# The Decision to Discount

Because (P") differs from (P') we now understand that under the conditions stated, the introduction of any cash discount into a firm's terms of sale will influence the demand for its product and working capital requirements. So, when formulating credit policy, management must consider the division of sales between discounting and non-discounting customers.

For any combination of credit policy variables, the buyer's decision to discount depends upon the cost of not taking it exceeding the benefit.

We have already established that the annual benefit of trade credit can be represented by the customer's annual opportunity cost of capital rate (r). Because the non-discounting customer delays payment by (T - t) days and foregoes a percentage (c), the annual cost of trade credit (k) to the non-discounting customer can be represented by: Thus, if purchases are funded by borrowing at an opportunity rate (r) less than the annual cost of trade credit (k) such that: The buyer will logically take the discount.

Equation (13) also confirms our preceding effective price decision where r =18 per cent with credit terms of (2/10:30) since: Of course, Equation (13) is extremely crude. When cash discounts are not taken, customers forego an amount (Pc) over the additional days (T - t). In other words, if the invoice price (P) equals \$100 with terms of (2/10:30) then the "real" price is \$98.

To continue with our example, if the firm does not remit payment within 10 days but delays for 30 days, it is effectively borrowing \$98 and paying \$2 interest for the loan by foregoing the 2% discount.

The rate of interest may be determined by solving for (i) in the following equation, (analogous to an IRR computation): Rearranging terms and simplifying: However, this rate of interest only relates to (T - t) which equals 20 days.

The annual cost of trade credit (k) on a simple interest basis can be calculated by applying the following formula: For the above example: Thus, the customer with an opportunity capital cost rate of 18% would still take the discount, since: As our example illustrates, opting for the credit period can prove expensive. We can also observe from Equation (12) onwards that:

The annual cost of trade credit becomes greater, the larger the cash discount and the smaller the difference between the credit period and the discount period.

For example even modest changes to 3/10:30 or 2/10:20 significantly increase implicit costs to 56.4% and 74.46% respectively.

We should also note that the effective annual percentage rate (APR) is even higher than any simple interest rate that is given, because of the compounding effect. You may verify this by the familiar formula for an annual compound rate (k a): This may be rewritten; Where:

k = the annual rate of simple interest, (Equation 15) 365

m = the number of compounding periods per year, ^r~^

Thus, using 360 days to simplify the arithmetic, the annual interest of 36.72% becomes: Activity 3

Before we proceed, confirm that if the credit terms became (3/10:30) or (2/10:20) using 360 days:

The annual costs of trade credit on an A.P.R basis are 73% and a staggering 107% respectively compared with simple interest of 55.67% and 73.47%.

Let us now summarise the discounting decision within a framework of effective prices.

- Any customer whose opportunity rate is less than the cost of trade credit will have an effective discount price that is lower than the effective credit price.

- A customer, whose cost of funds exceeds the cost of trade credit, will find the largest price reduction associated with the credit period.

- If management wishes to increase the demand for its products, cash discounts should be set to attract the marginal buyer with a low opportunity rate.

- Credit periods should be designed to attract the potential customer with a high rate, coupled with an acceptable credit rating.

For a customer with a relatively low opportunity rate, and hence a high effective credit price, a small discount would lower the effective discount price below the effective credit price. On the other hand, for a customer with a high opportunity rate, it could take a large discount to lower the effective discount price below the effective credit price.

All these factors pose an obvious dilemma for the financial manager. If decisions are taken to restructure the discount terms and credit period length simultaneously, their combined effects on profits may be difficult to unscramble. Individually, changes to either cash discount policy, or credit period, affect a number of variables.

Activity 4

Using the appropriate equations from our previous analysis, confirm that:

A change in the cash discount from (2/10:30) to (1/10:30) on goods marked at \$100 halves the effective cost of credit to 18.25% and raises the discount price by \$1.00.

A change in the credit period from (2/10:30) to (2/10:60) not only lengthens the delay in payment, thereby reducing the effective credit price received and paid, but also lowers the annual cost of trade credit from 36.5 per cent to 14.6 per cent.

For the purposes of analysis academics have long advocated that management should simplify the inter-relationships between credit policy variables by considering the credit period and discount policy separately. A common approach is to experiment with different credit policies using sensitivity analysis. For example, given a range of customer opportunity rates (k), the decision to take the discount for each buyer or class of buyers can be determined for different values of T, c and t by rearranging the terms of the following inequality derived from Equation (13) where k equals the annual cost of trade credit. In turn this yields: Alternatively, using the following indifference equation, customers would be indifferent to any discount policy and the credit period if: Activity 5

(a) Using Equation (18) confirm why a firm's customers with a 37.2% annual opportunity cost of capital rate (r) who are offered credit terms of (2/10:30) would be indifferent to its discount policy.

(b) Re-arrange Equation (18) to define equivalent indifference equations for T, c and t, respectively.

(c) If the company decided to revise its terms of sale, comment briefly on which credit policy variable, if any, should management alter first?

(a) Equation (18)

With T = 30 days, c = 2% and t = 10 days; customers with an annual opportunity rate of 37.2% will find that r is equivalent to their annual cost of trade credit (k = 37.2%). So, whether they take the cash discount at the end of the discount period, or opt for the credit period, is financially irrelevant.

(b) The Equivalent Indifference Equations

Rearranging terms and solving for the credit period, cash discount and discount period respectively (c) The Revised Terms of Sale

As we noted earlier, customers with relatively high opportunity rates are more insensitive to changes in discount policy. If they are not to be an expensive concession for all, cash discounts for prompt payment should only be used to attract the potential cash buyer with a low opportunity rate. Consequently, management should only evaluate different cash discount policies once an optimal credit period is established.

Review Activity

There is one final point I would like you to consider (perhaps you've picked upon it already). This relates to the availability of trade credit in the real world (which we shall return to later when reviewing the empirical evidence).

The various terms of sale substituted into the previous series of equations for analysis were not chosen by accident, but by design. They conform to those offered by many "real" creditor firms. Historically, for example, (2/10:30) used in our previous Activity is not unusual in the UK. Yet, like all the preceding illustrations and Activities, it produces an extremely high value for the annual cost of trade credit relative to observable customer costs of borrowing at an opportunity rate (even if we go back to the 1970s where inflation was in double figures).

So, why don't debtors always opt for these discount terms?

I'll leave you to think about it.

# Summary and Conclusions

We have explained how the terms of sale offered by a company to its customers can influence the demand for its goods and services. Mathematically, the present value (PV) time value of money concept reveals how the availability of credit periods and cash discounts for early payment provide customers with reductions in their cash price. Items bought on credit, therefore, create a utility in excess of their eventual purchase price, which can be measured by the debtors' opportunity to utilise this amount during the credit period, or discount period.

By conferring enhanced purchasing power upon its customers, a company's terms of sale should have true marketing significance. They represent an aspect of financial strategy whereby the creditor firm can translate potential demand into actual demand and increase its future profitability.

Future Chapters will confirm this view.