The payback period formula is one of the methods used to analyse investment projects. It’s time that needed to reach a break-even point, i.e. a period of time in which the cost of investment is expected to be covered with cash flows from this investment.

Payback period (PP) is not used to understand whether an investment is profitable or not. Payback period is often used to compare investment projects and decide which project will pay off in the shortest time.

### How to calculate payback period?

Payback period can be calculated by dividing an initial investment by annual cash flow from a project. The result is the number of years necessary to return the initial cost of the investment. Naturally, this number will not always be a whole number.

$Payback\;period = \frac{I}{CF}$

Where I is an initial investment (the amount of money that has been invested at the beginning) and CF is cash flow per period.

This formula can only be used if the cash flows are even. If the cash flows are uneven you can use the following formula:

$Payback\;period = A + \frac{B}{C}$

Where A is the last period where the cumulative cash flow is negative, B is an absolute value of cumulative cash flow at the end of the period A and C is the total cash flow during the period after A.

This formula is explained in example 3.

### Decision making process

Based on this method alone, you can make only a subjective decision whether to invest in a given project. The payback period of a given project is compared to the target payback period or to an average payback period from similar projects in the same industry.

If:

• Payback period of a project < payback period of similar projects -> invest,
• Payback period of a project < payback period of similar projects -> don’t invest,
• Payback period of a project = payback period of similar projects -> other factors should decide whether to invest or not, for example, the risk factor.

A longer payback period means that:

• The money will be frozen for a longer period.
• An increased risk of projects with a longer payback period. Benefits generated by this investment in the long term have a greater risk than benefits achieved in a shorter period.
• The longer the payback period, the lower the present value of money invested.
• It is worth considering the costs of lost opportunities because possibly two short-term investments made in the same or similar payback period will be more effective than one long-term one.

### Examples of payback period calculations

Example 1. Let’s say you plan to invest in a project that requires an initial investment of $10,000. You expect that the project will generate$2,000 annually for 10 years.

The payback period is then $10,000/$2,000 = 5 years.

That means that for the first 5 years the project will only cover the investment costs, while for the next 5 years it will bring $2,000 of “pure” profit. Example 2. Let’s say you consider buying a new machine for your factory. Machine A costs$10,000, machine B costs $15,000. Machine A generates$2,500 annually and machine B generates $3,500 annually. If all other criteria are equal, which machine should you buy? • Machine A payback period =$10,000/$2,500 = 4 years • Machine B payback period =$15,000/$3,500 = 4.29 years Therefore, you should buy machine A because the payback period is shorter. Example 3. Company ABC invests into a new project. The initial investment is$40,000. The investment is expected to generate: $17,000 in year 1;$22,000 in year 2; $24,000 in year 3;$16,000 in year 4.

What is the payback period of this project?

 Year Cash Flows Cumulative cash flows 0 -$40,000 -$40,000 1 $17,000 -$23,000 2 $22,000 -$1,000 3 $24,000$23,000 4 $16,000$39,000
• The last year where the cumulative cash flow is negative is year 2.
• The absolute value of cumulative cash flow at the end of year 2 is $1,000. • The total cash flow during the period after year 2 is$24,000.
$Payback\;period = 2 + \frac{1,000}{24,000} = 2.042$

Which means the payback period is 2.042 years or 2 years and 15 days (0.42×365=15 days).