question archive Beverly Mills has decided to lease a hybrid car to save on gasoline + expenses and to do her part to help keep the environment clean
Beverly Mills has decided to lease a hybrid car to save on gasoline + expenses and to do her part to help keep the environment clean
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Beverly Mills has decided to lease a hybrid car to save on gasoline + expenses and to do her part to help keep the environment clean. The car she selected is available from only one dealer in the local area, but that dealer has several leasing options to accommodate a variety of driving patterns. All the leases are for 3 years and require no money at the time of signing the lease. The first option has a monthly cost of $330, a total mileage allowance of 36,000 miles (an average of 12,000 miles per year), and a cost of $0.35 per mile for any miles over 36,000. The following table summarizes each of the three lease options: 3-YEAR MONTHLY MILEAGE COST PER EXCESS LEASE COST ALLOWANCE MILE Option 1 $330 36,000 $0.35 Option 2 $380 45,000 $0.25 Option 3 $430 54,000 $0.15 Beverly has estimated that, during the 3 years of the lease, there is a 40% chanc she will drive an average of 12,000 miles per year, a 30% chance she will drive an average of 15,000 miles per year, and a 30% chance that she will drive 18,000 miles per year. In evaluating these lease options, Beverly would like to keep her costs as low as possible. a. Develop a payoff (cost) table for this situation. b. What decision would Beverly make if she were optimistic? c. What decision would Beverly make if she were pessimistic? d. What decision would Beverly make if she wanted to minimize her expected . cost (monetary value)? e. Calculate the expected value of perfect information for this problem.
:3-32 Refer to the leasing decision facing Beverly Mills in Problem 3-31. Develop the opportunity loss table for this situation. Which option would be chosen based on the minimax regret criterion? Which alternative would result in the lowest expected opportunity loss?
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a. For a 3-year lease, there are 36 months of payments.
Option 1 total monthly payments: 36($330) = $11,880
Option 2 total monthly payments: 36($380) = $13,680
Option 3 total monthly payments: 36($430) = $15,480
Excess mileage costs based on 36,000 mileage allowance for Option 1, 45,000 for Option 2, and 54,000 for option 3.
Option 1 excess mileage cost if 45,000 miles are driven = (45000 - 36000)(0.35) = 3150
Option 1 excess mileage cost if 54,000 miles are driven = (54000 - 36000)(0.35) = 6300
Option 2 excess mileage cost if 54,000 miles are driven = (54000 - 45000)(0.25) = 2250
The total cost for each option in each state of nature is obtained by adding the total monthly payment cost to the excess mileage cost.
Total cost table
|
Lease option |
36000 miles driven |
45000 miles driven |
54000 miles driven |
|
Option 1 |
11,880 |
15030 |
18180 |
|
Option 2 |
13,680 |
13680 |
15930 |
|
Option 3 |
15,480 |
15480 |
15480 |
b. Optimistic decision: Option 1 because the best (minimum) payoff (cost) for this is 11,800 which is better (lower) than the best payoff for each of the others.
c. Pessimistic decision: Option 3 because the worst (maximum) payoff (cost) for this is 15,480 is better (lower) than the worst payoff for each of the others.
d. Select Option 2.
EMV(Option 1) = 11,880(0.4) + 15,030(0.3) + 18,180(0.3) = 14,715
EMV(Option 2) = 13,680(0.4) + 13,680(0.3) + 15,930(0.3) = 14,355
EMV(Option 3) = 15,480(0.4) + 15,480 (0.3) + 15,480(0.3) = 15,480
(e) EVPI for a minimization problem = (Best EMV without PI) - (EV with PI)
EV with PI = 11,880(0.4) + 13,680(0.3) + 15,480(0.3) = 13,500
EVPI = 14,355 - 13,500 = 855
