## Evaluating a Proposed Credit Policy

To illustrate how credit policy can be analyzed, we will start with a relatively simple case. Locust Software has been in existence for two years, and it is one of several successful firms that develop computer programs. Currently, Locust sells for cash only.

Locust is evaluating a request from some major customers to change its current policy to net one month (30 days). To analyze this proposal, we define the following:

P = Price per unit v = Variable cost per unit Q = Current quantity sold per month Q = Quantity sold under new policy R = Monthly required return

For now, we ignore discounts and the possibility of default. Also, we ignore taxes because they don't affect our conclusions.

NPV of Switching Policies To illustrate the NPV of switching credit policies, suppose we have the following for Locust:

If the required return, R, is 2 percent per month, should Locust make the switch?

Currently, Locust has monthly sales of P X Q = \$4,900. Variable costs each month are v X Q = \$2,000, so the monthly cash flow from this activity is:

This is not the total cash flow for Locust, of course, but it is all that we need to look at because fixed costs and other components of cash flow are the same whether or not the switch is made.

2The cost of short-term debt is not necessarily the required return on receivables, although it is commonly assumed to be. As always, the required return on an investment depends on the risk of the investment, not the source of the financing. The buyer's cost of short-term debt is closer in spirit to the correct rate. We will maintain the implicit assumption that the seller and the buyer have the same short-term debt cost. In any case, the time periods in credit decisions are relatively short, so a relatively small error in the discount rate will not have a large effect on our estimated NPV.

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

VII. Short-Term Financial Planning and Management

21. Credit and Inventory Management

### CHAPTER 21 Credit and Inventory Management

If Locust does switch to net 30 days on sales, then the quantity sold will rise to Q = 110. Monthly revenues will increase to P X Q', and costs will be v X Q'. The monthly cash flow under the new policy will thus be:

Cash flow with new policy

Going back to Chapter 8, we know that the relevant incremental cash flow is the difference between the new and old cash flows:

Incremental cash inflow

100)

This says that the benefit each month of changing policies is equal to the gross profit per unit sold, P - v = \$29, multiplied by the increase in sales, Q' - Q = 10. The present value of the future incremental cash flows is thus:

For Locust, this present value works out to be:

Notice that we have treated the monthly cash flow as a perpetuity because the same benefit will be realized each month forever.

Now that we know the benefit of switching, what's the cost? There are two components to consider. First, because the quantity sold will rise from Q to Q', Locust will have to produce Q - Q more units at a cost of v(Q' - Q) = \$20 X (110 - 100) = \$200. Second, the sales that would have been collected this month under the current policy (P X Q = \$4,900) will not be collected. Under the new policy, the sales made this month won't be collected until 30 days later. The cost of the switch is the sum of these two components:

For Locust, this cost would be \$4,900 + 200 = \$5,100. Putting it all together, we see that the NPV of the switch is:

NPV of switching = -[PQ + v(Q' - Q)] + [(P - v)(Q' - Q)]/R

For Locust, the cost of switching is \$5,100. As we saw earlier, the benefit is \$290 per month, forever. At 2 percent per month, the NPV is:

NPV = -\$5,100 + 290/.02 = -\$5,100 + 14,500 = \$9,400

Therefore, the switch is very profitable.

We'd Rather Fight than Switch

Suppose a company is considering a switch from all cash to net 30, but the quantity sold is not expected to change. What is the NPV of the switch? Explain.

In this case, Q' - Q is zero, so the NPV is just - PQ. What this says is that the effect of the switch is simply to postpone one month's collections forever, with no benefit from doing so.

Ross et al.: Fundamentals I VII. Short-Term Financial I 21. Credit and Inventory I I © The McGraw-Hill of Corporate Finance, Sixth Planning and Management Management Companies, 2002

Edition, Alternate Edition

716 PART SEVEN Short-Term Financial Planning and Management

A Break-Even Application Based on our discussion thus far, the key variable for Locust is Q' - Q, the increase in unit sales. The projected increase of 10 units is only an estimate, so there is some forecasting risk. Under the circumstances, it's natural to wonder what increase in unit sales is necessary to break even. Earlier, the NPV of the switch was defined as:

We can calculate the break-even point explicitly by setting the NPV equal to zero and solving for (Q' - Q):

NPV = 0 = -[PQ + v(Q' - Q)] + [(P - v)(Q' - Q)]/R Q - Q = PQ/[(P - v)/R - v] [.]

For Locust, the break-even sales increase is thus:

This tells us that the switch is a good idea as long as Locust is confident that it can sell at least 3.43 more units per month.

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