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The One-Shot Approach Looking back at our example for Locust Software (in Section 21.3), we see that if the switch is not made, Locust will have a net cash flow this month of (P - v)Q = \$29 X 100 = \$2,900. If the switch is made, Locust will invest vQ = \$20 X 110 = \$2,200 this month and will receive PQ = \$49 X 110 = \$5,390 next month. Suppose we ignore all other months and cash flows and view this as a one-shot investment. Is Locust better off with \$2,900 in cash this month, or should Locust invest the \$2,200 to get \$5,390 next month?

The present value of the \$5,390 to be received next month is \$5,390/1.02 = \$5,284.31; the cost is \$2,200, so the net benefit is \$5,284.31 - 2,200 = \$3,084.31. If we compare this to the net cash flow of \$2,900 under the current policy, then we see that Locust should switch. The NPV is \$3,084.31 - 2,900 = \$184.31.

In effect, Locust can repeat this one-shot investment every month and thereby generate an NPV of \$184.31 every month (including the current one). The PV of this series of NPVs is:

Present value = \$184.31 + 184.31/.02 = \$9,400 This PV is the same as our answer in Section 21.3.

The Accounts Receivable Approach Our second approach is the one that is most commonly discussed and is very useful. By extending credit, the firm increases its cash flow through increased gross profits. However, the firm must increase its investment in receivables and bear the carrying cost of doing so. The accounts receivable approach focuses on the expense of the incremental investment in receivables as compared to the increased gross profit.

As we have seen, the monthly benefit from extending credit is given by the gross profit per unit (P - v) multiplied by the increase in quantity sold (Q' - Q). For Locust, this benefit is (\$49 - 20) X (110 - 100)= \$290 per month.

If Locust makes the switch, then receivables will rise from zero (because there are currently no credit sales) to PQ, so Locust must invest in receivables. The necessary investment has two components. The first part is what Locust would have collected under the old policy (PQ). Locust must carry this amount in receivables each month because collections are delayed by 30 days.

The second part is related to the increase in receivables that results from the increase in sales. Because unit sales increase from Q to Q', Locust must produce the latter quantity today even though it won't collect for 30 days. The actual cost to Locust of

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

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