Think & Done

Discounted payback period DPP is explained and illustrated with example calculation using the Discounted payback period formula. On this web page we take a look into the way discounted payback period or DPP is used in investment analysis. We will look at finding discounted payback period for cash flows that have varying frequencies (annual, quarterly, monthly, weekly and daily).

Discounted Payback Period Calculator

Here you will find an online Discounted payback period calculator that calculates discounted payback period given that you provide the series of cash flows and the discount rate

Excel Discounted Payback Period Formula

Please visit this page for details on using a procedural approach to find discounted payback period in Excel.

What is Discounted Payback Period

Payback Period does not consider time value of money when providing an answer whereas with Discounted Payback Period we get to see the real value of cash inflows when they are measured in today's amount of money as these are discounted at an interest rate called the Discount Rate. We get to see the number of years required to recoup the initial cash outlay or our investment.

What is the formula for Discounted Payback Period?

Discounted Payback Period Example

Let us illustrate finding Discounted Payback Period for an example investment proposal. Let us say you were offered a series of cash inflows at the end of each of the next four years as $50,000, $40,000, $30,000, and $10,000. Say the Initial Cost Outlay for this proposal is $100,000.

Year	Cash Flows	DCF	Cumulative DCF
0	-$100,000(q)
1	$50,000	$47,169	$47,169
2(p)	$40,000	$35,599	$82,769(r)
3	$30,000	$25,188	$107,958
4	$10,000	$7,920	$115,879

Discounted Payback Period Step by Step

• We add up the discounted cash inflows beginning after the initial cash outlay in the cumulative cash inflows column
• We keep an eye on this last column and track the last year for which the cumulative total does not exceed the initial cash outlay
• We compute the part or fraction of the next year's cash inflow need to payback the initial cash outlay by taking the initial cash outlay less the cumulative total in the last step then divide this amount by the next years discounted cash flow.
  E.g., ( $100,000 - $82,769 ) / $25,188 = 0.684
• To now obtain the Discounted Payback Period in years , we take the figure from the last step and add it to the year from the step 2. Thus our Discounted Payback Period is 2 + .684 = 2.684 years
• Instead of represent the years as decimal value we could represent the Discounted Payback Period in years and months this way We take the fraction 0.684 and multiply it by 12 to get the months which is 8.20 months. Thus our Discounted Payback Period is 2 years and 8 months

Discounted Payback Period Calculation Online

This online tool will perform discounted payback period calculation and will display step by step workout similar to one you have seen in this discussion.

Discounted Payback Period for Quarterly Cash Flow

If the cash flows are quarterly instead of yearly as we illustrated above, we will still resort to use the same tabular format and arrive at at time period to recover the initial cash flow. The only difference would be when we are to find the remaining months of the payback period. Say if the cash flows in our last example are on quarterly basis, thus the payback period would be 2.684 Quarters. And now to find the months from this value we would multiply the fraction 0.684 times 3 months. So the payback period would be 2 quarters and 2 month ( 0.684 x 3 = 2.052 months)

Discounted Payback Period for Monthly Cash Flows

If the cash flows are monthly instead of yearly as we illustrated above, we will still use the same tabular format and arrive at at time period to recover the initial cash flow. The only difference would be when we are to find the remaining days of the payback period. Say if the cash flows in our last example are on monthly basis, thus the payback period would be 2.684 months. And now to find the days from this value we would multiply the fraction 0.684 times 30 days. So the payback period would be 2 months and 21 days ( 0.684 x 30 = 20.52 days)

Discounted Payback Period for Weekly Cash Flows

If the cash flows are weekly instead of yearly as we illustrated above, we will still use the same tabular format and find at at time period to recover the initial cash flow. The only difference would be when we are to find the remaining days of the payback period. Say if the cash flows in our last example are on weekly basis, thus the payback period would be 2.684 weeks. And now to find the days from this value we would multiply the fraction 0.684 times 7 days. So the payback period would be 2 weeks and 5 days ( 0.684 x 7 = 4.788 days)

Discounted Payback Period for Daily Cash Flows

If the cash flows are daily instead of yearly as we illustrated above, we will still use the same tabular format and calculate at at time period to recover the initial cash flow. The only difference would be when we are to find the remaining hours of the payback period. Say if the cash flows in our last example are on daily basis, thus the payback period would be 2.684 days. And now to find the hours from this value we would multiply the fraction 0.684 times 24 days. So the payback period would be 2 days and 17 hours ( 0.684 x 24 = 16.416 hours)

Regular Payback Period

Although discounted payback period is a preferred method since it takes time value of money in to considertaion yet regular undisconted payback period is a more popular method. With undiscounted payback period the cash flows are not discounted unlike the discounted payback period where each of the net cash flows is discounted before an attempt is made to find the time period required to regain the initial cost of the investment. Another tutorial explains the payback period

Related DCF analysis methods

Following is a list of related readings that cover other 5 commonly used DCF analysis methods

1. Internal Rate of Return
2. Modified Internal Rate of Return
3. Net Present Value
4. Profitability index
5. Payback period