Question C: Credit Decisions of Small, Medium and Micro Enterprises
In practice, due to the relatively small scale of small, medium and micro enterprises and lack of mortgage assets, banks usually provide loans to enterprises with strong strength and stable supply-demand relationship based on credit policies, corporate transaction bill information and the influence of upstream and downstream enterprises , And can give preferential interest rates to companies with high reputation and low credit risk. Banks first evaluate the credit risk of small, medium and micro enterprises based on their strength and reputation, and then determine whether to lend and credit strategies such as loan limits, interest rates, and maturity based on factors such as credit risk.
A certain bank has a loan limit of 101 million yuan to an enterprise determined to lend; the annual interest rate is 4% 15%; the loan period is 1 year. Attachments 1 to 3 respectively give the relevant data of 123 companies with credit records, the relevant data of 302 companies without credit records, and the 2019 statistics on the relationship between loan interest rates and customer churn rates. The bank asks your team to establish a mathematical model to study the credit strategy for small, medium and micro enterprises based on the actual situation and the data and information in the attachment, and mainly solve the following problems:
(1) Quantify the credit risk of the 123 companies in Annex 1, and give the bank's credit strategy for these companies when the total annual credit is fixed.
(2) On the basis of question 1, conduct a quantitative analysis of the credit risk of the 302 companies in Annex 2, and give the bank's credit strategy for these companies when the total annual credit is 100 million yuan.
(3) The production, operation and economic benefits of enterprises may be affected by some sudden factors, and sudden factors often have different effects on different industries and different types of enterprises. Comprehensively considering the credit risks of each company in Annex 2 and the impact of possible sudden factors (such as the new crown virus epidemic) on each company, give the bank's credit adjustment strategy when the total annual credit is 100 million yuan.
Annex 1 Relevant data of 123 companies with credit records
Annex 2 Relevant data of 302 companies with no credit history
Annex 3 Statistics on the relationship between the annual interest rate of bank loans and the customer churn rate in 2019
Data description in the attachment:
- Input invoice: the invoice issued by the seller when the company purchases (purchasing products).
- Output invoice: The invoice issued to the buyer when the company sells the product.
- Valid invoice: an invoice issued for normal trading activities.
- Void Invoice: After issuing an invoice for a transaction activity, the transaction is cancelled for some reason, making the invoice invalid.
- Negative invoice: After issuing an invoice for the transaction, the company has entered the account for tax, and then the buyer returns and refunds the goods for some reason. At this time, a negative invoice must be issued.
- Credit rating: According to the actual situation of the company, the bank internally evaluates the company manually. In principle, the bank does not lend to companies with a credit rating of D.
- Customer Churn Rate: The rate at which banks lose potential customers due to factors such as loan interest rates.
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