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discounted payback period

In finance, the discounted payback period is one of the key measure that determines the investor's return on investment. A simple discounted payback period is the time needed to recover the initial cost of the investment whereas the discounted payback period ensures that such cash flows are discounted to reflect their present value when finding the payback period. Finding the discounted payback period is however not that easy as there are no formulas to find the discounted or simple payback period. Thus to find the discounted payback period, an analyst would draw up a table of data showing the timings of the cash flows, the cash flows, the discounted amounts and the running sum of the discounted amounts. The analyst would watch out for the row where the running sum of discounted amounts turns positive thus resulting in the time period for the recovery of the initial cost incurred in undertaking the investment.

A sample discounted payback period calculation is provided herein illustrating the steps taken in computing the time period required to recover the initial expense incurred in an investment when the cash flows are discounted to reflect their present value. This example assumes that you had invested an amount of \$100 million dollars and expected four annual receipts of \$70 million. Your cost of capital is 4% and the task is to find the discounted payback period that ensures the recovery of the \$100 million.

Finding discounted payback period in Excel

Up until Excel 2013, there were no native financial functions in Excel to find the discounted payback period. It is unclear as to what Microsoft is planning with its upcoming Excel 2015 or 2016, yet if it does introduce a new set of financial functions in the new release of Excel then more than likely such financial functions will be based up the tadXL series of financial functions. tadXL add-in for Excel 2007, 2010 and 2013 were released to the market in March of 2012 and it offered a large number of financial functions for Excel users. One of these financial functions is the tadDPP financial function that accepts a discount rate and series of cash flows to find the discounted payback period. There are other options that are part of this function that allow you to use compounding frequencies of interest and to define the payment period's length in addition permits the use of discounting conventions such as mid-year discounting.

Using tadXL functions such as tadDPP, finding discounted payback period in Excel 2007, 2010 and 2013 becomes really easy. Let us take the cash flows from our previous investment, to find the discounted payback period in Excel we would type the following:
=tadDPP( 4%, {-100, 70, 70, 70, 70} )
1.505142857

or
That is all that would be required, and the tadDPP function will return the discounted payback period.

Now let us say that we were interested in finding the real discounted 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, 70, 70, 70, -70, 70 where there is an interim outgoing amount of \$50 million. To find the discounted payback period in Excel we would now use a different financial function from tadXL called tadTPP where TDPP stands for true discounted payback period. Here is how:
=tadTDPP( 4%, {-150, 70, 70, 70, -70, 70} )
4.270790802

Now the discounted 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.