# Cost of Offering Early Payment Discount

When preparing financial projections one of the parameters that needs to be entered is the days sales outstanding. This represents the average number of days it takes a customer to pay an invoice and results in an additional working capital requirement for the business.

The higher the days sales outstanding, the longer it is taking customers to pay, and the higher the working capital and additional funding requirements will be.

While it is important for a business to try and keep the credit terms offered to customers as low as possible, a cash strapped startup business will often look to try and reduce their normal credit terms by offering an early payment discount to customers for prompt settlement of the invoice.

For example, a business which normally requires customers to pay in 30 days might offer a 2% early payment discount if the invoice is settled within 10 days. The impact of this in the financial projections is to reduce the days sales outstanding from 30 days to 10 days, providing cash for an additional 20 days, and reducing the working capital and funding requirements.

While on the face of it the reduction in the funding requirements is a good thing, the true cost of reducing the days sales outstanding this way needs to be understood to fully appreciate the impact of giving early payment discount to customers.

## Early Payment Discount Example

Suppose for example, a business issues invoices to customers for the amount of 10,000 with 30 day terms but offers a 2% early payment discount for settlement within 10 days (2/10 net 30 terms).

If the customers choose to take the early payment discount the amount paid will be 9,800 (10,000 – 2% x 10,000). As the invoices were paid after 10 days instead of 30 days, the business now has the use of the amount of 9,800 for an additional 20 days, which in turn reduces the funding requirement it needs from lenders by a similar amount.

The 2% early payment discount of 200 is in effect a cost (interest) of obtaining the use of the amount paid by the customer (9,800) for an additional 20 days.

If this cost is expressed as an interest rate, then the rate for obtaining the additional funding is calculated as follows:

```Interest rate for 20 days = Interest / Principal
Principal = 9,800 (amount received from customer)
Interest = 200 (discount offered)
Term = 20 days (normal terms - discount terms)

Interest rate for 20 days = 200 / 9,800 = 2.04%
```

This is the rate for the use of the funds for 20 days, to convert this to an annual percentage rate (APR) we simply divide by 20 to convert it to a daily rate, and then multiply by 365.

```Interest rate for 20 days = 2.04%
Daily interest rate = 2.04% / 20
Annual interest rate = (2.04% / 20)  x 365
Annual interest rate = 37.24%
```

However, this is the cost if the customers take the early payment discount on one occasion. If the customers repeatedly take the discount such that invoices are issued every 30 days and subsequently paid after 10 days taking the 2% discount, then the effective annual rate (EAR) represents the effective cost of the early payment discount as a result of the compounding, and is given by the following formula

```EAR = (1 + i / m )m - 1
```
Where
EAR = Effective annual rate
i = Annual nominal rate of interest
m = Number of compounding periods in a year

In this effective interest rate formula, the annual nominal interest rate i is the rate we calculated above without compounding (37.24%), and the number of compounding periods in the year is simply the number of times the funding is available for each year. Since in our example the funding is available for 20 days each time, then the number of compounding periods in a year is 365 / 20 or 18.25.

The effective interest rate of offering a 2% early payment discount for settlement within 10 days can now be calculated as follows

```Effective interest rate = (1 + i / m )m - 1
i = 37.24%
m = 365 / 20 = 18.25

Effective interest rate = (1 + 37.24% / 18.25 )18.25 - 1
Effective interest rate = 44.6%
```

## Cost of Early Payment Discount Formula

By rearranging the effective interest rate formula above, we can arrive at the cost of early payment discount formula to give the cost in terms of the known parameters of early payment discount, normal credit term days, and discount term days as follows: Using this formula we get the same answer as follows:

```Cost of early payment discount = (1 + d / (1 - d))(365 / Days) - 1
d = 2%
Days = 30-10 = 20

Cost of early payment discount = (1 + 2%/(1-2%))  (365 / 20) - 1
Cost of early payment discount = 44.6%
```

To avoid having to carry out this calculation, the table below summarizes the cost of early payment discount for typical discount percentages and days. In this table the days value refers to the additional days the funds are available which is the difference between the normal credit term days and the discount days.

Effective cost of early payment discount
Days 1% 2% 5%
10 44.3% 109.0% 550.3%
15 27.7% 63.5% 284.4%
20 20.1% 44.6% 155.0%
25 15.8% 34.3% 111.5%
30 13.0% 27.9% 86.7%

So in the example above, the terms were 2/10 net 30, which means that a 2% discount is offered for paying 20 days (30-10) early. Using the table above the 2% for 20 days early gives an effective annual rate of 44.6% as calculated above.

Using another example, if the terms were 5/60 net 90, meaning a 5% discount is given for payment within 60 days with normal terms of 90 days, then the invoices are paid 30 days early (90 – 60), and from the table 5% for 30 days is an effective annual rate of 86.7%.

## Summary

To summarize, in this example the business offers 2/10 net 30 terms to customers, the effect of this early payment discount is to reduce the days sales outstanding from 30 days to 10 days resulting in a reduced working capital and funding requirement.

As the business has now received the 9,800 twenty days early, it does not need to borrow from other sources. However, the cost of giving the 2% early payment discount repetitively throughout the year results in an effective annual interest rate of 44.6%.

It is not difficult to see that if the business could borrow at a rate which is less than the calculated effective annual interest rate, then it would be preferable to do so rather than offer the customer the early payment discount.

While it is not always feasible for a business to borrow to finance working capital requirements, in the absence of other factors, careful consideration should be given before offering early payment discount to customers.