Assume that you have a riding lawn mower that is in need of repairs.You can choose to repair or replace it.You are interested in your net cost over the next two years.If you choose to repair,it will cost $300 and there is a 50/50 chance of whether or not it will need additional repairs within the next two years.If it does need additional repairs,there is a 40 percent chance of needing another $400 of repairs,and a 60 percent chance of needing another $200 of repairs.At the end of the two years you estimate that the repaired mower would be worthless. If you choose to replace the mower by trading in the old mower,the cost after deducting the trade in value is $1500.At the end of the two years you estimate there is a 75 percent chance you could resell it for $1000,and a 25 percent chance that you can resell it for $1300.
After folding back the tree which of the following is correct?
A)Choose to repair for an expected cost of $300
B)Choose to repair for an expected cost of $440
C)Choose to replace for an expected cost of $275
D)Choose to replace for an expected cost of $425

Question

Quizplus · Accepted Answer

To find the expected cost of each option, we need to calculate the net present value (NPV) of each option.

For the repair option: 
- Cost of initial repair: $300 
- Chance of needing additional repairs: 50% 
- Cost of additional repairs: 
    - 40% chance of $400: $160 
    - 60% chance of $200: $120 
- Salvage value after 2 years: $0

NPV of repair option: 
-300 - (0.5 * (160 + 120)) = -$550

For the replace option: 
- Cost after trade-in: $1500 
- Chance of reselling for $1000: 75% 
- Chance of reselling for $1300: 25%

Expected resale value after 2 years: 
- (0.75 * $1000) + (0.25 * $1300) = $1075

NPV of replace option: 
-$1500 + $1075 = -$425

Since the NPV of the replace option is less than the NPV of the repair option, we should choose to repair the lawn mower, even though the expected cost of repairing is higher. Therefore, the best choice is D: Choose to replace for an expected cost of $425.

Assume That You Have a Riding Lawn Mower That Is