Look back at Example 27.2. A large bank is willing to provide the float reduction service for $175 per year, payable at the end of each year. The relevant discount rate is 8 percent. Should Lambo hire the bank? What is the NPV of the investment? How do you interpret this discount rate? What is the most per year that Lambo should be willing to pay?

The PV to Lambo is still $2,000. The $175 would have to be paid out every year forever to maintain the float reduction, so the cost is perpetual and its PV is $175 / .08 = $2,187.50 .

The NPV is $2,000 − 2,187.50 = − $187.50 ; therefore, the service is not a good deal.

Ignoring the possibility of bounced checks, the discount rate here corresponds most closely to the cost of short-term borrowing. The reason is that Lambo could borrow $1,000 from the bank every time a check was deposited and pay it back three days later. The cost would be the interest that Lambo would have to pay.

The most Lambo would be willing to pay is whatever charge results in an NPV of zero. This zero NPV occurs when the $2,000 benefit exactly equals the PV of the costs—that is, when $2,000 = C /.08 , where C is the annual cost. Solving for C, we find that C = .08 × $2,000 = $160 per year.

Example 27.2

Instead of eliminating the float, suppose Lambo can reduce it to one day. What is the maximum Lambo should be willing to pay for this? If Lambo can reduce the float from three days to one day, then the amount of the float will fall from $3,000 to $1,000. From our immediately preceding discussion, we see right away that the PV of doing this is equal to the $2,000 float reduction. Lambo should be willing to pay up to $2,000.