Think & Done

Payback period PP is explained and illustrated with example calculation using the payback period formula. On this web page we take a look at how Payback Period or PP is used in capital budgeting analysis. We show you payback period calculation for cash flows that have varying frequencies such as annually, quarterly, monthly, weekly and daily.

Payback Period Calculator

Here you will find an online payback period calculator that calculates payback period given that you provide the series of cash flows

Excel Payback Period Formula

Please visit this page for details on using a proedural approach to find payback period in excel.

What is Payback Period

Payback period is the one of the oldest and most widely used method used for evaluating a capital investment proposal. As the name implies it refers to the time required to recover the initial investment or the initial cash outlay as it is called in financial terms.

What is the formula for Payback Period?

The payback period formula only provides a solution when we have tabulated the periodic cash flows using a column for cummulative sum of the cash flows. This procedural approach permits us to first ascertain the time period (a year, a quarter, a month, a week or a day) and then having to calculate the remaining part of time period needed to recover the partial sum of cash flow for the time period in which capital recovery is made.

Payback Period Example

I will begin with an illustration that finds payback period for an example investment proposal. Let us say, we were offered a series of cash inflows at the end of each of the next four years as $5000, $4000, $3000, and $1000. Assuming the initial cash outlay for this proposal is $10,000. We are faced with finding the payback period for this hypothetical investment. Below you will find a tabular format that shows the time period, the corresponding cash flow, and the cummulative sum of the cash flows

Year	Cash Flows	Cumulative Cash Flows
0	-$10,000(q)
1	$5,000	$5,000
2(p)	$4,000	$9,000(r)
3	$3,000	$12,000
4	$1,000	$13,000

Payback Period Step by Step

1. We add up the cash inflows beginning after the initial cash outlay in the cumulative cash inflows column
2. 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
3. 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 cash inflow. 
   E.g., ( $10,000 - $9,000 ) / $3,000 = 0.334
4. Since we said these were annual cash flows thus to obtain the payback period in years , we take the figure from the last step and add it to the year from the step 2.
   Thus our payback period is 2 + .334 = 2.334 years
5. Instead of representing the years as a decimal value we could represent the payback period in years and months this way We take the fraction 0.334 and multiply it by 12 to get the months which is 4.01 months. Thus our payback period is 2 years and 4 months

Payback Period Calculation Online

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

Alternate method for Payback Period

This page showed you a way of calculating payback period where we aggregated the sum of values to find the year where the sum exceeded the initial costs, an alternative approach to for payback period calculation is illustrated that counts up the sum starting from the initial cash outlay to the year where such sum turns positive or zero.

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 2.334 Quarters. And now to find the months from this value we would multiply the fraction 0.334 times 3 months. So the payback period would be 2 quarters and 1 month ( 0.2334 x 3 = 1.01 months)

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 2.334 months. And now to find the days from this value we would multiply the fraction 0.334 times 30 days. So the payback period would be 2 months and 10 days ( 0.2334 x 30 = 10.01 days)

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 2.334 weeks. And now to find the days from this value we would multiply the fraction 0.334 times 7 days. So the payback period would be 2 weeks and 3 days ( 0.2334 x 7 = 2.338 days)

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 2.334 days. And now to find the hours from this value we would multiply the fraction 0.334 times 24 days. So the payback period would be 2 days and 8 hours ( 0.2334 x 24 = 8.016 hours)

Discounted Payback Period

Although payback period is the time period in which we recoup the initial cost of the project, yet it has a major drawback as it doesn't consider the time value of money. Thus a better measure to use instead of regular payback period is Discounted Payback Period. Discounted payback period allows us to use discounted cash flow technique to find the time period in which present value of future cash flows equals the initial cash outlay.

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. Discounted payback period