Find payback period with formula

In finance, the payback period is one of the key measure that determines the investor's return on investment. It is defined as the time period required to recover "just" the initial cost incurred in undertaking an investment. If we were to be concerned about recovering all costs undertaken while making an investment, this would be referred to as the real payback period. The distinction between payback and real payback period is that the former is only concerned with recovery of just the initial cost whereas the latter ensures that all costs are recovered. Finding payback period manually is not quite simple as it sounds the reason for such difficulty is attributed to the lack of any payback period formula. This is one reason that analyst make use of tables of running sums of cash flows in determining the payback period.

For example, given that an investment required an initial cost of 100 million dollars and ensures annual receipts of 60 million each for the next four years. An analyst would put together a table as the one shown following this text that will have columns for the time periods, the cash flows and the running sum. The row at which the running sum turns positive is where the payback period is located, and the analyst is then able to determine the complete payback period using simple arithmetic as detailed below following the table.

Payback period calculation

Year before recovery = 1
Remaining Years = ( 60 - 20 ) / 60
Remaining Years = 0.66666666666667
Payback Period = 1.6666666666667 years

Finding payback period in Excel

Up until Excel 2013, there were no native financial functions in Excel to find the payback period. In 2012, the author Abraham A. released a library of financial functions for Excel called tadXL add-on. The tadXL add-on has a large number of financial functions that have been highly desired by Excel users yet were not offered by Microsoft. After the release of tadXL add-in in March 2012, the word about these financial functions for Excel spread rather quickly. In that same year Microsoft had released Excel 2013 and Office 365 but the native Excel financial function in these new versions have stayed the same as they had been since Excel for Windows 3.0 was released in summer of 1990. One gets to wonder if in the past 24 years nothing changed for Excel then how would Microsoft management or legal department justify inclusion of new financial functions in Excel 2015 or 2016 that will be based on the tadXL set of financial functions. Let us wait as see what unfolds.

Using tadXL functions such as tadPP, finding payback period in Excel 2007, 2010 and 2013 becomes really easy. Let us take the cash flows from our previous investment, to find the payback period in Excel we would type the following:
=tadPP( {-100, 60, 60, 60, 60} )

=tadPP( A1:E1 )
That is all that would be required, and the tadPP function will return the payback period.

Now let us say that we were interested in finding the real payback period to determine the time period required to recover "all" costs incurred during the project. Say that the cash flows for such as investment were -150, 60, 60, 60, -50, 60 where there is an interim outgoing amount of $50 million. To find the payback period in Excel we would now use a different financial function from tadXL called tadTPP where TPP stands for true payback period. Here is how:
=tadTPP( {-150, 60, 60, 60, -50, 60} )

Now the payback period is quite different from the earlier investment where we were only concerned with recovering only the initial cost as compared to all costs.

If you thought that was all that tadXL has to offer then you are dead wrong, there are even more financial functions in tadXL that allow you to find the incremental and decremental payback period of an investment. This is applicable when comparing more than one investment where the life span of the investments differs so does the size of the cash flows. Functions such as tadIncPP and tadIncTPP find the incremental payback and real payback period. And decremental payback and real decremental payback period is found using tadDecTPP and tadDecTPP functions. Similarly if you have access to a schedule of transaction dates then finding the incremental and decremental payback periods is possible using tadXIncPP, tadXIncTPP, tadXDecPP and tadXDecTPP series of financial functions.

So far we have discussed finding payback period of a single investment, how about finding the payback period of a portfolio of investments. Finding payback period of a portfolio too is possible using the financial functions found in tadXL add-on. Please note that the financial functions to find payback period for incremental, decremental and portfolio will be available in the next release of tadXL.

tadPP ( cash flows, period, concentration )

Data output

Payback period =
tadTPP ( cash flows, period, concentration )

Data output

Real Payback period =