You work for a company that sells expensive equipment to other companies. The marketing director has closed on a substantial sale (for your company) but the customer has requested that the sale be done on a credit basis instead of being paid in full on delivery. In order to evaluate this request, you make the following assumptions:
- If we deny the credit request, there is a 20% chance the customer will buy the machine with cash anyway.
- If we grant the credit request, there is a 70% chance that the customer will be a good credit risk.
- If we grant credit and the customer is a good credit risk, then the bill will be paid in full.
The issue that requires some analysis comes if we grant the credit request and the customer turns out to be a bad credit risk. In this case, your company has two options. First, we could continue to send the customer a bill and hope eventually to be paid. Under this option, we would receive all of the money with a probability of 10%, we would get only half the money with a probability of 20%, and we would get nothing with a probability of 70%. The second option would be to more actively pursue the collection of the amount owed. To take the necessary actions would cost the company about 20% of the amount the customer owes, regardless of what amount is eventually collected, as a payment to the company pursuing the collection. As before, the customer might pay all, half or nothing. The probabilities of these three outcomes are 30%, 50% and 20%, respectively. The machine the customer is considering sells for $80,000 and costs us $45,000 to make. Note that this means that the collection cost of the second option would be $20,000.
1.) Create a decision tree representation for this problem in Excel. What are the decision nodes, what are the chance nodes.
2.) What is the expected value of this customer order? What decisions lead to this value?
3.) Suppose that the probability that the customer will buy without being offered credit changes. Create a data table to show what decisions should be made for different probabilities.
4.) Suppose that the cost of the credit collection process changes. Create a data table to show what decisions should be made for different costs.
5.) Consider the first option for collections. Suppose that the probability for the customer paying in full ranges from 0% to 40%, and that the probability that they pay half ranges from 0% to 50%. Create a two-way data table and determine the value of the potential sale under the various possible conditions.
Part Two
In order to make a more informed decision, you decide to collect some sample information by talking to local CPA that knows a little about your potential customer. They can tell you that they think the customer is "strong" or "weak." They also tell you that out of the companies that were good risks, they rated 75% of them as strong. Of the companies that were bad risks, they rated only 15% as strong.
Assume that the collection probabilities of the two options are not affected by the sample information about the customer.
1.) Calculate the probability that the CPA will rate the customer strong. The probability of a weak rating.
2.) If the CPA gives you a strong rating, what are the probabilities about whether the customer is a good or bad credit risk. What are the probabilities if the CPA rates the customer as weak.
3.) Create a decision tree that incorporates the sample information. What are the best decisions to make? What is the expected value of the potential customer.
4.) What would you be willing to pay the CPA for the information about the customer?