropriate probabilities to
include in the decision tree. Finally, calculate the EVII for the geologist. If she
charges \$7,000, what should you do?

Problem 6:

Assess your utility function in two different ways.
a. Use the certainty-equivalent approach to assess your utility function for wealth over a range of
\$100 to \$20,000.
b. Use the probability-equivalent approach to assess U(\$1500), U(\$5600), U(\$9050), and U(\$13,700).
Are these assessments consistent with the assessments made in part a? Plot these assessments and
those from part a on the same graph and compare them.

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