Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionVII. Short−Term Financial
Planning and Management- Cash and Liquidity
Management
© The McGraw−Hill^707
Companies, 2002the float is this extra $3,000 that comes in immediately. No other cash flows are af-
fected, so Lambo is $3,000 richer.
In other words, the PV of eliminating the float is simply equal to the total float.
Lambo could pay this amount out as a dividend, invest it in interest-bearing assets, or do
anything else with it. If it costs $2,000 to eliminate the float, then the NPV is $3,000
2,000 $1,000; so Lambo should do it.Ethical and Legal Questions The cash manager must work with collected bank cash
balances and not the firm’s book balance (which reflects checks that have been de-
posited but not collected). If this is not done, a cash manager could be drawing on un-680 PART SEVEN Short-Term Financial Planning and Management
FIGURE 20.2
Effect of Eliminating
the Float
Beginning float
Checks received
Checks cleared
(cash available)
Ending float$3,000
1,000- 4,000
$ 0
tt + 1 t + 2Day$ 0
1,000- 1,000
$ 0
$ 0
1,000- 1,000
$ 0
...
...
......
...Reducing the Float: Part I
Instead of eliminating the float, suppose Lambo can reduce it to one day. What is the maxi-
mum 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 discussion immediately preceding, we see right away
that the PV of doing this is just equal to the $2,000 float reduction. Lambo should thus be will-
ing to pay up to $2,000.EXAMPLE 20.2Reducing the Float: Part II
Look back at Example 20.2. 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 Cis the annual cost. Solving for C,we find that C.08 $2,000
$160 per year.EXAMPLE 20.3