# Payback Period Calculator

Created by Bogna Szyk and Wei Bin Loo
Reviewed by Steven Wooding
Last updated: Jun 05, 2023

This payback period calculator is a tool that lets you estimate the number of years required to break even from an initial investment. You can use it when analyzing different possibilities to invest your money and combine it with other tools, such as the net present value (NPV calculator) or internal rate of return metrics (IRR calculator).

In this article, we will explain the difference between the regular payback period and the discounted payback period. You will also learn the payback period formula and analyze a step-by-step example of calculations.

## What is the payback period?

Imagine that you are going to invest $100,000 and purchase an apartment. You are going to rent it to tenants for$24,000 a year. How many years do you need for this investment to pay back?

The period from now to the moment when you will recover your investment is called the payback period. Intuitively, you can say that it is equal to the total investment sum divided by the annual cash inflow:

$\footnotesize {\rm PP} = \frac{I}{C}$

where:

• $\rm PP$ – Payback period in years;
• $I$ – Total sum you invested; and
• $C$ – Annual cash inflow – the money you earn.

In the apartment example, you could estimate the payback period with this equation:

$\footnotesize PP = \frac{\\text{100,000}}{\\text{24,000}} = 4.17\ \text{years}$

The situation gets a bit more complicated if you'd like to consider the time value of money formula (see time value of money calculator). After all, your 100,000 will not be worth the same after ten years; in fact, it will be worth a lot less. Every year, your money will depreciate by a certain percentage, called the discount rate. Unlike the regular payback period, the discounted payback period metric considers this depreciation of your money. The value obtained using the discounted payback period calculator will be closer to reality, although undoubtedly more pessimistic. If the cash flows are regular (each year, you gain the same amount of money), it's pretty easy to compute this metric. All you have to do is apply the following formula: $\footnotesize {\rm DPP} = \frac{-\ln(1 - I \times R / C)}{\ln(1 + R)}$ where: • $\rm DPP$ – Discounted payback period in years; • $R$ – Discount rate; • $I$ – Total sum you invested; and • $C$ – Annual cash inflow – the money you earn. You can check the difference between the PP and DPP of the apartment example. Let's assume a discount rate of 5%: \footnotesize \begin{align*} {\rm DPP} &= \frac{-\ln\left(1 - \\text{100,000} \times \frac{0.05}{ \\text{24,000}}\right)}{\ln(1 + 0.05)}\\[1em] &= 4.79\ \text{years} \end{align*} ## How to calculate payback period with irregular cash flows Now, suppose your project will not bring you a steady cash flow. Let's analyze the example with the apartment more closely. For instance, you can say that you will not be able to find long-term tenants for the first two years and will only assume15,000 of annual income. Additionally, during the fifth year, you will have to renovate the apartment and hence decrease your total profit to $10,000. If you assume a discount rate of 5%, what will be the discounted payback period? To answer this question, you need to follow the steps below. 1. First, you need to write down your cash flow for each year. We suggest you construct a table: Time Cash flow Initial investment$100,000

Year 1

$15,000 Year 2$15,000

Year 3

$24,000 Year 4$24,000

Year 5

$10,000 Year 6$24,000

Year 7

$24,000 Year 8$24,000

1. Then, you need to calculate the present value of each of these cash flows (see present value calculator). You should use the following formula:
$\footnotesize \qquad PV_i = \frac{C_i}{(1 + R)^i}$

where:

• $R$ – Discount rate – in this case, 5%;

• $PV_i$ – Present value of the cash flow in year $i$;

• $C_i$ – Future value of the cash flow in year $i$; and

• $i$ – The year, which is equal to zero at the moment of investing, then one for year 1, etc.

Again, put all of your results in a table.

Time

Cash flow

Present value

Initial investment

$100,000$100,000

Year 1

$15,000$14,286

Year 2

$15,000$13,605

Year 3

$24,000$20,732

Year 4

$24,000$19,745

Year 5

$10,000$7,835

Year 6

$24,000$17,909

Year 7

$24,000$17,056

Year 8

$24,000$16,244

1. In this step, find the cumulative value of your cash flows. You can find it by adding the amount of cash flow in year $i$ to the sum of all cash flows that occurred in the preceding years. Remember that the initial investment is actually an expense, so it should be considered a negative value in this step.

After you're finished with the calculations, create your final table with the results.

Time

Cash flow

Present value

Cumulative present value

Initial investment

$100,000$100,000

$-100,000 Year 1$15,000

$14,286$ -85,714

Year 2

$15,000$13,605

$-72,109 Year 3$24,000

$20,732$ -51,377

Year 4

$24,000$19,745

$-31,632 Year 5$10,000

$7,835$ -23,797

Year 6

$24,000$17,909

$-5,887 Year 7$24,000

$17,056$ 11,169

Year 8

$24,000$16,244

27,413 1. Look at the table above. You will break even at the moment when the cumulative present value will change from a negative to a positive number – in this case, sometime between years 6 and 7. To find the exact time, use the following discounted payback period formula: $\footnotesize \qquad DPP = X + Y / Z$ where: • $X$ – Year before which DPP occurs – in other words, the last year with a negative balance; • $Y$ – Cumulative cash flow in year $Y$ (expressed as a positive value); and • $Z$ – Discounted cash flow in the year following year $Y$. In our example, you have to input the following values: \footnotesize \qquad \begin{align*} DPP &= 6 + \\text{5,887} / \\text{17,056}\\ &= 6.35\ \text{years} \end{align*} 1. Oof, that was a lot of calculations! The discounted payback period can be estimated as 6.35 years for this specific investment. You can, of course, save yourself a lot of effort if you input all of the initial data directly into this payback period calculator and let it do all the work. Go ahead and try it! 🙂 💡 You might also be interested in our future value calculator. Bogna Szyk and Wei Bin Loo Discount rate % Initial investment
Annual cash flow
$Payback period yrs mos Discounted payback period yrs mos Irregular cash flow Year 1$
Year 2
$Year 3$
Year 4
$Year 5$
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