# Pay back period explained with formula and example

## Definition

Payback period is one of the capital budgeting decision making techniques which can be defined as

“The minimum period required to earn back “the cash” that was invested initially.”

In other words it is the length of time during which cash flows generated from an investment will recover the initial cost of taking that investment.

For example an investment can be purchased with \$100. This investment will earn interest at 10% per year. The cost of initial investment will be recovered in 10 years i.e. 100 * 10% = \$10 per year and \$100 in 10 (10*10) years.

## Calculation & interpretation

Payback period has no formal formula. We are concerned with calculating the length of time during which initial cash investment is recovered.

• Identify and predict the cash inflows & outflows associated with the investment in question in respect of time.
• Add these cash flows until it equals to initial investment.
• Calculate the point of time (in respect of months or years) at which the cash inflows equal the initial cost of investment.
• Determine the “standard pay back period”. Standard or required pay back period determination is a SUBJECTIVE DECISION. In other words it does not involve formulas or scientific methods. It depends on experience, knowledge & requirements of the financial manager.
• Compare the calculated payback period with that of standard payback period.
• Make decision
• ACCEPT the project. If calculated payback period is less than standard payback period.
• REJECT the project. if calculated payback period is greater than standard payback period.

The method can best be understood by the example.

## Example

Suppose we have two investments A, B & C. Initial costs of investments are

• Investment A: \$10,000
• Investment B: \$ 5,000
• Investment C: \$ 8,000

Standard payback period is 5 years. Cash flows associated with investments is as follows.

 Year Investment A Investment B Investment C 1 2,000 500 1,000 2 4,000 500 1,000 3 (1,000) 500 1,000 4 5,000 500 1,000 5 2,000 500 2,000 6 2,000 500 2,000

#### Investment A

Investment “A” cash flows equal to its initial investment of \$ 10,000 at year 4 i.e. 2,000 + 4,000 – 1,000 + 5,000 = 10,000. By comparing 4 years with our standard payback period of 5 years, we can conclude that this investment shall be accepted since its payback period is less than standard payback period.

#### Investment B

Investment “B” cash flows never recovered their initial investment i.e. 500 + 500 +500 +500 +500 +500 = \$ 3,000. Calculation of length of time is out of question because investment is not covering the initial cash outflows. Therefore the investment shall be rejected.

#### Investment C

Investment “C” cash flows equal to its initial investment of \$ 8,000 in 6 years i.e. 1,000 + 1,000 +1,000 +1,000 +2,000 +2,000 = \$8,000. By comparing this calculated period with standard payback period of 5 years, we can make the decision that this investment shall be rejected since our pay back period is greater than standard pay back period i.e. 6 > 5.

• Payback period is simple & quick to calculate.
• As payback period is concerned with recovery of initial cash investment, it is used by the companies to make liquidity decisions. In other words decisions of huge quantity of short term investments are made by using this technique.
• The timing of costs & benefits are appreciated by this technique sine free cash flows are used for decision making instead of accounting profits. Accounting profits used the accrual concept for recording costs & benefits thus ignore the actual receipt & payment timings of such costs & benefits.

• Ignores the time value of money. In other words this technique does not realize the fact that “A dollar today is worth more than a dollar after one year.” This fact has extremely limited the usefulness of this technique. Therefore it is not more often for evaluating long term projects as the npv is used.
• Ignores risk associated with investments. Payback period does not realize the fact that “all investments are not equal due to their inherent risks. Some are more risky than others.” Again due to this fact the usefulness of this technique for evaluation long term projects is extremely limited.
• The decision making criteria is subjective. Payback period uses standard payback period for making comparisons and decision making. How standard payback period is determined? It depends on financial manager. There is no theory or scientific calculations involved therefore the decision making criteria is somewhat inferior.

In nutshell, for capital budgeting decisions payback period has severe deficiencies. However it can be used as a rough filtering technique for short listing the projects under question.