## When Should Credit Be Granted

Imagine that a firm is trying to decide whether or not to grant credit to a customer. This decision can get complicated. For example, note that the answer depends on what will happen if credit is refused. Will the customer simply pay cash or will the customer not

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CHAPTER 21 Credit and Inventory Management 719

make the purchase at all? To avoid being bogged down by this and other difficulties, we will use some special cases to illustrate the key points.

A One-Time Sale We start by considering the simplest case. A new customer wishes to buy one unit on credit at a price of P per unit. If credit is refused, then the customer will not make the purchase.

Furthermore, we assume that, if credit is granted, then, in one month, the customer will either pay up or default. The probability of the second of these events is In this case, the probability can be interpreted as the percentage of new customers who will not pay. Our business does not have repeat customers, so this is strictly a one-time sale. Finally, the required return on receivables is R per month, and the variable cost is v per unit.

The analysis here is straightforward. If the firm refuses credit, then the incremental cash flow is zero. If it grants credit, then it spends v (the variable cost) this month and expects to collect (1 - ^)P next month. The NPV of granting credit is:

For example, for Locust Software, this NPV is:

NPV = -$20 + (1 - <*) X 49/1.02 With, say, a 20 percent rate of default, this works out to be:

Therefore, credit should be granted. Notice that we have divided by (1 + R) here instead of by R because we now assume that this is a one-time transaction.

Our example illustrates an important point. In granting credit to a new customer, a firm risks its variable cost (v). It stands to gain the full price (P). For a new customer, then, credit may be granted even if the default probability is high. For example, the break-even probability in this case can be determined by setting the NPV equal to zero and solving for

Locust should extend credit as long as there is a 1 - .584 = 41.6% chance or better of collecting. This explains why firms with higher markups will tend to have looser credit terms.

This percentage (58.4%) is the maximum acceptable default probability for a new customer. If an old, cash-paying customer wanted to switch to a credit basis, the analysis would be different, and the maximum acceptable default probability would be much lower.

The important difference is that, if we extend credit to an old customer, then we risk the total sales price (P), because this is what we collect if we don't extend credit. If we extend credit to a new customer, we only risk our variable cost.

Repeat Business A second, very important factor to keep in mind is the possibility of repeat business. We can illustrate this by extending our one-time sale example. We make one important assumption: a new customer who does not default the first time around will remain a customer forever and never default.

If the firm grants credit, it spends v this month. Next month, it gets nothing if the customer defaults, or it gets P if the customer pays. If the customer pays, then the customer

Ross et al.: Fundamentals of Corporate Finance, Sixth Edition, Alternate Edition

VII. Short-Term Financial Planning and Management

21. Credit and Inventory Management

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PART SEVEN Short-Term Financial Planning and Management will buy another unit on credit and the firm will spend v again. The net cash inflow for the month is thus P - v. In every subsequent month, this same P - v will occur as the customer pays for the previous month's order and places a new one.

It follows from our discussion that, in one month, the firm will receive $0 with probability With probability (1 - however, the firm will have a permanent new customer. The value of a new customer is equal to the present value of (P - v) every month forever:

PV = (P - v)/R The NPV of extending credit is therefore:

For Locust, this is:

NPV = -$20 + (1 - <*) X (49 - 20)/.02 = -$20 + (1 - <*) X 1,450

Even if the probability of default is 90 percent, the NPV is:

Locust should extend credit unless default is a virtual certainty. The reason is that it only costs $20 to find out who is a good customer and who is not. A good customer is worth $1,450, however, so Locust can afford quite a few defaults.

Our repeat business example probably exaggerates the acceptable default probability, but it does illustrate that it will often turn out that the best way to do credit analysis is simply to extend credit to almost anyone. It also points out that the possibility of repeat business is a crucial consideration. In such cases, the important thing is to control the amount of credit initially offered to any one customer so that the possible loss is limited. The amount can be increased with time. Most often, the best predictor of whether or not someone will pay in the future is whether or not they have paid in the past.

Web-surfing students should peruse the Dun & Bradstreet home page— this major supplier of credit information can be , found at www.dnb.com.

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