# Discounted Payback Period Method

By Yuriy Smirnov Ph.D.

## 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:

 Discounted Payback Period = p + |CDCFp| CDCFp+1 + |CDCFp|

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.

 Initial Cost, CF0 Cash flows at the end of relevant year, CFt 0 1 2 3 4 5 Project Y -\$20,000,000 \$9,000,000 \$8,000,000 \$6,000,000 \$5,000,000 \$3,000,000 Project Z -\$20,000,000 \$4,000,000 \$5,000,000 \$7,000,000 \$9,000,000 \$10,000,000

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,

 Discounted cash flows, DCFt 0 1 2 3 4 5 Project Y -\$20,000,000 \$8,035,714.29 \$6,377,551.02 \$4,270,681.49 \$3,177,590.39 \$1,702,280.57 Project Z -\$20,000,000 \$3,571,428.57 \$3,985,969.39 \$4,982,461.73 \$5,719,662.71 \$5,674,268.56

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,

 Cumulative discounted cash flows, CDCFt 0 1 2 3 4 5 Project Y -\$20,000,000 -\$11,964,285.71 -\$5,586,734.69 -\$1,316,053.21 \$1,861,537.19 \$3,563,817.75 Project Z -\$20,000,000 -\$16,428,571.43 -\$12,442,602.04 -\$7,460,140.31 -\$1,740,477.60 \$3,933,790.96

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.

 DPP of Project Y = 3 + |-\$1,316,053.21| = 3.41 Years \$1,861,537.19 + |-\$1,316,053.21|

 DPP of Project Z = 4 + |-\$1,740,477.60| = 4.31 Years \$3,933,790.96 + |-\$1,740,477.60|

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