CIMA P1 Syllabus D. Dealing With Risk And Uncertainty - Payoff Tables - Notes ^{3 / 6}

A profit table (pay­off table) is useful for scenario where there is a range of possible outcomes and a variety of possible responses.

A pay­off table simply illustrates all possible profits/losses.

Illustration

Mr. Luck runs a small shop with milk products. 

He buys his products for $10 and sell them for $15. 

The product is not possible to store, any unsold item is scrapped at the end of day at scrap value of $2 per product.

Supplies of product to the shop is made before the number of sales is known, however Mr. Luck has records about last 150 days sales.

Based on the records the sales were:
50 days of 150 days - 150 products sold
70 days of 150 days - 200 products sold
30 days of 150 days - 100 products sold

1. STEP 1: Calculate probabilities of outcomes:
   150 products will be sold with probability of 50 days/150 days, which is 0.33
   200 products will be sold with probability of 70 days/150 days, which is 0.47
   100 products will be sold with probability of 30/150 days, which is 0.2

2. STEP 2: Calculate all possible outcomes:
   E.g. if supply is 150 and sales are also 150, the profit is 150*(15-10)=$750;
   however if supply is 150 and sales are only 100, the profit will be 100*(15-10)+50*(2-10)=$100

3. STEP 3: Fill the outcomes to the payoff table.

STEP 4: Make a decision:

a. Maximax (risk seeker) - choose the best - order a supply of 200 products

b. Maximin (risk averse) - choose the outcome with the highest expected return under the worst possible conditions - order a supply of 100 products

c.Using expected values (EV - risk neutral approach) - calculate EV of each choice using probabilities - e.g. EV of outcome 150 ordered, 150 sold is $750*0,33. See following table:

Using EV we should choose order of 150 products.

d. Minimax regret - outcome with the lowest possible regret (opportunity costs) - regret is calculated as a difference between the best outcome profit and other choices, see the table:

So based on minimax regret regret decision rule we should choose order of 150 products.