solution

Amy Lloyd is interested in leasing a new car 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
Dealer A $289 36,000 $0.15
Dealer B $300 45,000 $0.20
Dealer C $315 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 Dealer A lease will cost her

36($289) + $0.15(36,000 – 36,000) = $10,404

if she drives 12,000 miles per year,

36($289) + $0.15(45,000 – 36,000) = $11,754

if she drives 15,000 miles per year, or

36($289) + $0.15(54,000 – 36,000) = $13,104

if she drives 18,000 miles per year.

(a)

What is the decision, and what is the chance event?

The decision is to choose —Select— the best lease option the number of miles driven . There are ? 2 3 4 9 alternatives. The chance event is —Select— the best lease option the number of miles driven . There are ? 2 3 4 9 possible outcomes.

(b)

Construct a payoff table. (Enter your answers in $).

Dealer Annual Miles Driven
12,000 15,000 18,000
Dealer A $10,404 $11,754 $13,104
Dealer B $ $ $
Dealer C $ $ $

(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?

The recommended decision using the optimistic approach is —Select— Dealer A Dealer B Dealer C Dealer A or B Dealer A or C Dealer B or C . The recommended decision using the conservative approach is —Select— Dealer A Dealer B Dealer C Dealer A or B Dealer A or C Dealer B or C . The recommended decision using the minimax regret approach is —Select— Dealer A Dealer B Dealer C Dealer A or B Dealer A or C Dealer B or C .

(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?

EV(Dealer A) = $ EV(Dealer B) = $ EV(Dealer C) = $ The best decision is —Select— Dealer A Dealer B Dealer C Dealer A or B Dealer A or C Dealer B or C .

(e)

Develop a risk profile for the decision selected in part (d). What is the most likely cost, and what is its probability?

Based on the risk profile, the most likely cost is $ at a probability of .

(f)

Suppose that after further consideration Amy concludes that the probabilities that she will drive 12,000, 15,000, and 18,000 miles per year are 0.3, 0.4, and 0.3, respectively. What decision should Amy make using the expected value approach?

EV(Dealer A) = $ EV(Dealer B) = $ EV(Dealer C) = $

 
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