EXPECTED VALUE AND UNCERTANTY Problem 1: Expected Value Determine whether you wo

Question

EXPECTED VALUE AND UNCERTANTY Problem 1: Expected Value Determine whether you would decide, based on profitability, to go with the product cluster of Product A, Product B, and Product C or the product cluster of Product X, Product Y, and Product Z. Product cluster ABC has a fixed cost of 8.7% of revenue. Product cluster XYZ has a fixed cost of 9.3% of revenue. Product A is expecting revenues of $900,000 and variable costs of $300,000. Product B is expecting revenues of $700,000 and variable costs of $200,000. Product C is expecting revenues of $800,000 and variable costs of $400,000. The probability of achieving these revenues and costs are 5% for Product A and 25% for Product C? Product X is expecting revenues of $700,000 and variable costs of $300,000. Product Y is expecting revenues of $800,000 and variable costs of $250,000. Product Z is expecting revenues of S600,000 and variable costs of $300,000. The probability of achieving these revenues and costs are 35% for Product X and 15% for Product Z? Your goal is to maximize profits. Which product cluster would you choose? For any credit, you must show all your work. ANSWER:

Explanation / Answer

Cluster ABC

Revenue of A = 900000 ( 1-0.087) -300000 = 521700

Revenue of B = 700000( 1-0.087) -200000 = 439100

Revenue of C = 800000 ( 1-0.087) - 400000 =330400

EV of revenues = 5% x 521700+70%x439100+25%x330400 = 26085+303370+82600 = 412055

Revenue of X = 700000( 1-.093) -300000 = 334900

Revenue of Y = 800000( 1-0.093) -250000 =475600

Revenue of Z = 600000( 1-0.093) -300000 = 244200

EV of revenues = 35%x334900+50%x475600+15%x244200 =117215+237800+36630 = 391645

Since EV value is higher for ABC, this cluster should be chosen.

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