How to Calculate a Payback Period with Inconsistent Cash Flows

Welcome to Alanis Business Academy. I’m Matt
Alanis and this is How to Calculate a Payback Period with Inconsistent Cash Flows. In our last we learned about the payback period
as well as how to calculate the payback period assuming consistent cash flows. For access
to this video select the link above or go to the Alanis Business Academy YouTube channel
page and search for the video titled How to Calculate the Payback Period. Unfortunately cash flows are anything but
consistent, which makes the basic formula for calculating a payback period somewhat
unhelpful. So in this video we are going to walk through how to calculate the payback
period when our expected future cash flows fluctuate from one period to the next. The formula to calculate the payback period
assuming inconsistent cash flows is A plus the result of B divided by C. This probably
makes little sense at this point, but let me attempt to elaborate. In this formula,
A represents the last period with negative cash flow. Essentially this is the period
just before we recover our initial investment. B represents the amount of cash that is remaining
at the end of A. C represents the total amount of cash generated in the period immediately
following A. If this is still somewhat unclear that’s okay. It will make more sense once
we work through a problem. Lets assume that we will be investing \$9,000
in a project. Since this is our investment so we include the \$9,000 in parenthesis, which
represents a negative figure or cash outflow. The Abbreviation CF stands for cash flow,
and the subscript 0 indicates the period. A period of 0 represents the present time. Assume that based upon our calculations that
we project to receive positive cash flows of \$2,000, \$2,500, \$3,750, and \$4,500 in periods
one through four respectively. When calculating the payback period for inconsistent cash flows
I find it helpful to use a two-column approach. The first column contains our expected cash
flows in order from when we expect to receive them. The second column contains the remaining
cash need to cover our initial investment of \$9,000. Now that we’ve organized our problem we simply
need subtract each of our expected future cash flows from our initial investment. So
in the first period we subtract \$2,000 from \$9,000 to get \$7,000. This means that after
the first period we still need \$7,000 to cover our initial investment. In the second period
we subtract our expected cash flows from year 2 of \$2,500 from our remaining unrecovered
investment of \$7,000 to get \$4,500. For year 3 we subtract expected cash flows of \$3,750
from \$4,500 to get \$750. At this point we only need \$750 in positive cash flow to break-even
and cover our startup costs of \$9,000. Now in year 4 we expect to receive \$4,500 in cash,
which is much greater than the \$750 needed to cover our initial investment. Since we
will experience positive cash flow in year 4, year 3 represents the last period that
we will have negative cash flow. As a result, year 3 presents A. So already we know that
our payback period is going to be somewhere in between 3 and 4 years. Now that we have A we need to see if we have
enough information to solve this problem. Once again, B represents the amount of cash
that is remaining at the end of A. Since we know that A is period 3 or the third year,
and the corresponding cash remaining at the end of A is \$750, \$750 will be used as B.
The last variable in our formula is C, which represents the total amount of cash generated
in the period immediately following A. This is \$4,500 since we expect to receive \$4,500
in cash at the end of year 4, and year 4 is the period immediately following A. At this point we simply substitute these values
into their corresponding variable and solve. Doing so gives us a payback period of 3.17
years or 3 years and 2 months if you convert the decimal into months. Whether this payback
period is acceptable will depend in large part on the other opportunities that we have
to generate positive cash flow. This has been How to Calculate a Payback Period
with Inconsistent Cash Flows. For questions or comments please utilize the comment box
below and I’ll do my best to get back to those in a timely fashion. For access to additional
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