Expected Monetary Value for a sugar supplier was considering changing packaging from a bag to a box. Probability of a 20% increase in sales = 0.6.

Question

I have a probability and statistics question that is part of a Master's programme. The scenario is the following:

A sugar supplier was considering changing its packaging from a bag to a box. The increased cost would be 0.5p each, which would reduce the profit per pack from 5.5p to 5.0p. However, the box would be more convenient to the customer and might generate extra sales. Management considered the probability of a 20% increase in sales to be 0.6. (The alternative is no change in sales.) Their planning horizon was two years, during which they might currently expect to sell 1 million packs. What are the expected monetary values of changing to the box or remaining with the bag?

My thoughts so far are that the expected monetary value = Payoff x Probability

Payoff Box = 5

Payoff Bag = 5.5

But this is where I get stuck.

Many thanks.

Answer 1

Very very easy

• they remain with bags, the expected profit, expressed in Million monetary units is 5.5

• they pass to boxes, the expected profit, expressed in Million monetary units is

$$5\times 0.4+(5\times 1.2)\times 0.6=5.6$$

Thus the expected scenario shows that it is convenient to pass to boxes given that

$$5,600,000>5,500,000$$