### Calculate the net values at the ends of the branches

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These and other repairs that an older car may require could lead you to pay anywhere from \$500 to \$2,500 in each of the next 3 years. If you are lucky, the repair bills will be low or will come later. But you could end up paying a lot of money when you least expect it. Draw a decision tree for this problem. To simplify it, look at the situation on a yearly basis for 3 years. If you buy the new car, you can anticipate cash outflows of 12 × \$201.85 = \$2,422.20 plus maintenance costs. For the used car, some of the repair costs are known (immediate repairs this year, tires next year), but we must model the uncertainty associated with the rest. In addition to the known repairs, assume that in each year there is a 20% chance that these uncertain repairs will be \$500, a 20% chance they will be \$2,500, and a 60% chance they will be \$1,500. (Hint: You need three chance nodes: one for each year!) To even the comparison of the two cars, we must also consider their values after 3 years. If you buy the new car, it will be worth approximately \$8,000, and you will still owe \$4,374. Thus, its net salvage value will be \$3,626. On the other hand, you would own the used car free and clear (assuming you can keep up with the repair bills!), and it would be worth approximately \$2,000. Include all of the probabilities and cash flows (outflows until the last branch, then an inflow to represent the car's salvage value) in your decision tree. Calculate the net values at the ends of the branches.

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