In our example concerning the Atlantic Corporation’s proposed lockbox system, suppose 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 1.00025 365 − 1 = .09553 , or 9.553%. The PV of the fixed fee (which is paid each year forever) is $20,000 / .09553 = $209,357.52 . Because the NPV without the fee is $400,000, the NPV with the fee is $400,000 − 209,357.52 = $190,642.48.

It’s still a good idea.