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(36,000 - 36,000) = $10,764 if she drives 12,000 miles per year, 36($299) + $0.15(45,000 - 36,000) = $12,114 if she drives 15,000 miles per year, or 36($299) + $0.15(54,000 - 36,000) = $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.
	- Select your answer Option (iii)
(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 Hepburn Conservative approach Hopkins Automotive Minimax approach Hopkins Automotive
(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?
	- Select your answer - Midtown Motors
(e)	Develop a risk profile for the decision selected in part (d). What is the most likely cost?
	$
	What is its probability?
	If required, round your answer to one decimal place.

Answer 1

(a) Amy must make a decision regarding the dealer (dealer named He, dealer named M Motors, or the dealer named as H Automotive). Now, the decision to be made is the dealer. When the decision is implemented, the chance events are driving 12,000 miles per year, 15,000 miles per year or 18,000 miles per year.

(b) If it is assumed that she will be driving 12,000 miles per year, 15,000 miles per year or 18,000 miles per year, then this assumption will help to estimate the total cost for each of the three lease options.

Hepburn Honda:

If she drives 12,000 miles per year, that is, 36,000 miles for 3 years, then it will cost her

.

If she drives 15,000 miles per year, that is, 45,000 miles for 3 years, then it will cost her

.

If she drives 18,000 miles per year, that is, 54,000 miles for 3 years, then it will cost her

Midtown Motors:

If she drives 12,000 miles per year, that is, 36,000 miles for 3 years, then it will cost her:

.

If she drives 15,000 miles per year, that is, 45,000 miles for 3 years, then it will cost her:

.

If she drives 18,000 miles per year, that is, 54,000 miles for 3 years, then it will cost her:

.

Hopkins Automotive:

If she drives 12,000 miles per year, that is, 36,000 miles for 3 years, then it will cost her:

.

If she drives 15,000 miles per year, that is, 45,000 miles for 3 years, then it will cost her:

.

If she drives 18,000 miles per year, that is, 54,000 miles for 3 years, then it will cost her:

.

The payoff table for Amy’s problem is given as follows:

Miles per Year

(c)

The minimum and maximum payoffs for each of Amy’s three alternatives are:

Thus, the optimistic approach is resulting in the assortment of the He Automotive lease option (which has the least minimum cost of the three alternatives, that is, $10,764).

The conservative approach is resulting in the selection of the H Automotive lease option (which has the least maximum cost of the three alternatives, that is, $11,700). To find out the lease option in order to select under the approach named as minimax regret approach, firstly it is required to construct an opportunity loss (or regret) table. For each of the three chance events (that is, driving 12000 miles, driving 15000 miles, and driving 18000 miles) perform the subtraction of the minimum payoff from the payoff for each of the decision substitute (or alternative).

The regret table for this problem is shown below:

State of Nature (Actual Miles Driven Annually)

Thus, from the above table, it is evident that the minimax regret approach is resulting in the selection of the lease option named as Hopkins Automotive lease option (which has the least regret of the three alternatives, that is, $936).

(d) Here, firstly find the expected value for the payoffs associated with each of Amy’s three alternatives as shown below:

Thus, the expected value approach is resulting in the selection of the Midtown Motors lease option (which has the smallest expected value of the three alternatives, that is, $11,340).

(e)

The risk profile for the decision to lease from M is created below:

As shown in the risk profile, the best likely cost is $11,160 which is having a probability of 0.9. Note that although there are three chance outcomes (that is, drive 12000 miles annually, drive 15000 miles annually, and drive 18000 miles annually), there are two unique costs on the above graph. The reason for this is, because for this decision alternative, (lease from M Motors) there are only two unique payoffs related with the three chance outcomes. The payoff (cost) related with the Midtown Motors lease is the identical for two of the chance outcomes (whether Amy drives 12000 miles or 15000 miles annually, her payoff is $11,160).

Here, firstly find the expected value for the payoffs associated with each of Amy’s three alternatives:

Thus, the expected value approach is resulting in selection of either the M lease option or the H Automotive lease option (both of which have the smallest expected value of the three alternatives, that is, $11,700).