Discounted Payback PeriodDefined along with Formula & How to Calculate

Written By:
Lisa Borga

The discounted payback period (DPP) refers to the period of time over which an investment will “pay back” the initial outflow of cash while accounting for the time value of money.

This means that it measures the period of time it will take for the proposed capital investment to break even.

The discounted payback period is used to measure the feasibility of particular projects with greater accuracy than the basic payback equation, which does not discount future payments.

By factoring in the time value of money, DPP can offer far more accurate results at the cost of a significant increase in complexity.

Discounted Payback Period Explained

Before investing in a particular project, any company or investor will want to know when their investment will break even.

This is an important metric because, in most cases, there is more than one investment opportunity available to choose from and understanding which offers the fastest payback period can be an important factor in making the best investment decision.

The DPP allows companies and investors the ability to look at the profitability and speed of returns for a particular capital outflow.

Using this calculation, future cash flows will be estimated and then discounted to their present value.

This will allow a company or investor to determine when a project will break even and then begin to generate cash flows in excess of the initial cost.

Generally, the shorter the DPP is, the sooner an investment or project will create cash inflows to cover the initial cost of the investment and break even.

When used to decide between mutually exclusive opportunities, the company or investor should choose the option offering the shortest DPP.

Formula for Calculating the DPP

In order to calculate DPP for a cash outflow the formula is:

DPP = y + abs(n) / p,

Where:

y = the period before the time that total cash flow becomes positive,

p = discounted value of the cash flow during time in which total cash flows are => 0

abs(n) = the absolute value of cumulative discounted cash flows during period y.

Using the Formula for the Discounted Payback Period

There will be two steps to follow in computing the DPP. The first step will be to discount the net cash flows for every year of the project.

For the second step, you will take the initial cost amount and subtract the discounted cash flows from it.

This will give you the DPP.

After computing the discounted cash flows, they can be subtracted from the initial cost amount until the initial cost of the project is paid off.

Example of DPP

Suppose Business X is thinking about investing in a new project.

The project would require an initial investment of $5,000 in cash.

The project is forecasted to provide returns of $1,500 each year for the next four years, and the discount rate is 5%.

To start calculating the discounted payback period, you would first consider the -$5,000 in the initial period.

Then, the first period would have a positive $1,500 cash flow.

Then, you will need to calculate the discounted cash flows.

For the first year, this would be $1,442.31 ($1,500 / 1.05).

So, when the first period has ended, the project will still need to make $3,557.69 ($5,000 – $1,442.31) to break even.

For the second year, the discounted cash flow would be $1,360.54 [$1,500 / (1.05)^2].

This means when the second period ends, the project will still need to make $2,197.15 ($3,557.69 – $1,360.54) to break even.

For the third year, the discounted cash flow would be $1,295.76 [$1,500 / (1.05)^3].

This means that when the third year ends, the project will still need to make $901.39 to break even.

For the fourth year, the discounted cash flow would be $1,234.05 [$1,500 / (1.05)^4].

This means the discounted payback period would occur at some point during the fourth year.

Payback Period

Since the DPP occurs during the year, we will need to calculate the exact discount payback period.

To do this, we subtract the initial cost that still needed to be reduced from the discounted cash flow for the fourth year.

This would result in $332.66 ($1,234.05 – $901.39).

Next, we will divide the $332.66 by the discounted cash flow for the fourth year of $1,234.05.

This will tell us what percentage of the year is remaining once the project has reached the break-even point, which is .27.

We subtract this number from one and multiply it by 100 to get 73%.

When we convert this figure into months, we find that the discounted payback period is 3 years and 9½ months.

Advantages and Disadvantages of DPP

The DPP can show how profitable a project should be when taking into account the time value of money.

This can help companies to decide whether or not they want to invest in a project.

Should a project have a DPP that is longer than the useful life of the project, the company should not invest in the project.

A disadvantage of using DPP analysis is the fact that it does not consider any cash flows that occur once the payback period is complete.

Because of this, the analysis does not provide managers or investors any information about the profitability of the investment after the payback period or how worthwhile the investment is as a whole.

Therefore, DPP may not agree with the results of the NPV analysis.

It’s possible for a project to have a payback period that is longer than another project being considered and yet still have a higher NPV if it has a lot more cash inflows once the discounted payback period ends.

DPP analysis could, therefore, cause a manager to pass up a more profitable project.

Key Takeaways

• The discounted payback period is a metric used to determine the feasibility of potential capital investments.
• The discounted payback period offers a more accurate alternative to the basic payback period calculation by accounting for the time value of money.
• By showing the time it will take an investment to break even while discounting future income to present value, the discounted payback period can be used to compare different investment opportunities.