Fri. Aug 12th, 2022

Dec 6, 2021

# Payback Period

Payback period is the length of time an investment reaches a breakeven point.

An investor will ask himself the question of what are the investments that will allow him to recover his investment as quickly as possible. It is therefore a significant indicator. It allows the company to orient its decision-making in the investments it intends to make.

### Payback Period formula

Payback period = Initial investment / Cash flow per year

or

Payback Period = (p – n)÷p + ny
= 1 + ny– n÷p (unit:years)

Where:

• ny= The number of years after the initial investment at which the last negative value of cumulative cash flow occurs.
• n= The value of cumulative cash flow at which the last negative value of cumulative cash flow occurs.
• p= The value of cash flow at which the first positive value of cumulative cash flow occurs.

This formula can only be used to calculate the soonest payback period; that is, the first period after which the investment has paid for itself. If the cumulative cash flow drops to a negative value some time after it has reached a positive value, thereby changing the payback period, this formula can’t be applied. This formula ignores values that arise after the payback period has been reached.

Additional complexity arises when the cash flow changes sign several times; i.e., it contains outflows in the midst or at the end of the project lifetime. The modified payback period algorithm may be applied then.

The sum of all of the cash outflows is calculated.
The cumulative positive cash flows are determined for each period.
The modified payback is calculated as the moment in which the cumulative positive cash flow exceeds the total cash outflow.

### There are two types of payback : simple and discounted

##### Simple

Simple payback is defined as the number of periods (years, months, weeks, etc.) to recover the initial investment and is calculated by adding the amounts of cash flows earned, period by period, until this sum equals the value of the initial investment.

##### Discounted

Discounted payback is calculated from the cash flow, the result between income and expenses. But then, a discount rate is added to the calculation that will correct the values ​​for the period. This rate is usually the minimum attractiveness rate.

### How to Calculate the Payback Period in Excel

While is it possible to have a single formula to calculate the payback, it is better to split the formula into several partial formulas. This way, it is easier to audit the spreadsheet and fix issues.

##### Steps to calculate the payback in Excel:

1. Enter all the investments required. Usually, only the initial investment.
2. Enter all the cash flows.
3. Calculate the Accumulated Cash Flow for each period
4. For each period, calculate the fraction to reach the break even point. Use the formula “ABS”
5. Count the number of years with negative accumulated cash flows. Use the formula “IF”
6. Find the fraction needed, using the number of years with negative cash flow as index. Use the formula “INDEX”
7. To get the exact payback period, sum the number of years with negative accumulated cash flow and the corresponding fraction.

### The limits of the Payback Period

The limits of the payback period are rather severe, even prohibitive. The most important is related to how to take into account financial flows. These are never updated. In other words, every financial flow has the same importance, even the most distant, although the most hypothetical. The time value is totally ignored.

The second limit is the setting of the maximum payback. Why, for example, choose a maximum payback period of two years instead of four? On what objective basis is the payback decided? The most distant financial flows are also ignored. However, many fixed assets are sold at the end of their life, generating a significant flow. The latter is likely to be excluded from the calculations by arbitrarily setting a maximum calculation period. Potentially profitable investments can be excluded from any analysis by means of this method.

Thirdly, the indicator does not take into account the time value of money . When comparing projects with the same payback periods, but with different payment schemes, the fact is ignored that the inflow of funds in the first periods of the project is not equal to the inflow of subsequent periods. The principle is excluded that it is always preferable to receive funds as early as possible.

The indicator does not take into account all cash receipts after the date of full reimbursement of initial costs. When comparing projects with the same payback period, the amount of cash inflow after the payback period for projects is ignored.

When choosing from several investment projects, if we proceed only from the payback period of investments, the amount of profit created by the projects will not be taken into account.

## Examples

##### 1. Consider an example of an investment of \$ 100,000 euros. At the same time, we assume a gain of \$ 20,000 per year. Find the payback time!

The formula becomes \$ 20,000 euros / \$ 100,000 euros = 20%, or 5 years.

Thus, by investing 100,000 euros, it will take 5 years to find your money.

In conclusion, return on investment is not the only important ratio in the life of a business. Quite simply by starting with the more complex break even point to calculate.

##### 2. In May 20XX, famous electronics maker Apple announced that it had bought Beats for \$ 3 billion, a company specializing in headphones and audio equipment. How many years will have to pass before this investment pays off? How to calculate the payback time? Formula & payback time rules, with a digital example. How many years must we wait before the cumulative financial flows exceed the initial investment?

The payback time formula, in its most classic version, therefore consists of establishing the relationship between the initial investment and the financial flows perceived on average, over a given period:

Return on investment time formula:

Payback time (y) = Initial investment / Cash flow per year

If, in practice, the flows are not perceived at the end of the year, but along it, in a linear fashion, the investor can more precisely calculate the payback time. The cumulative flows in the first year and the second year amount to € 60,000.

There is therefore only € 40,000 left to obtain, when the third year begins, for the investment to be profitable. The third year generates a total of € 60,000 in flows. It takes 40,000 € * 365 / 60,000 € = 243 additional days to reach the payback time. In total, it is therefore necessary to wait 2 years and 243 days for this investment to be reimbursed.

##### 3. If Company Apple has a project requiring an initial cash outlay of \$3,000. The project is expected to return \$1,000 each period for the next five periods, and the appropriate discount rate is 4%. The discounted payback period calculation begins with the -\$3,000 cash outlay in the starting period. The first period will experience a +\$1,000 cash inflow. Calculate the discounted payback period!

Using the present value discount calculation, this figure is \$1,000/1.04 = \$961.54. Thus, after the first period, the project still requires \$3,000 – \$961.54 = \$2,038.46 to break even. After the discounted cash flows of \$1,000 / (1.04)2 = \$924.56 in period two, and \$1,000/(1.04)3 = \$889.00 in period three, the net project balance is \$3,000 – (\$961.54 +\$924.56 + \$889.00) = \$224.90.

Therefore, after receipt of the 4th payment, which is discounted to \$854.80, the project will have a positive balance of \$629.90. Therefore, the discounted payback period is sometime during the fourth period.

##### 4. A firm may decide to invest in an asset with an initial cost of \$1 million. Over the next five years, the firm then receives positive cash flows that diminish over time. What is the payback period?

The initial investment is fully offset by positive cash flows somewhere between periods 2 and 3.

Photo credit: Pxhere