EXTENDING CREDIT OR NOT:

A common problem for business, especially when selling to small business customers, is whether or not to grant them credit. Most small businesses cant or wont buy from you unless you do, so you cant avoid risk altogether all you can do is manage it for best expected value.

You are in the business of website design and development for corporate clients. You have a startup company as a prospective client a segment that is riskier than the market as a whole. You estimate that the job will bill at $125,000 and will cost you $75,000 to deliver. If the client pays up, your profit will be $50,000, but if it does not, your loss will be the full $75,000 since nothing is recoverable. You believe that one of three situations will occur; the client will pay in full and on time, the client will be out of business by the time the invoice is due so nothing will be collectible, or the client will still be in business, but doesnt pay. In the last case, you can sell the receivable to a collection agency for 20% of the amount due. You estimate that the probability of getting paid on time is 50%, the probability of a no-pay is 30% and the probability of a total default is 20%.

Construct a payoff table showing the decision alternatives, the states of nature and the expected values. Would you take this job?

GARMENT PURCHASING:

You are a buyer for fashion skiwear and must purchase your inventory long before the season and before demand is known. A particular jacket costs $80 each to buy from the manufacturer and will sell for $150 if the demand is there. Leftovers (where the stock exceeded the demand) are sold to a salvage broker for $15. You have been directed to use the following estimate of demand (a discrete probability distribution):

Demand		Probability
8,000		11%
10,000		11%
12,000		28%
14,000		22%
16,000		18%
18,000		10%

You can order any quantity of jackets you wish, but clearly it would make no sense to order less than 8,000 or more than 18,000. For convenience, assume you will order one of these six values.

Construct a payoff table and calculate the expected values for your choices. Which order quantity do you recommend?