Question

A manufacturer wants to introduce a new product family. The demand for the product family is somewhat predictable. The manufacturer can choose among the following three types of processes to produce the new products: Process A, Process B, and Process C. Demand can be classified into three states: Low, Moderate, and High.

The table below summarizes the payoffs (in $1,000s) associated with each process/demand combination, as well as the probabilities of each possible demand state.

	Low (20%)	Moderate (50%)	High (30%)
Process A	- $10,000	$20,000	$50,000
Process B	-$20,000	$30,000	$80,000
Process C	-$40,000	$30,000	$100,000

(a) Calculate the EMVs for each of the three alternatives. For each alternative, please include at least one step of calculation and the correct answer for full credit. (12 points)

(b) What is the EVwPI in this case? Please provide the formula, at least one step of calculation and the correct answer for full credit. (6 points)

(c) How much would the manufacturer be willing to pay for a forecast that would accurately determine the demand level in the future? Hint: It is the EVPI. Please provide at least one step of calculation and the correct answer for full credit. (4 points

Answer 1

(a)

EMV for Process A = 0.20*(-$10,000) + 0.50*$20,000 + 0.30*$50,000 = $23,000
EMV for Process B = 0.20*(-$20,000) + 0.50*$30,000 + 0.30*$80,000 = $35,000
EMV for Process C = 0.20*(-$40,000) + 0.50*$30,000 + 0.30*$100,000 = $37,000 (max.)

(b)

EVwPI = 0.20*max(-10000, -20000, -40000) + 0.50*max(20000, 30000, 30000) + 0.30*max(50000, 80000, 100000) = $43,000

(c)

EVPI = EVwPI - max.EMV = $43,000 - $37,000 = $6,000

So, the manufacturer will be willing to pay any amount less than $6,000.