Payback Period (Definition, Formula)

Payback Period Definition

Payback period can be defined as period of time required to recover its initial cost and expenses and cost of investment done for project to reach at time where there is no loss no profit i.e. breakeven point.

source: Lifehacker.com.au

The above article notes that Tesla’s Powerwall is not economically viable for most people. As per the assumptions used in this article, Powerwall’s payback ranged from 17 years to 26 years. Considering Tesla’s warranty is only limited to 10 years, the payback period higher than 10 years is not ideal.

Payback Period Formula

Payback period formula is one of the most popular formulas used by investors to know how long it would generally take to recoup their investments and is calculated as the ratio of the total initial investment made to the net cash inflows.

Steps to Calculate Payback Period

The first step in calculating the payback period is determining the initial capital investment and
The next step is calculating/estimating the annual expected after-tax net cash flows over the useful life of the investment.

Calculation with Uniform cash flows

When cash flows are uniform over the useful life of the asset then the calculation is made through the following formula.

Payback period Formula = Total initial capital investment /Expected annual after-tax cash inflow

Let us see an example of how to calculate the payback period when cash flows are uniform over using the full life of the asset.

Example:

A project costs $2Mn and yields a profit of $30,000 after depreciation of 10% (straight line) but before tax of 30%. Lets us calculate the payback period of the project.

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Profit before tax $ 30,000

Less: Tax@30%(30000*30%) $ 9,000

Profit after tax $ 21,000

Add: Depreciation(2Mn*10%) $ 2,00,000

Total cash inflow $ 2,21000

While calculating cash inflow, generally depreciation is added back as it does not result into cash out flow.

Payback Period Formula = Total initial capital investment /Expected annual after-tax cash inflow

= $ 20,00,000/$2,21000 = 9 Years(Approx)

Calculation with Nonuniform cash flows

When cash flows are NOT uniform over the use full life of the asset then the cumulative cash flow from operations must be calculated for each year. In this case, the payback period shall be the corresponding period when cumulative cash flows are equal to the initial cash outlay.

In case, the sum does not match, then the period in which it lies should be identified. After that, we need to calculate the fraction of the year that is needed to complete the payback.

Example:

Suppose ABC ltd is analyzing a project which requires an investment of $2,00,000 and it is expected to generate cash flows as follows

Year	Annual cash inflows
1	80,000
2	60,000
3	60,000
4	20,000

In this cash payback period can be calculated as follows by calculating cumulative cashflows

Year	Annual cash inflows	Cumulative Annual cash inflows	Payback period
1	80,000	80,000
2	60,000	1,40,000(80,000+60,000)
3	60,000	2,00,000(1,40,000+60,000)	In this Year 3 we got initial investment of $ 2,00,000 so this is the pay back year
4	20,000	2,20,000(2,00,000+20,000)

Suppose, in the above case, if the cash outlay is $2,05,000 then pa back period is

Year	Annual cash inflows	Cumulative Annual cash inflows	Payback period
1	80,000	80,000
2	60,000	1,40,000(80,000+60,000)
3	60,000	2,00,000(1,40,000+60,000)
4	20,000	2,20,000(2,00,000+20,000)	The payback period is between 3 and 4 years

Since up to three years a sum of $2,00,000 is recovered, the balance amount of $ 5,000($2,05,000-$2,00,000) is recovered in a fraction of the year which is as follows.

Forgetting $20,000 additional cash flows the project is taking complete 12 months. So for getting additional of $ 5,000($2,05,000-$2,00,000) it will take (5,000/20,000) 1/4^th Year. i.e 3 months.

So, the project payback period is 3 years 3 months.

Advantages

It is easy to calculate.
It is easy to understand as it gives a quick estimate of the time needed for the company to get back the money it has invested in the project.
The length of the project payback period helps in estimating the project risk. The longer the period, the riskier the project is. This is because the long-term predictions are less reliable.
In the case of industries where there is a high obsolescence risk like software industry or mobile phone industry short payback periods often become determining a factor for investments.

Disadvantages

The following are the disadvantages of the payback period.

It ignores the time value of money
It fails to consider the investment total profitability (I.e it considers cash flows from the initiation of the project until the payback period and fails to consider the cash flows after that period.
It may cause company to place importance on projects which are short payback period thereby ignoring the need to invest in long-term projects( i.e A company cannot just determine a project feasibility only based on the number of years in which it is going to give your return back, there are number of other factors which it does not consider)
It does not take into account the social or environmental benefits in the calculation.

Payback Reciprocal

Payback reciprocal is the reverse of the payback period and it is calculated by using the following formula

Payback reciprocal = Annual average cash flow/Initial investment

For example, a project cost is $ 20,000 and annual cash flows are uniform at $4,000 per anum and the life of asset acquire is 5 years then the payback period reciprocal will be as follows.

$ 4,000/20,000 = 20%

This 20% represents the rate of return the project or investment gives every year.