Days Past Due

The following summarises the requirements and approach for calculating days past due for a loan with a regular and specified payment schedule. The requirement to calculate days past due is a necessity for determining loan provisions, regulatory capital requirements and enforcing loan contracts.

Calculation requriements

In Australia APS 220, Credit Risk Management, provides the required definition of Days Past Due, Default and Impairment to be used in classifying loans. With respect to the calculation of days past due, APS 220, Attachment A, paragraph 16 states:

16. A facility subject to a regular repayment schedule is regarded for the purposes of this Prudential Standard as 90 days past due when:

at least 90 calendar days have elapsed since the due date of a contractual payment which has not been met in full; and
the total amount unpaid outside contractual arrangements is equivalent to at least 90 days worth of contractual payments.

Note that the requirement is a reference to calendar days and amounts equivalent to calendar days worth of payments which would be applied to facilities on weekly or monthly schedule. Although facilities in which even some small amounts of payment had been made over the course of 90 days should not be considered in default, they may still be considered past due. The regulatory requirements while specific about measuring when days past due first exceed 90 days, are less specific about when and how days past due should decrease as payments are received.

The following outlines a methodology for the calculation of days past due which can form the basis for measuring and reporting delinquency, impairment and portfolio health.

Mathematical concepts

Days past due requires the calculation of the missed previous payments and their age in days. Each month the calculation of days past due requires:

identifying which previous expected payments are outstanding, and the current time since the payment was expected;
if a payment is received, allocating the payment to any of the previous missing payments, the regulatory requirement is to allocate a payment to the oldest missing amount.

In mathematical terms the calculation requires the vector of historical expected payments from origination (0) to current time T:

and the vector of history of received payments for each period:

Fundamentally the calculation of days past due must address the differences in time value of money of the expected and the actual payment stream received to date on the loan. As the customer is liabile for interest charged on missed payments, the payment stream is compounded to the present value:

Where:

is the customer interest rate;
is periods ago in which the payment was received.

The logic of performing the calculation in present value terms is that missed payments shift the receipt of payments in time and accrue interest. As a result when making whole on missed payments the accrued interest should also be paid which is addressed when days past due includes the interest component. If the interest rate is zero, then the same calculation is performed in strictly nominal terms. Example of the impact of discounting is provided in below. The calculation is expressed in continuous time as this facilitates the application of the calculation to any payment interval and also allows for off cycle payments (either late or early) to be incorporated when they occur.

The payments expected are a vector defined as the cumulative sum of the present value of all payments expected to date.

Days past due is defined as the age (in days) of the oldest payment shortfall. When a payment is received after a number of payments are missed the requirement is to allocate that payment to the oldest outstanding payment. This drives the accumulation of expected payments from the beginning of the loan to the current time (T).

Where:

is the age of the payment cycle, where the loan is T periods since origination;
is an indicator function which indicates whether the cumulative present value of paymments received to time t are less than the total present value of payments expected by time T;
is a tolerance amount by which the payment received is less than the payment expected to be considered past due.

A tolerance amount is often applied to default listing, for example at the credit bureau a minimum default amount of $150.00 is used. A tolerance amount should not be used for days past due as this would lead to a double tolerance in the default listing. Hence in the implementation below the tolerance is set to zero.

This calculation underscores the importance of maintaining a clear payment schedule for assessing the customers payment performance.

Worked example

In the following example the borrower misses 4 payments of $10, and makes whole those 4 payments with 4 payments of $20. On an undiscounted payments the extra makes rectify the arrears, on a discounted basis, the missed payments result in small increase in arreas. The extent of the increase in arrears depends on the interest rate on the loan, which can be adjusted.