Company Y has refused to extend trade credit to its clients so far. Now, in order to increase sales, it is considering the possibility to sell on credit. You are in charge of designing the decision-making model. The executive manager has provided you the following information:

- Clients buying on credit must pay in three months.

- The present value of the cost of production and delivery of the good is $10,000.

- The sale price is $12,500, which is the same both when the client pays in cash or on credit.

- The sale contract stipulates that the company has the right to take back control of the product in case of failure of payment. Due to depreciation losses, it is estimated that the value of the product once back in the company will be 40% lower.

- The company can invest money in risk-free securities at an annual interest rate of 6%.

- Due to the large portfolio of clients, the company considers trade credit as risk neutral.

- The sales department will estimate specific probabilities of default for each client.

a) Write a decision-making model to decide whether to extend credit or not.

b) Above what probability of default the company will refuse to extent credit?

c) Now suppose that the company is risk-averse. How can risk-aversion be taken into account in your model?