Question

A small retailer began as a mom-and-pop operation selling crafts and consignment items. During the past two years, the store's volume grew significantly. The owners are trying to decide whether to purchase an automated checkout system. The store's current manual system is slow. They are concerned about lost business due to inability to ring up sales quickly. The automated system would also offer some accounting and inventory advantages. The problem is that the automated system carries a large fixed cost, and the owners feel that sales volume would have to grow to justify the cost. The following decision table contains the decision alternatives for this situation, the possible states of future sales, probabilities of these states occurring, and the payoffs. Use this information to compute the expected values for the alternatives. Future Sales Level Reduction Constant Increase V(x) P(x) V(x) P(x) V(x) P(x) Decision Alternative Automate −$40,000 0.15 −$8,000 0.35  $60,000 0.50 Don't Automate   $5,000 0.15  $2,000 0.35 −$30,000 0.50

Answer 1

The payoff matrix looks like this:-

v1 v2 v3 p2 p3 p1 Automate -40000 0.15 0.35 -8000 60000 0.5 Do not automate 2000 0.35 -30000 5000 0.15 0.5

Now calculating the expected returns:

(payoff from state i)*(probability of state i to occur) Expected Value= Expected value -40000*0.15 - 8000*0.35 + 60000*0.5 21200 Automate 5000*0.15 2000*0.35 - 30000*0.5 Do not automate -13500 +

Hence it is wise to invest in the automated technology.