Mary Lamb is trying to decide what to do about an apartment building she inherited from her

aunt in Walla Walla. If she were to sell it today she could get $100,000. Since Mary doesn't

need the money immediately, she is considering holding on to the property for sale later.

Mary has considered three options: she can sell the building now, at the end of next year (year

1), or at the end of the following year (year 2). She has decided not to keep it more than 2

years. For each year that Mary keeps the building, she receives $4,000 in rents. Mary consults

with the local Walla Walla real estate gurus and then assesses the following probabilities about

increases or decreases in the value of the property:

During the first year (year 1) there is a 20% chance that the value of the building will increase

by 10%, 30% chance that the value will stay the same and 50% chance that the value will

decrease by 10%.

Also, what happens in the first year and the second are not independent. Mary believes that if

the value increases in the first year, then there is a 50% chance that the value will also increase

in the second year and a 30% that the value will stay the same during the second year. If the

value decreases in the first year then there is a chance of 70% that it will also decrease in the

second and a chance of 20% that it will stay the same. Finally, if the value stays the same in

the first year, then chances are 50% that it will also stay the same in the second and 25% that

it will increase. (All decreases and increases are considered to be 10% in the second year too

to simplify)

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7

a.

Make a decision tree for this decision problem. Include payoff values at the ends of the

tree and probability values where appropriate.

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8