Question

Martin Denny is an investor who recently purchased a circa-1800 Victorian mansion. He plans to remodel it into a multi-family rental property in 6 months, after the current tenant moves out. Recently, the tenant complained that the refrigerator was not working properly. As Martin’s cash flow was not extensive, he was not excited about purchasing a new refrigerator. Therefore, he also considers two other options: purchasing a used refrigerator, or repairing the current unit.

? He can purchase a new one for $400, and it will easily last six months.

? If he repairs the current one, he estimates a repair cost of $150, but he also believes that there is only a 30% chance that it will last a full six months. If the repaired refrigerator does not last six months, he will have to buy a new one for $400.

? If he buys a used refrigerator for $200, he estimates that there is a 60% probability that it will last at least six months. If it breaks down, he will still have the option of repairing it for $150 or buying a new one. If he repairs, there is a 30% chance that it will last. If it does not last, he will have to buy a new one for $400.

a) Construct a decision tree for this problem. Label all nodes and branches.

b) Identify the strategy that minimizes Martin’s expected cost for the next six months. Describe all the contingency plans. (For instance, “Buy a used refrigerator” is not a complete answer.)