Stonehurst Credit Union (SCU) is trying to identify clients who are likely to get into financial difficulty and default on their loans. Their goal is to intervene early, before the debt situation gets out of control, so that not only do they limit their exposure to losses, but they may be able to salvage their relationship with a member (credit unions are owned by their members).

One of the first indicators of a deteriorating debt situation is a missed loan payment. That is, a payment was due on a certain date, but no payment was received on that date or during the subsequent weeks.

Missed credit card loan payments occur 6% of the time.

SCU has examined the records of over 1,000 customers over the last 2 years to examine the amount owing on their credit cards. Among those that missed last months payment, the balance owing was over $3,000 for 60% of them. But, among those who made their payment on time, only 15% owed more than $3,000.

Among those with a balance over $3,000 and who missed their last payment, 80% paid less than 20% of the balance owing, the previous month. Among those owing less than $3,000 and who missed their last payment, 40% paid less than 20% of the balance owing.

Among those with a balance over $3,000 and who made their last payment on time, 30% paid less than 20% of the balance owing in the previous month. Among those owing less that $3,000 and who made their last payment on time, only 10% paid less than 20% of the balance owing in the previous month.

Clearly, those who missed the last payment and those who paid on time are different in many respects with respect to their previous borrowing and payment behaviours. Maybe these can be used as early indicators of deteriorating credit worthiness and SCU can make interventions to assist clients before they get into more trouble.

SCU would like to identify customers who are high risk to default and send them information about how having a good credit score reduces the cost of borrowing and makes it easier to borrow when you need to. They would explain factors that go into the determination of a credit score and the importance of making loan payments on time. They would offer assistance to clients who were concerned that their credit score may decline and what could SCU do to help them.

1. Construct a tree diagram to describe the events in terms of the sequence of information provided above (missed payment, balance, previous payment amount). Note that this sequence is actually going backwards in time, but we will reverse that later. Label each branch as to the event it represents as well as the probability of travelling down that branch. If you are using labels, then you must define them (e.g., M = Missed payment). You may try to create the tree in Word, but you may find it easier to draw the tree by hand, take a picture and paste the picture into your assignment.

2. Calculate the final probabilities at the end of each branch and summarize them in a table like the one below:

	Missed Payment	On Time	Total
Balance > $3,000 Last Payment < 20%
Balance >$3,000 Last Payment >20%
Balance <$3,000 Last Payment < 20%
Balance < $3,000 Last Payment > 20%
Total