Module 3 Decision Theory and the Normal Distribution

Module 3 Decision Theory and the Normal Distribution M3-1

Learning Objectives Students will be able to • Understand how the normal curve can be used in performing break-even analysis. • Compute the expected value of perfect information (EVPI) using the normal curve. • Perform marginal analysis where products have a constant marginal profit and loss. M3-2

Module Outline M3.1 Introduction M3.2 Break-Even Analysis and the Normal Distribution M3.3 EVPI and the Normal Distribution M3-3

Normal Distribution for Barclay’s Demand Break-even point (Units) Fixed Cost Price/Unit - Variable Cost/Unit = Mean of the Distribution, µ 15 Percent Chance Demand Exceeds 11,000 Games 15 Percent Chance Demand is Less Than 5,000 Games X 5,000 11,000 Demand (Games) µ=8,000 Demand - µ Z =  M3-4

Barclay’sOpportunity Loss Function In general, the opportunity loss function can be computed by: Opportunity loss K (Break-even point - X) for X < Break-even $0 for X > Break-even = where K = the loss per unit when sales are below the break-even point X = sales in units. M3-5

Barclay’s Opportunity Loss Function Opportunity loss $6 (6,000 - X) for X < 6,000 games $0 for X > 6,000 games = Loss Profit Normal Distribution Loss ($) µ = 8,000 = 2,885 Slope = 6 X µ Demand (Games) Break-even point (XB) 6,000 M3-6

Expected Value of Perfect Information EVPI = EOL = KN(D) Where EOL = expected opportunity loss, K = loss per unit when sales are below the break-even point  = standard deviation of the distribution µ = mean sales N(D) = the value for the unit normal loss integral given in Appendix B, for a given value of D. M3-7

Expected Value of Perfect Information – cont. K = $6  = 2,885 N(.69) = .1453 Therefore EOL = K N(.69) = ($6)(2885)(.1453) = $2,515.14 EVPI = $2515.14 M3-8

Module 3 Decision Theory and the Normal Distribution