# Discounted Payback Period Method

## Definition

The discounted payback period (DPP) method is based on the discounted cash flows technique and is used in project valuation as a supplemental screening criterion. In simple words, it is the number of years needed to recover initial cost (cash outflows) of a project from its future cash inflows. To calculate it, we need consequentially add the discounted value of each future cash inflow as long as the initial cost will be recovered.

## Formula

The discounted payback period can be calculated as follows:

where p is a number of a period with the last negative value of cumulative discounted cash flow, |CDCFp| is an absolute value of the last cumulative discounted cash flow, and CDCFp+1 is the first positive value of cumulative discounted cash flow.

## Decision rule

It’s not recommended to use the discounted payback period as a single screening criterion unlike the net present value (NPV) or internal rate of return (IRR). In case of a mutually exclusive project, however, it can be used as a supplemental criterion. Other things being equal, the project with a shorter payback period should be accepted.

## Example

Two mutually exclusive projects are shown in the table below.

Both of them have a positive NPV of \$3,563,817.75 for Project Y and \$3,933,790.96 for Project Z and a cost of capital of 12%. In terms of NPV as a single screening criterion, Project Z contributes more to shareholder value than Project Y and therefore should be accepted. In terms of liquidity and uncertainly risk, however, the acceptance of Project Z is not as obvious as it might seem at first glance. Let’s use the discounted payback period method as a supplemental criterion.

As a first step, we need to calculate all values of discounted cash flows for both projects,

e.g., discounted cash flows of Project Y are as follows:

DCF0 = -\$20,000,000 ÷ (1+0.12)0 = \$-20,000,000

DCF1 = \$9,000,000 ÷ (1+0.12)1 = \$8,035,714.29

DCF2 = \$8,000,000 ÷ (1+0.12)2 = \$6,377,551.02

DCF3 = \$6,000,000 ÷ (1+0.12)3 = \$4,270,681.49

DCF4 = \$5,000,000 ÷ (1+0.12)4 = \$3,177,590.39

DCF5 = \$3,000,000 ÷ (1+0.12)5 = \$1,702,280.57

As a second step, we need to calculate all values of cumulative discounted cash flows for both projects,

e.g., cumulative discounted cash flows of Project Y are as follows:

CDCF1 = -\$20,000,000 + \$8,035,714.29 = -\$11,964,285.71

CDCF2 = -\$11,964,285.71 + \$6,377,551.02 = -\$5,586,734.69

CDCF3 = -\$5,586,734.69 + \$4,270,681.49 = -\$1,316,053.21

CDCF4 = -\$1,316,053.21 + \$3,177,590.39 = \$1,861,537.19

CDCF5 = \$1,861,537.19 + \$1,702,280.57 = \$3,563,817.75

The last negative value of cumulative discounted cash flow for Project Y was during the third year and during the fourth year for Project Z. Thus, the discounted payback period of Project Y is 3.41 years and 4.31 years for Project Z.

In terms of the discounted payback period, Project Y looks more attractive because it has greater liquidity and lower uncertainty risk.

The main disadvantage of the discounted payback period method is that it does not take into account cash flows coming in after break-even. Furthermore, it shows only the time needed to recover the initial cost of a project and is some break-even analysis technique. For this reason, this method can conflict with NPV and therefore can be wrong. Also, there isn’t any way to determine how short the payback period should be to accept the project. In academic studies, using this method is not recommended for mutually exclusive projects.

The main advantage of the discounted payback period method is that it can give some clue about liquidity and uncertainly risk. Other things being equal, the shorter the payback period, the greater the liquidity of the project. Also, the longer the project, the greater the uncertainty risk of future cash flows. Therefore, the shorter the payback period, the lower the overall risk of a project. However, the choice of a project solely on the basis of the payback criterion is purely an arbitrary decision.