Question

John Doe, a super-genius student (known also under his nick-name Wile E. Coyote, super-genius) has just graduated from SPEA and found a job that will allow him to purchase a car to finally catch Roadrunner. He can either buy a new car at a cost of $22,000, buy a used car for $12000 or lease a new car for one year at a cost of $8,500 (assume total cash purchase up front, no financing or monthly payments required). The new car has a 20% chance of a serious break down resulting in a permanent impairment to the trade-in value. The trade-in value for the new car without a serious break down after one year is $18,000 but only $10,000 if the break down occurs. On the other hand, the used car has a 40% chance of suffering a major break down with a $8,000 decrease in the resale value. However, if it does not break down, Wile can sell it to a friend one year from now for $9,000 cash (assume he can also sell it to the friend for $4,000 if the breakdown occurs). Finally, the leased car has a 10% chance of breaking down with a repair cost of only $2,000, and if it doesn’t, Wile will not gain or lose anything by returning the car at the end of a one year lease period. NOTE: For the new and used car purchases all related repair costs resulting from a breakdown have been netted against the trade-in / resale value.

a. Construct a decision tree for Wile
b. What is the expected value of the new car?
c. What is the expected value of the used car?
d. What is the expected value of leasing the car?

Answer 1

Answer: See explanation

Explanation:

a. Construct a decision tree for Wile

The solution to the question has been attached.

b. What is the expected value of the new car?

= [(0.2 × $10,000) + (0.8 × $18,000)] - $22,000

= $2000 + $14400 - $22000

= $16400 - $22000

= -$5600

c. What is the expected value of the used car?

= [(0.4 × $4000) + (0.6 ×$9000] - $12000

= $1600 + 5400 - $12000

= $7000 - $12000

= -$5000

d. What is the expected value of leasing the car?

= [(0.1 × -$2000) + (0.9 ×0)] - $8500

= -$200 - $8500

= -$8700