# Payback period and discounted payback period

## Definition – Payback period

Payback is the period required by the project to recover its invested funds back in the form of cash. In other words, it is the period in which the project just breaks even. For example, a business wants to invest in a project that will cost \$3,000. The project will yield returns of \$1,000 per year. So, the payback period will be 3 years (3,000/1,000).

Why does management use the Payback Period? When a business invests in a project, management wants to measure how quickly it can recover its investment. Let’s suppose, you have money, and you want to invest in a profitable project. The first thing that you will consider is the time it takes to recover your investment. Remember that the longer it takes the project to return the original investment, the greater the risk will be. However, if the project generates the original investment quickly, the risk of loss will be much lower. Thus, management can use the payback period to identify suitable projects which will generate the returns quickly.

### Payback Period – Calculation

There are two ways to calculate the payback period of the project depending upon the nature of cash flows from the project. These can either be:

• Payback period – Constant Annual Cashflow
• Payback period – Uneven Annual Cashflows

### Payback Period – Constant Annual Cashflow

When the cash flows are constant each year, the payback period is found by dividing the initial investment by the annual cash flow.

Payback period = Initial investment / Annual cashflow

#### Example

Let us take an example, if we buy a machine for \$2,000,000 and rent it out, we get equal annual rent of \$400,000. The payback period is calculated as:

Payback period = \$2,000,000 / \$400,000

Payback period = 5 years

### Payback Period – Uneven Annual Cashflow

When the annual cash flows are uneven, the payback period is found by a tabular approach. We need to make a cumulative column and see where the cumulative figure turns from negative into ‘0’. That is the payback period of the project. However, to find where exactly the payback period occurs when payback occurs between two years, we need to divide the cumulative figure that is just before the positive figure by the cash flow after which the cumulative figure becomes positive.

The payback period occurs somewhere between the 4th and 5th year. However, to find where exactly the payback period occurs when payback occurs between two years, we need to divide the cumulative figure that is just before the positive figure (5,000) by the cash flow after which the cumulative figure becomes positive (30,000).

Payback Period = 4 years + (5,000/30,000) years

Payback Period = 4 years + 0.17 years

Payback Period = 4.17 years

OR,

Payback Period = 4 years + 0.17 *12 months

Payback Period = 4 years + (5,000/30,000) years

Payback Period = 4 years & 2 months.

## Definition Discounted Payback Period

A more sophisticated approach to payback period calculation is discounted payback period.

Discounted Payback Period is the period required by the project to recover invested funds back in the form of cash after considering the time value of money.

Determination of Discounted Payback Period: There are two steps to determine the payback period using discounted payback period method:

1. Convert the future cash flows into present value using an appropriate discount rate.
2. Determine the payback period using the tabular approach (same as the simple payback period).

### Example – Discounted Payback Period

Let us take an example of a company, Foster Digitals Limited. The management of a company is evaluating a new investment project. The cost of capital has been estimated at a rate of 10%. The life of the project is 4 years at the end of which the project will be sold as scrap for \$20,000. The following cash flows are expected to arise in this period (including the residual proceeds from the project).

Thus, the discounted payback period lies somewhere between the 3rd and 4th year.
To find where exactly the payback period exists, we need to divide the cumulative figure that is just before the positive figure (78,285) by the cash flow after which the cumulative figure becomes positive (81,960).

Discounted Payback Period = 3 years + (78,295/81,960) years

Discounted Payback Period = 3 years + 0.955 years

Discounted Payback Period = 3.955 years

Or,

Discounted Payback Period = 3 years + (0.955 years *12) Discounted Payback Period = 3 years and 11 months approximately.