# Payback Period Formula – Capital Appraisal Method

The payback period formula is one of the capital appraisal methods used to understand whether a project is worthwhile. The question that the Payback Period answers is how long it will take to recoup your initial investment. If you, therefore, spend \$10,000 as an initial investment, the payback period method will help you calculate how long it will take to get the \$10,000 back and break even. Based on the payback period, an investment is more attractive the shorter its break-even time.

The Payback Period method is mainly an initial screening capital appraisal method and should not be used as the only method to make investment decisions. The reasons for that are explained below but for now, let’s see how the payback period is calculated and a couple of examples.

## Payback Period Formula and Calculation

The payback period has two variants of its formula, depending on whether project cash flows are stable and equal. What that means is that if you have a project with the same cash inflows during all periods, then we can use the first formula. On the other hand, if your cash flows are not the same, then the second approach is used.

### Formula and Calculation for Equal Cashflows

First of all, if a project’s yield equals cash inflows for all the years that it will last, then the formula is:

Payback Period = (Investment at Period 0)/(Cash Inflow per period)

Remember that the payback period calculates the time it takes to break even. For example, if you have a project that will initially cost you \$10,000 and you know that it will bring \$5,000 per year, then the payback period is two years (see table below).

TimeCash Flow
Period 0(\$10,000)
Period 1\$5,000
Period 2\$5,000

### Formula and Calculation for Unequal Cashflows

In the real world, you rarely find a project that brings the same revenue throughout its duration. You will therefore find it helpful to know how to calculate the payback period for more complex scenarios. An example might help:

The initial investment is again \$10,000, but the cash inflows are not the same for none of the three periods. The first year the project will generate \$3,000, the second \$6,000 and the third \$2,000.

You might have noticed that we will manage to break even somewhere within the third year. So the payback period is not precisely three years, but it’s 2.5 years.

TimeCash Flow
Period 0(\$10,000)
Period 1\$3,000
Period 2\$6,000
Period 3\$2,000

## Payback Period Examples

We have two more examples to illustrate why we should not use this method solely in capital appraisals. It can be used as an initial screening process, but it’s not advised to be used on its own. The internal rate of return or the net present value methods will give you a more robust analysis.

### Example One

We have the following scenario: an initial \$10,000 investment is required. We estimate the project will generate \$3,000 in year one, \$7,000 in year two and then \$200 residual cash inflows per year for three more years. The payback period is two years.

TimeCash Flow
Period 0(\$10,000)
Period 1\$3,000
Period 2\$7,000
Period 3\$200
Period 4\$200
Period 5\$200

### Example Two

Let’s see another example that helps us understand the most significant disadvantage of the payback period when used to rank investments. The initial investment in the example below is the same. The annual income generated differs, and the payback period is three years and two months.

It’s clear that if we had to use the payback period to choose one of these investments, we would pick the first since it has a lower payback period. However, having a second look can reveal that the second investment might take more time to break even, but the total present value is higher.

It will generate \$11,000 profit compared to the \$600 profit that the first investment will generate.

TimeCash Flow
Period 0(\$10,000)
Period 1\$3,000
Period 2\$3,000
Period 3\$3,000
Period 4\$6,000
Period 5\$6,000

## Payback Period vs IRR or ARR

It should be clear by now that the payback period method is not the most robust capital appraisal technique. Caution needs to be exercised, and it should never be used as the single capital appraisal method. It would help if you used the internal rate of return (IRR) or even the accounting rate of return (ARR) to supplement your analysis.

In particular, the IRRanswers a different question (the cost of capital required to break even). It considers the time value of money and considers the whole duration of the project. The IRR and does not stop when the project has generated enough profits to help us break even.

## Payback Period Advantages

However, while the payback period has disadvantages, it also has some advantages, which can be summarised as:

• By using the payback period, we get to choose projects that will help bring liquidity since faster breakeven ranks higher;
• The payback period is straightforward and can be used with all the inputs that are used for a NPV calculation; and
• We can hedge against the risk that long term projects bring due to the uncertainty that the future holds.

## Payback Period Disadvantages

A summary of the disadvantages of the payback period is as follows:

• The payback period does not account for the whole duration of the project; it stops at the point a project breaks even;
• It does not account for the time value of money. If you would like more information about using payback with discounted cash flows, check out our article; and
• It does not account for not quantitative characteristics (such as brand name or customer loyalty generation).