. Copy Makers Inc. (CMI) has just received a credit request from a new customer

Question

. Copy Makers Inc. (CMI) has just received a credit request from a new customer who wants to purchase a copying machine. The purchase price of the machine is $8000. As input to its decision of whether to grant credit or not, CMI has made the following estimates and assumptions:

• If CMI denies the customer credit, there is a 20 percent chance that the customer will buy the copying machine and pay the full purchase price with cash. (80% chance there will be no sale.)

• If CMI grants credit, there is a 70 percent chance the customer will be a good credit risk. o If CMI grants credit and the customer is a good credit risk, CMI will collect the entire purchase price . o If CMI grants credit and the customer is a bad credit risk, CMI has two options. One is to continue to send the customer a bill. Under this option, the company expects to collect the entire purchase price ($8000) with a probability of .40, and collect half of the purchase price ($4000) with a probability of .60 The second option is to vigorously pursue collection of the amount owed. Under this option, the company expects to collect the entire amount with a probability of .70, and half of the purchase price with a probability of .30. However, there is a cost of $1000 associated with this option that must be subtracted from the collected amount.

a. Draw and solve a decision tree for this problem

b. Write your recommendation.

Explanation / Answer

$ Cost of machine 5000 Selling Price 8000 Profit 3000 Option I CMI Rejects Credit Chances of customer buying machine with cash 20% Chances of customer not buying a machine 80% Option II CMI extends credit Good credit risk chances 70% Total expected amount recovery in $ Bad Credit Risk Chances 30% Option A amount recovery $ 8000 4000 0 Probability 0.1 0.2 0.7 We have considered a case where a customer buys 1 machine Expected amount recovery in $ 800 800 0 1600 Option B amount recovery in $ 8000 4000 0 Total expected amount recovery in $ Probability 0.3 0.5 0.2 Expected amount recovery in $ 2400 2000 0 4400 payment of value of 25% of amount owed to agent in $ 2000 Net amount recovered in $ 2400 So as we can see amount recovered in case of Option B is more so it is better to hire an agent for recovery of amount owed. Now let us examine optimal expected value of a customer of machine and at what price charged to customers CMI should consider extending credit Let us say for example CMI sells 100 machines Selling Price of machines 100*8000 $ 800000 Probability of good credit 0.7 Amount recovered on account of good credit $ 560000 Amount to be recovered on account of bad credit $ 240000 we will be following option B for recovery as discussed above $ So 100% recovery with probability of 30% $ 72000 50% recovery with probability 50% $ 60000 0 recovery with probability 20% $ 0 Total expected recovery $ 132000 amount to be paid to the agent (25% of the amount owed) $ 60000 Net recovery from bad credit $ 72000 Total amount received back $ 632000 cost of machines 100*5000 $ 500000 Net profit $ 132000 Selling Price of machines 100*8000 $ 800000 Profit if 100% amount has been recovered $ 300000 Decline in profit on account credit $ 168000 % of profit in selling price 37.5 % age decline in profit 56 Now let us find out optimal expected value of a customer who wishes to buy a machine b From above calculation we have found out that Total amount recovered from sale of 100 machines is $632000 so from customer's point of view cost per machine should be $632000/100 = $6320 c Now let us find out the selling price of machines so that our net profit remains same per machine through excel solver Selling Price of machines 100*8000 $ 1012659 Probability of good credit 0.7 Amount recovered on account of good credit $ 708861.3 Amount to be recovered on account of bad credit $ 303797.7 we will be following option B for recovery as discussed above $ So 100% recovery with probability of 30% $ 91139.31 50% recovery with probability 50% $ 75949.43 0 recovery with probability 20% $ 0 Total expected recovery $ 167088.7 amount to be paid to the agent (25% of the amount owed) $ 75949.43 Net recovery from bad credit $ 91139.31 Total amount received back $ 800000.6 cost of machines 100*5000 $ 500000 Net profit $ 300000.6 So $ 1012659 is selling price of 100 machines. Selling price of 1 machine will be 1012659/100 = $10126.59

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