 # PayBack Period as a Capital Appraisal Method

Payback Period is one of the capital appraisal methods that can be 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 if it takes a shorter period of time to break even.

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 different formulas which are used depending on whether your cash flows are stable and equal throughout the duration of the project. What that means is that if you have a project with the same cash inflows during all periods, then the first formula can be used. 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 the project yield equal cash inflows for all the years that it will last, then the formula is simply:

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

Remember that the payback period calculates the time it takes to break even (in years, months or anything you are using to count the periods). 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 2 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 will rarely find a project that will bring the same amount of revenue throughout its duration. You will therefore find it useful 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 exactly 3 years but it’s 2.5 years.

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

## Payback Period Examples

We will use two more examples to illustrate why the payback period should not be the only method that you will use to appraise a project. It can be used as an initial screening process but it’s not advised to be used on it’s own. The internal rate of return or the net present value methods will give you a more robust analysis.

### Payback Period Example 1

We have the following scenario: An initial \$10,000 investment is required which will bring \$3,000 in the first year, \$7,000 in the second year and \$200 residual cash inflows per year for three more years. It’s clear that the the payback period is 2 years.

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

### Payback Period Example 2

Now let’s see another example that can help us understand what’s the biggest disadvantage of the payback period when it’s used to rank investments (from the most attractive to the least attractive). The initial investment in the example below are the same. The annual income generated differs and the payback period is 3 years and 2 months.

It’s clear that if we had to use the payback period to choose one of the 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 a total of \$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 and should not be used on it’s own. The internal rate of return or even the accounting rate of return should be used to supplement your analysis.

In particular, the internal rate of return answers a different question (the cost of capital that is required to break even) but it takes into account the time value of money and it also takes into account the whole duration of the project and does not stop when the project has generated enough profits to help us break even.

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

• By using the payback period, we get to choose projects that will help us bring liquidity since the earliest a project breaks even, the highest it gets ranked based on the payback period.
• The payback period is very straightforward and can be used with all the inputs that are used for a simple NPVcalculation.
• By using the payback period, we hedge against the risk that the long term projects bring due to the uncertainty that the future has.