The discounted payback period method is part of the large family of capital budgeting techniques.
Here’s what you need to know about discounted payback:
The discounted payback method is not as simple as the “regular” payback method.
Discounted payback is close to, but not as “complete” as Net Present Value.
Very often the discounted payback period method leads to the same project selection as the
payback method.
The discounted payback calculation outcome (in number of years) is always longer than
the outcome of the “regular” payback method calculation.
All of these insights will be discussed in this video!
The payback method is often used as a first screening method for an investment.
The payback method asks a very simple central question: How many years does it take to recover
the initial investment?
Let’s calculate the payback period for project A.
In year 0 (today), we have a cash outflow of $1000.
The brackets around the number indicate that it is a negative, a cash outflow.
Over the course of the project, we have $1600 worth of benefits (cash inflows) in total,
split evenly over 4 years of $400 each.
It’s fairly easy to calculate that the payback period is 2.5 years: $400 of benefits in year
1, plus $400 of benefits in year 2, plus six months’ worth of benefits in year 3 making
up the final $200, at which point the total investment equals the total benefits.
An alternative way to phrase the central question is: When do the cumulative cash flows reach
zero?
After year 1, the cumulative cash flows are minus $600, which is the sum of the $1000
investment cash outflow in year 0, and the $400 benefits (cash inflows) in year 1.
After year 2, the cumulative cash flows are minus $200.
After year 3, a positive $200.
We have overshot our target, as we are looking for the point when cumulative cash flows reach
zero.
$200 divided by $400 is 0.5.
Our payback period is 2.5 years.
The final step in payback period calculations is to accept or reject the project.
You can do this in absolute terms: is the payback period for the project shorter than
the target payback of 3 years that the company has set?
Yes, it is!
Or you can do this in relative terms: is project A more attractive, does it have a shorter
payback period, than project B and project C. If the payback period for project B is
1.8 years, then A (with a payback period of 2.5 years) is less attractive than B, but
more attractive than project C at 3 years.
The discounted payback method is very closely related to the payback method, but it poses
a slightly different central question: When do the cumulative cash flows reach zero, if
time value of money is applied?
The “regular” payback method ignores the time value of money, while the discounted
payback method incorporates it!
So what we have to do is to convert the nominal cash flows of project A to their present value
equivalents.
As you can see, the present value of $400 of benefits two years from now is lower than
the present value of $400 of benefits one year from now.
And the present value of benefits three and four years from now is even lower.
How did I get to the specific present value numbers shown here?
I chose a 20% discount rate.
What is the present value of a $400 benefit that we expect one year from now?
To calculate that present value, we need to take the nominal amount of $400 and divide
it by 1 + the discount rate.
1 + 20% equals 1.2. $400 divided by 1.2 equals $333.
The present value of a nominal amount of $400 one year from now is $333 as today’s equivalent.
What is the present value of a $400 benefit that we expect two years from now?
Take the nominal amount of $400 and divide it by 1 + 20%, to the power 2 (as we need
to take two steps: from year 2 to year 1, from year 1 to today).
This is the same as saying $400 divided by 1.2 * 1.2, or $400 divided by 1.44, which
is $278.
For the year 3 benefits, take the nominal amount of $400 and divide it by 1 + 20%, to
the power 3 (as we need to take three steps: from year 3 to year 2, from year 2 to year
1, from year 1 to today).
This is the same as saying $400 divided by 1.2 * 1.2 * 1.2, or $400 divided by 1.728,
which is $231.
What is the present value of a $400 benefit that we expect four years from now?
$400 divided by 1.2 * 1.2 * 1.2 * 1.2, or $400 divided by 2.0736, which is $193.
Now we perform our cumulative cash flow test again, this time on the present values.
When do these cumulative cash flows reach zero?
After year 1, the cumulative present value cash flows are minus $667, which is the sum
of the $1000 investment cash outflow in year 0, and the $333 present value of the benefits
(cash inflows) in year 1.
After year 2, the cumulative cash flows are minus $389.
After year 3, minus $158.
After year 4, a positive $35.
We have overshot our target, as we are looking for the point when cumulative cash flows reach
zero.
$158, the amount we needed after year 3 to close the gap to zero, divided by $193, is
0.8.
Our discounted payback period is 3.8 years.
The final step in discounted payback period calculations is to accept or reject the project.
You can do this in absolute terms: is the payback period for the project shorter than
the target payback of 4 years?
Yes, it is!
Or you can do this in relative terms: is project A more attractive, does it have a shorter
discounted payback period, than project B and project C. Well, it turns out that once
again project A is more attractive than project C, but less attractive than project B.
To speed up the discounted payback calculations, I plugged the numbers for each of the projects
into an Excel spreadsheet.
For project A, the present value of the cumulative cash flows is positive within 4 years.
For project B, within 3 years.
For project C, the present value of the cumulative cash flows fails to turn positive at all!
Here are the outcomes of the calculations.
Project A has a payback period of 2.5 years, and a (longer) discounted payback period of
3.8 years.
Project B has a payback period of 1.8 years, and a (longer) discounted payback period of
2.9 years.
Project C has a payback period of 3 years, and a discounted payback period that cannot
be calculated, as the present value of the cumulative cash flows never turns positive.
When comparing projects A, B and C, both the “regular” payback period method and the
discounted payback period method will declare victory for project B.
So are there cases where the two methods will give you different answers, in terms of which
project wins?
Certainly.
When comparing project A and project E, we find that both of them have a payback period
of 2.5 years.
The regular payback method looks just at the nominal amounts.
Project A: $400 + $400 + $200 = $1000.
Project E: $200 + $400 + $400 = $1000.
Using the discounted payback period method, the time value of money is taken into account.
Earlier benefits have a bigger impact than later benefits.
While it’s a tie between the two projects when using the “regular” payback period
method, project A wins using the discounted payback period method.
However, both the regular payback method, which is nice and simple, as well as the discounted
payback period method, which is slightly more complicated, have a crucial blind spot.
The regular payback method answers the question “How many years does it take to recover
the initial investment?”
Nothing more, nothing less.
So if project A has an investment of $1000 and 4 years of $400 benefits per year, and
project D has an investment of $1000 with 5 years of $400 benefits per year, the payback
method tells you that both projects are equally attractive at a payback period of 2.5 years.
It simply ignores what happens after those 2.5 years!
The discounted payback period method answers the question “When do the cumulative cash
flows reach zero, if time value of money is applied?”
So if project A and project D have the exact same nominal cash flows as well as the exact
same discounted cash flows in year 1 through 4 (as we apply the same discount rate), but
project D provides one more year of benefits in year 5, then the discounted payback period
method tells you bluntly that both projects are equally attractive at a discounted payback
period of 3.8 years.
It simply ignores what happens after those 3.8 years!
This is where more sophisticated methods like Net Present Value or Internal Rate of Return
have to come in to provide a very different answer.
The discounted payback method is not as simple as the “regular” payback method.
Discounted payback is close to, but not as “complete” as Net Present Value.
Very often the discounted payback period method leads to the same project selection as the
payback method.
The discounted payback calculation outcome (in number of years) is always longer than
the outcome of the “regular” payback method calculation.
I hope you enjoyed this explanation of the discounted payback period method.
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