# Discounted Payback Period

It determines how long it will take for an investment's discounted cash flows to equal its initial cost

Author: Manu Lakshmanan
Manu Lakshmanan
Management Consulting | Strategy & Operations

Prior to accepting a position as the Director of Operations Strategy at DJO Global, Manu was a management consultant with McKinsey & Company in Houston. He served clients, including presenting directly to C-level executives, in digital, strategy, M&A, and operations projects.

Manu holds a PHD in Biomedical Engineering from Duke University and a BA in Physics from Cornell University.

Reviewed By: Himanshu Singh
Himanshu Singh
Investment Banking | Private Equity

Prior to joining UBS as an Investment Banker, Himanshu worked as an Investment Associate for Exin Capital Partners Limited, participating in all aspects of the investment process, including identifying new investment opportunities, detailed due diligence, financial modeling & LBO valuation and presenting investment recommendations internally.

Himanshu holds an MBA in Finance from the Indian Institute of Management and a Bachelor of Engineering from Netaji Subhas Institute of Technology.

Last Updated:October 31, 2023

## What Is the Discounted Payback Period?

A discounted payback period determines how long it will take for an investment's discounted cash flows to equal its initial cost. The rule states that investment can only be considered if its discounted payback covers its initial cost before the cutoff time frame.

I will briefly explain how the payback period functions to help you better understand the concept.

The payback period is the time it takes an investment to break even (generate enough cash flows to cover the initial cost). Certain businesses have a payback cutoff which is essential to consider when proceeding with investment projects.

This is why the payback period function is essential for companies. It enables firms to compare projects based on their payback cutoff to decide which is most worth it.

Suppose company XYX invested \$30,000 into a new operating machine that generates \$8,000 yearly for six years. The company XYX imposes a payback cutoff of four years. Should you accept this project?

Let's set up the cash flows as so:

Cash Flows
Years Cash Flow Payback Period
0 (-\$30,000)
1 \$8,000 \$30,000 - \$8,000 = \$22,000
2 \$8,000 \$22,000 - \$8,000 = \$14,000
3 \$8,000 \$14,000 - \$8,000 = \$6,000
4 \$8,000 \$6,000 / \$8,000 = 0.75
5 \$8,000 Not available after year 4
6 \$8,000 Not available after year 4

Looking at the year's column, you can see that it took 3.75 years for the investment to break even. Since the payback cutoff is four years, company XYX should accept this project!

In real-life scenarios, depreciation is considered as it is unlikely an operating machine would remain optimal for an extended period.

• Simple to understand
• Adjusts for uncertain cash flows in the future
• Biased for liquidity

• It does not account for the time value of money
• Requires arbitrary cutoffs
• Cash flows beyond the cutoff date are ignored
• Favors short-term projects over long-term ones that may be more profitable
• Ignores the risks that come with a project.

## Key Takeaways

• As part of capital budgeting, discounted payback periods determine which projects to take on.
• The DPP accounts for the time value of money and is, therefore, more accurate than standard payback periods.
• It calculates the time it will take to recover an investment based on observing the present value of the project's projected cash flows.
• A project or investment with a shorter discounted payback period will generate cash flows sooner, so the initial investment will be recovered sooner.

## Understanding the Discounted Payback Period

When deciding on which project to undertake, a company or investor wants to know when their investment will pay off, i.e., when the project's cash flows cover the project's costs.

This is especially useful because companies and investors frequently have to choose between multiple projects or investments. Knowing when one project will pay off versus another makes the decision easier.

It is calculated by taking a project's future estimated cash flows and discounting them to the present value. Therefore, we are comparing the investment's initial capital outlay.

The time it takes for the present value of future cash flows to equal the initial cost of a project indicates when the project or investment will break even. After that, cash flows will be greater than the initial cost.

The faster a project or investment generates cash flows to cover the initial cost, the shorter the discounted payback period. Generally, projects should only be accepted if the payback period is shorter than the cutoff time frame.

• Includes the time value of money
• Simple to understand
• Investments with negative NPV are not accepted
• Biased towards liquidity

• Investments with a positive NPV may be rejected
• Requires arbitrary cutoffs
• After the cutoff, cash flows are ignored
• Favors short-term projects over long-term ones that may be more profitable

## Discounted Payback Period Calculation

To calculate, you must go through two steps. To begin, we must discount (that is, bring to present value) the cash flows that will occur throughout the project's years.

PV = FV / (1+i)^n

Where,

• FV = Cash flows or payments expected to happen.
• i = Discount rate/interest rate.
• n = Number of periods.

Second, we must subtract the discounted cash flows from the initial cost figure to calculate. So, once we calculate the discounted cash flows for each project period, we can subtract those discounted cash flows from the initial cost until we reach zero.

Let's look at an example.
A project has annual cash inflows of \$4,500, \$5,100, \$5,900, and \$6,800, and a discount rate of 12 percent. What is the discounted payback period for these cash flows if the initial cost is \$8,000? What if it was \$14,000?

Let's set up the cash flows as so:

Cash Flows
Years Cash Flow Discounted Payback Period (DPP)
0 (-\$8,000)
1 \$4,500 PV = \$4,500 / (1.12)^1 = \$4,017.86
DPP = \$8,000 - \$4017.86 = \$3982.14
2 \$5,100 PV = \$5,100 / (1.12)^2 = \$4,065.69
DPP = \$3,982.14 / \$4,064.69 = 0.98
3 \$5,900 Already reached the initial cost, so this part is discarded.
4 \$6,800 Already reached the initial cost, so this part is discarded.

*I am dividing the cost of \$3,982.14 and the present value of \$5,100 in year two due to the cash flow being more significant than the remaining initial cost. This method gives us how much less than a year it takes to complete.

So, the discounted payback period would take 1.98 years to cover the initial cost of \$8,000.

Years Cash Flow Discounted Payback Period (DPP)
0 (-\$14,000)
1 \$4,500 PV = \$4,500 / (1.12)^1 = \$4,017.86
DPP = \$14,000 - \$4017.86 = \$9,982.14
2 \$5,100 PV = \$5,100 / (1.12)^2 = \$4,065.69
DPP = \$9,982.14 - \$4,065.69 = \$5,916.45
3 \$5,900 PV = \$5,900 / (1.12)^3 = \$4,199.50
DPP = \$5,916.45 - \$4,199.50 = \$1,716.95
4 \$6,800 PV = \$6,800 / (1.12)^4 = \$4,321.52
DPP = \$1,716.95 / \$4,321.52 = 0.40

It would take 3.40 years to cover the initial cost of \$14,000.

## Payback Periods Vs. discounted Payback Periods

Now that we know the payback period is the length of time for an investment to break even, you may ask, isn't that the same thing as the discounted payback period?

The answer is yes and no.

The discounted payback period involves using discounted cash inflows rather than regular cash inflows. It involves the cash flows when they occurred and the rate of return in the market.

From another perspective, the payback period is when an investment breaks even from an accounting standpoint. Discounted payback, in contrast, includes the time value of money, so it is viewed from a financial perspective.

Due to the discounting of cash flows, these two similar calculations may not yield the same result because of compound interest.

Projects with higher cash flows toward the end of their life will experience more significant discounting. As a result, the payback period may yield a positive result, whereas the discounted payback period yields a negative outcome.

Researched & Authored by Michael Rahme | LinkedIn

Reviewed and edited by James Fazeli-Sinaki | LinkedIn