CNP Bank Card: Case Analysis

Problem Statement

In the world of the market economy, credit cards are becoming more popular, and they are swiftly displacing traditional forms of payment. However, with the growing acceptance of the medium, the risk of default is increasing over time. In this regard, credit card issuers are constantly faced with the challenges of identifying the main drivers which indicate the possibility of default on a customer’s part. Using the CNP bank card case, the project intends to create a method that can forecast credit-card defaults and identify possible client bases that may be supplied with various credit instruments.

Analysis of the Case Problem

Before issuing a credit card, banks typically grade or score the consumer based on the likelihood of being a lucrative customer.

Table 1: Example of a score table

Age Under 25

(12 Points)


(5 points)


(0 points)


(18 points)

Time at Same Address < 1 Yr.

(9 points)

1-2 yrs.

(0 points)

3-4 yrs.

(13 points)

5+ yrs.

(20 points)

Auto Age None

(18 points)

0-1 yrs.

(12 points)

2-4 yrs.

(13 points)

5+ yrs.

(3 points)

Monthly Car Payment None

(15 points)


(6 points)


(4 points)


(0 points)

Housing Cost $1-$199

(0 points)


(10 points)


(12 points)

Lives with relatives (24 points)
Checking/Saving Accounts Both

(15 points)

Checking only

(3 points)

Savings Only

(2 points)


(0 points)

The score is the result of adding the points from each of the six items. Sushi Brown, for instance, is under 25 years old (12 points), has lived at the same home address for two years (0 points), owns a four-year-old automobile (13 points), has $75 in car payments (6 points), $200 in housing (10 points), and a bank account (3 points.). She would get a score of 44 points.

Table 2: Scoring system against probability of defaulting

Score 30 40 50 60 70 80 90
Probability 0.70 0.78 0.85 0.90 0.94 0.95 0.96

Sushi gets a score of 44, which means it has a 0.81 chance of becoming profitable. Conversely, 81% of consumers, such as Sushi, will profit from bank card transactions.

Table 3: The findings of three potential customers’ interviews

Name David Born Edward Brendan Ann McLaughlin
Age 42 23 33
Time at same address 9 2 5
Auto Age 2 3 7
Monthly car payment $140 $99 $175
Housing cost $300 $200 Owns clear
Checking/saving accounts Both Checking only Neither


  • Score each of these customers and estimate their probability of being profitable.

Table 4: Points scored for each customer and their probabilities.

Name David Born Edward Brendan Ann McLaughlin
Age 18 12 0
Time at same address 20 0 20
Auto Age 13 13 3
Monthly Car Payment 4 6 4
Housing Cost 10 10 12
Checking/saving accounts 15 3 0
Total points 80 44 39
Estimated Probability 0.95 +0.78+0.07*4/10

= 0.808



The study variables, as indicated in the table above, will help to clarify the problem statement. The personal information and their probability rates give issuers and organizations insight into the account holder’s credit patterns. When the consumer has no past financial history, personal data is required (Ogundimu, 2019). Financial data gives issuers a sense of security by safeguarding their capital. Below are the solutions to the questions that facilitated the evaluation of the credibility of all three customers.

  • What is the probability that all three are profitable?

P (A) =0.95, P (B) =0.808, P(C) = 0.772

P (All three are profitable) = P (A)*P (B)*P(C)



  • What is the probability that none of them are profitable?

P (None are profitable) = (1-P (A))*(1-P (B))*(1-P(C))

= (1-0.95)*(1-0.808)*(1-0.772)


  • Find the entire probability distribution for the number of profitable customers among this group of three.

P (exactly 1 is profitable) = P (A)*(1-P (B))*(1-P(C)) + (1-P (A))*P(B)*(1-P(C))+ (1-P(A))*(1-P(B))*P(C)

=0.95*(1-0.808)*(1-0.772)+(1-0.95)*0.808*(1-0.772)+ (1-0.95)*(1-0.808)*0.772 =0.0582 P(exactly 2 are profitable) = P(A)*P(B)*(1-P(C))+ P(A)*(1-P(B))*P(C) + (1-P(A))*P(B)*P(C)

=0.95*0.808*(1-0.772) + (1-0.95)*0.808*0.772+ 0.95*(1-0.808)*0.772


Table 5: The summary of the probability is as indicated below.

No of profitable Customers (X) Probability (P)
0 0.0022
1 0.0582
2 0.3470
3 0.5926
Total 1.0000


Write a brief summary of your findings.

From the above case analysis, the following are the main inferences. David Born has the best chance of making a gain for the CNP bank. Similarly, Edward Brendan has a good chance of generating a profit for the bank through loans. However, Ann McLaughlin has the highest risk of losing money because of the high probability of default. If all three consumers are picked, the threat of losing money is nearly negligible because there is a decent probability that two of them will be valuable to the bank.

The current case analysis has examined the six major elements that influence the likelihood of credit-card default. The probability has also been transformed into a credit-scoring system that may be comprehended easily using a particular score mapping. Based on the data analysis shown above, it is possible to infer that the CNP bank card modeling is effective for predicting consumers’ desire to repay credit card debt. Therefore, it is justifiable to argue that using the above CNP bank card modeling system, a new paradigm for future credit-card default can be established.


From the above analysis, it is imperative to state that clients with higher scores will require less attention (David Born and Edward Brendan). On the other hand, clients with lower scores and a higher probability of defaulting can receive customized management in proportion to their increased risk (Ann McLaughlin). Therefore, banks and other lending firms may need to establish further precautions for consumers with low scores. As such, with the help of a credit score system, the efficiency of financial institutions is enhanced.


Ogundimu, E.O. (2019) Prediction of default probability by using statistical models for rare events. Journal of the Royal Statistical Society, 182 (4), 1143-1162.