Amy Lloyd is interested in leasing a new Honda and has contacted three automobil

Question

Amy Lloyd is interested in leasing a new Honda and has contacted three automobile dealers for pricing information. Each dealer offered Amy a closed-end 36-month lease with no down payment due at the time of signing. Each lease includes a monthly charge and a mileage allowance. Additional miles receive a surcharge on a per-mile basis. The monthly lease cost, the mileage allowance, and the cost for additional miles follow: Dealer Monthly Cost Mileage Allowance Cost per Additional Mile Hepburn Honda $299 36,000 $0.15 Midtown Motors $310 45,000 $0.20 Hopkins Automotive $325 54,000 $0.15 Amy decided to choose the lease option that will minimize her total 36-month cost. The difficulty is that Amy is not sure how many miles she will drive over the next three years. For purposes of this decision, she believes it is reasonable to assume that she will drive 12,000 miles per year, 15,000 miles per year, or 18,000 miles per year. With this assumption Amy estimated her total costs for the three lease options. For example, she figures that the Hepburn Honda lease will cost her 36($299) + $0.15(36000 - 36000) = $10,764 if she drives 12,000 miles per year, 36($299) + $0.15(45000 - 36000) = $12,114 if she drives 15,000 miles per year, or 36($299) + $0.15(54000 - 36000) = $13,464 if she drives 18,000 miles per year. (a) What is the decision, and what is the chance event? Choose the correct answer below. (i) The decision is to select the number of miles Amy will drive and the chance event is the three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive). (ii) The decision is to select the monthly cost and the chance event is the three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive). (iii) The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the number of miles Amy will drive. (iv) The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the monthly cost that Amy will incur. (b) Construct a payoff table for Amy's problem. Actual Miles Driven Annually Dealer 12,000 15,000 18,000 Hepburn Honda $ $ $ Midtown Motors $ $ $ Hopkins Automotive $ $ $ (c) If Amy has no idea which of the three mileage assumptions is most appropriate, what is the recommended decision (leasing option) using the optimistic, conservative, and minimax regret approaches? Optimistic approach Conservative approach Minimax approach (d) Suppose that the probabilities that Amy drives 12,000, 15,000, and 18,000 miles per year are 0.5, 0.4, and 0.1, respectively. What option should Amy choose using the expected value approach?

Explanation / Answer

a) The decision is to select the best lease option from three alternatives (Hepburn Honda, Midtown Motors, and Hopkins Automotive) and the chance event is the number of miles Amy will drive.

b)

c)

Optimistic approach= Hepburn Honda=$10764

Conservative approach = Hopkins Automotive = $11160

Opportunity Loss or Regret Table:

Minimax regret Approach = Hopkins Automotive

d)

EV Hepburn Honda =0.5($10764)+0.4($12114)+0.1($13464)= $11574

EV Midtown Motors =0.5($11160)+0.4($11160)+0.1($12960)= $11340

EV Hopkins Automotive=0.5($11700)+0.4($11700)+0.1($11700)= $11700

Best Decision is Midtown Motors

Dealer Hepburn Honda Midtown Motors Hopkins Automative Monthly cost $299 $310 $325 Mileage allowance 36000 45000 54000 Cost per additional mile $0.15 $0.20 $0.15 Total Cost Total Cost Total Cost 12000 Miles per year=36000 miles in 3 years 36($299)+$0.15(36000-36000) = $10764 36($310)+no additional cost = $11160 36($325)+no additional cost =$11700 15000 miles per year=45000 miles in 3 years 36($299)+$0.15(45000-36000) =$12114 36($310)+no additional cost = $11160 36($325)+no additional cost =$11700 18000 miles per year=54000 miles in 3 years 36($299)+$0.15(54000-36000) =$13464 36($310)+$0.20(54000-45000)=$12960 36($325)+$0.15(54000-54000)=$11700

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