# Strategic Debtor Investment

## The Effective Credit Price and Decision to Discount

### Introduction

Our analysis so far, has:

- Distinguished between the * internal *working capital management function and an

*interpretation of a firm's working capital position, revealed by its published accounts,*

**external**- Explained the significance of a company's working capital * operating *cycle and

*cycle derived from published data and analysed the inter-relationship between the two, namely its*

**financing***operating cycle,*

**net**- Defined the * dynamics *of a company's credit-related funds system and the

*role of its terms of sale, as a basis for efficient working capital management.*

**pivotal**Throughout the remainder of the text we shall:

- Explain how the terms of sale (represented by the credit period, cash discount and discount period) underpin the credit related funds system and determine the demand for a firm's goods and services,

- Evaluate the impact of alternative credit policies on the revenues and costs which are associated with a capital budgeting decision,

- Compare the disparities between the theory and practice of working capital management, given our fundamental normative assumption that firms should maximise wealth.

### The Effective Credit Price

If we assume that the availability of trade credit is designed to generate profitable sales, the impact of credit terms is best demonstrated by the influence they can exert on the demand for a firm's goods and services. To illustrate, let us consider a firm that sells products at a cash price (P) but also allows its customers (T) days in which to pay. This means that during the credit period the customer has the opportunity to use the firm's funds at no explicit cost. Their value is therefore best measured by the interest rate at which customers can obtain funds from elsewhere to finance their purchases.

For the moment let us simply denote this * opportunity cost of capital *by the annual rate (r). We can then translate the benefit of trade credit to the customer who buys on credit into an

**effective price reduction.**In turn, this can be deducted from the amount (P) that is paid at the end of the credit period to yield the present value (PV) of that amount according to the customer's opportunity rate (r). This * effective credit price *(P') is defined as follows:

**Activity 1**

Consider a firm that offers goods for sale at $100 with 30 days credit to a customer with an annual opportunity cost of capital equal to 18%.

Calculate the effective credit price.

Using Equation (9) we can define:

Hence, the price reduction associated with the credit period, defined by Equation (8) is $1.50.

Clearly, an effective credit price P' may differ from customer to customer, since it depends upon their own opportunity cost of capital rate that may be unique. However, we can discern three significant points.

Credit customers with * positive *opportunity rates will experience an effective price reduction. The longer the period of credit, the greater that price reduction will be.

In the presence of uniform credit terms, the buyer with the highest opportunity rate will experience the greatest price reduction

Expressed mathematically:

So from the seller's perspective, the important points are whether:

Price relates to specific quantities demanded, and in particular whether lower prices relate to higher quantities or * vice versa. *If this is true, then it follows that the introduction of a credit period (or the extension of an existing one) can increase the demand for a firm's product.

### The Effective Discount Price

Management not only has the choice of varying the credit period length (T) but also the option of offering a percentage cash discount (c) for immediate payment. For the seller this means the receipt of less money but earlier. For the buyer its availability provides a lower cash price P (1 - c) which is the same for all customers in the presence of uniform credit terms. Therefore, it differs from the effective credit price (P') which may be unique.

Of course in practice, it is more usual for the buyer of a firm's product at a price (P) to face terms of (c / t: T). For example (2/10:30) where:

(c) = the cash discount, (2%)

(t) = the discount period, (10 days)

(T) = the credit period, (30 days)

These terms provide alternative options to utilise the seller's funds during the discount period. Given the customer's annual opportunity cost of capital rate (r), we can translate the discount into an * effective price reduction, *which is equal to:

In turn, we can deduct this from P (1 - c) which is the amount the customer actually pays at the end of the discount period. This represents the present value (PV) of that amount discounted at their opportunity rate. In other words, an * effective discount price *(P") equivalent to (P) on terms (c / t: T)

**Activity 2**

Consider again the customer with an opportunity cost of capital rate of 18% per annum who is now offered terms of (2/10:30) on goods costing $100.

(a) Calculate the effective discount price.

(b) Should the buyer take the discount?

From Equation (11) we can calculate:

You should be able to confirm that the buyer who rejects the credit period now benefits from an increased price reduction of $2.49 (comprising the $2.00 discount and 49 cents associated with the use of $98 at no explicit cost over ten days). So, they should rationally opt for the discount.