Question

An improved design of a computerized piece of continuous quality measuring equipment used to control the

thickness of rolled sheet products is being developed. It is estimated to sell for $125,000 more than the

current design. Based on present test data, however, the typical user has the following probabilities of achieving

different performance results and cost savings (relative to the current unit) in the first year of operation

(assume these annual cost savings would escalate 5% per year thereafter; a five-year analysis period is used; the

MARR=18%, and the net market value after five years is 0):

Cost Savings in Year One (S) 60,000 40,000 18,000 Performance Results Optimistic Most likely Pessimistic Probability 0.30 0.55 0.15

(a) Based on the E(PW), is the new design preferable to the current unit?

(b) Based on a decision tree analysis, what is the EVPI? What does the EVPI tell you?

Answer 1

a. The cost of the equipment for the user is $125,000

Expected value of cost savings in:

1st year = 0.30 * 60,000 + 0.55 * 40,000 + 0.15 * 18,000 = $42,700

2nd year = $42,700 * (1+ 5%) = $44,235

3rd year = $44,235 * (1+ 5%) = $47,077

4th year = $47,077 * (1+ 5%) = $49,431

5th year = $49,431 * (1 + 5%) = 51,902

Therefore, E(PW) of the equipment = 42,700/(1 + 0.18) + 44,235/(1+ 0.18)² + 47,077/(1+ 0.18)³ + 49,431/(1 + 0.18)⁴ + 51,902/(1 + 0.18)⁵= $145,222

since, E(PW) is greater than the cost to user, the new design is preferable to the current limit.

b.

Introduce $18,000 dont introduce $O introduce $22,000 dont introduce $O introduce $2,700 dont introduce $O Optimistic 0.30 Most likely New Design (cost savings) 0.55 Pessimistic 0.15

the above diagram is the decision tree analysis of the above problem.

The above values for introduction of the new design are the expected cost savings in each case.

EVPI = EVUU - EVPP = $42,700 - $42,700 = 0

PAYOFF USING PERFECT INFORMATION $18,000 $22,000 $2,700 ALTERNATIVES PROBABILITY PERFORMANCE INTRODUCE RESULT OPTIMISTIC MOST LIKELY PESSIMISTIC DON'T INTRODUCE Ş0 Ş0 Ş0 $18,000 $22,000 $2,700 0.30 0.55 0.15 $42,700 EXPECTED VALUE $42,700

where, EVUU is expected value under uncertainity and EVPP is expected value under perfect prediction.

EVPI tells that value of the perfect information is zero.

Therefore, if we get perfect information at any cost above zero than we must refuse the offer.