Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionVII. Short−Term Financial
Planning and Management- Credit and Inventory
Management
(^742) © The McGraw−Hill
Companies, 2002
If Locust does switch to net 30 days on sales, then the quantity sold will rise to Q
- Monthly revenues will increase to PQ, and costs will be vQ. The monthly
cash flow under the new policy will thus be:
Cash flow with new policy (Pv)Q [21.3]
($49 20) 110
$3,190
Going back to Chapter 8, we know that the relevant incremental cash flow is the differ-
ence between the new and old cash flows:
Incremental cash inflow (P v)(Q Q)
($49 20) (110 100)
$290
This says that the benefit each month of changing policies is equal to the gross profit per
unit sold, P v$29, multiplied by the increase in sales, Q Q10. The present
value of the future incremental cash flows is thus:
PV[(P v)(Q Q)]/R [21.4]
For Locust, this present value works out to be:
PV($29 10)/.02 $14,500
Notice that we have treated the monthly cash flow as a perpetuity because the same ben-
efit will be realized each month forever.
Now that we know the benefit of switching, what’s the cost? There are two components
to consider. First, because the quantity sold will rise from Qto Q, Locust will have to pro-
duce Q Qmore units at a cost of v(Q Q) $20 (110 100) $200. Second,
the sales that would have been collected this month under the current policy (PQ
$4,900) will not be collected. Under the new policy, the sales made this month won’t be
collected until 30 days later. The cost of the switch is the sum of these two components:
Cost of switching PQv(Q Q) [21.5]
For Locust, this cost would be $4,900 200 $5,100.
Putting it all together, we see that the NPV of the switch is:
NPV of switching [PQv(Q Q)] [(P v)(Q Q)]/R [21.6]
For Locust, the cost of switching is $5,100. As we saw earlier, the benefit is $290 per
month, forever. At 2 percent per month, the NPV is:
NPV$5,100 290/.02
$5,100 14,500
$9,400
Therefore, the switch is very profitable.
CHAPTER 21 Credit and Inventory Management 715We’d Rather Fight than Switch
Suppose a company is considering a switch from all cash to net 30, but the quantity sold is
not expected to change. What is the NPV of the switch? Explain.
In this case,Q Qis zero, so the NPV is just PQ. What this says is that the effect of the
switch is simply to postpone one month’s collections forever, with no benefit from doing so.EXAMPLE 21.1