## Info

The Pacific Bank has agreed to operate this lockbox system for a fee of 25 cents per check processed. Should Atlantic give the go-ahead?

We first need to determine the benefit of the system. The average daily collections from the southwestern region are \$1.2 million (2,000 X \$600). The collection time will be decreased by two days, so the lockbox system will increase the collected bank balance by \$1.2 million X 2 = \$2.4 million. In other words, the lockbox system releases \$2.4 million to the firm by reducing processing, mailing, and clearing time by two days. From our earlier discussion, we know that this \$2.4 million is the PV of the proposal.

To calculate the NPV, we need to determine the PV of the costs. There are several different ways to proceed. First, at 2,000 checks per day and \$.25 per check, the daily cost is \$500. This cost will be incurred every day forever. At an interest rate of .025 percent per day, the PV is therefore \$500/.00025 = \$2 million. The NPV is thus \$2.4 million - 2 million = \$400,000, and the system appears to be desirable.

Alternatively, Atlantic could invest the \$2.4 million at .025 percent per day. The interest earned would be \$2.4 million X .00025 = \$600 per day. The cost of the system is \$500 per day; so, running it obviously generates a profit in the amount of \$100 per day. The PV of \$100 per day forever is \$100/.00025 = \$400,000, just as we had before.

Finally, and most simply, each check is for \$600 and is available two days sooner if the system is used. The interest on \$600 for two days is 2 X \$600 X .00025 = \$.30. The cost is 25 cents per check, so Atlantic makes a nickel (\$.30 - .25) on every check. With 2,000 checks per day, the profit is \$.05 X 2,000 checks = \$100 per day, as we calculated.

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

VII. Short-Term Financial Planning and Management

20. Cash and Liquidity Management

© The McGraw-Hill Companies, 2002

CHAPTER 20 Cash and Liquidity Management

### Accelerating Collections

In our example concerning the Atlantic Corporation's proposed lockbox system, suppose the Pacific Bank wants a \$20,000 fixed fee (paid annually) in addition to the 25 cents per check. Is the system still a good idea?

To answer, we need to calculate the PV of the fixed fee. The daily interest rate is .025 percent. The annual rate is therefore 1.00025365 - 1 = 9.553%. The PV of the fixed fee (which is paid each year forever) is \$20,000/.09553 = \$209,358. Because the NPV without the fee is \$400,000, the NPV with the fee is \$400,000 - 209,358 = \$190,642. It's still a good idea.

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