Question

A construction company has obtained a contract for a highway project and will need to lease an additional road grader for a month to fill out its equipment fleet. The company is trying to decide between two different lease options for the grader: 1) lease an older grader for $8,500, or 2) lease a newer grader for $10,000. The newer grader is still under warranty, so the lease cost covers all repair expenses. However, the company would be responsible for any repair expenses if it leases the older grader. The construction company’s maintenance foreman believes there is a 30% chance that there will be no need for repairs with the older grader, but also thinks there is a 45% chance that some repairs ($2,000) could be needed, and a 25% chance that significant repairs ($5,000) might be required.

1. Construct a decision tree to help the company make its decision. Make sure to label all decision and chance nodes and include appropriate costs, payoffs and probabilities. (Hint: Just like in your first project, make sure you calculate the payoff table correctly. Then the rest of this problem should be straight forward).

2. What is the best lease option? Why?

3. Suppose the company could hire an experienced mechanic to inspect the old grader to determine the repair cost before the company makes its final decision. If the mechanic is always correct in his assessments, what is the most the company would pay for the inspection?

Answer 1

Pay-off-diagram
New	Old
	30%	45%	25%
	No repairs	some repairs	Significant repairs
	8500*30%=	45%*(8500+2000)=	25%*(8500+5000)=
10000	2550	4725	3375
	10650

Pay-off for new grader= 10000

Pay-off for old grader

30% chance -- no repairs-- so 8500

45% chance ---some repairs--- 8500+2000= 10500

25% chance ---significant repairs--- 8500+5000= 13500

so, expected pay-off with old grader---- (30%*8500)+(45%*10500)+(25%*13500)=

10650

so, the best lease option will be the new grader

as its pay-off   $ 10000 < expected pay-off for the old grader , $ 10650

The most the company would pay for the inspection

the difference in the lease costs of new & old graders

ie. 10000-8500= $ 1500