# Payback Period Method

Payback period method comes under the traditional or non-time value technique of appraising the investment proposals. The term pay-back refers to the period in which the project will generate the necessary cash to recoup the initial investment.

Even cash flows:  For example, if a project requires \$20,000 as initial investment and it will generate an annual cash inflow of \$5,000 for ten years, the pay-back period will be 4 years calculated as follows:

Pay-back period = Initial Investment / Annual cash inflows = \$20,000 / \$5,000 = 4 years.

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The annual cash inflow is calculated by taking into account the amount of net income on account of the asset or project before depreciation but after taxation. The income so earned if expressed as a percentage of initial investment, is termed as "Unadjusted rate of return". In the above case, it will be calculated as follows:

Unadjusted rate of return  = Annual returns / Initial investment * 100 = \$5,000 / \$20,000 * 100 = 25%

Uneven Cash flows:  In cases of uneven cash flows, the cumulative cash inflows will be calculated and by interpolation the exact pay-back period can be calculated. For example, if the project requires an initial investment of \$20,000 and the annual cash inflows for 5 years period are \$6,000, \$8,000, \$5,000, \$4,000 and \$4,000 respectively, the pay-back period will be calculated as follows:

 Year Cash inflows Cumulative Cash inflows 1 \$6,000 \$6,000 2 \$8,000 \$14,000 3 \$5,000 \$19,000 4 \$4,000 \$23,000 5 \$4,000 \$27,000

The above table shows that in 3 years, the project recovers \$19000. So, \$1000 is left out of the initial investment. In the 4th year, the cash inflow is \$4000. This means that the pay-back period is between the 3rd and 4th years, ascertained as follows:

Pay-back period = 3 years + \$1,000 / \$4,000 = 3.25 years or 3 years and 3 months.

Accept/Reject criterion:

A project will be accepted if its pay-back period is lesser than the cut-off rate pre-determined by the management. It would be rejected if the pay-back period is more than the cut-off rate. Among mutually exclusive or alternative projects, where the pay-back periods are lower than the cut-off period, the project with shorter pay-back period would be selected. In case there are budget constraints, the procedure would be to rank the projects in the ascending order of pay-back periods and select the first X number of projects which the budget provision permits.

Merits of Pay-back period:
• This method is very useful in evaluation of those projects which involve high uncertainty. Political instability, rapid technological development of cheap substitutes etc., are some of the reasons which discourage one to take up projects having long gestation period. Pay-back period method is useful in such cases.
• This method makes it clear that no profit arises till the pay-back period is over. This helps companies in deciding when they should start paying dividends.
• Simple to understand and easy to calculate.
• This method reduces the possibility of loss on account of obsolescence as the method prefers investment in short-term projects.

Demerits of Pay-back period:
• This method ignores the returns generated by a project after its pay-back period.
• This method does not take into account the time value of money.

Suitability:
• Firms suffering from liquidity crisis.
• Firms enhancing short-term earning performance.

Discounted Pay-back period method:

To overcome the de-merit of time-value being ignored, a more advanced method over the pay-back period method, called as discounted pay-back period method can be applied which considers the time value of money.

Example: A project with initial investment of \$20,000 and cash inflows of \$5,000 for 10 years, if discounted at 15%, the discounted pay-back period would be:

 Years Cash inflows PV factor @ 15% PV of Cash inflows Cumulative Cash inflows 1 \$5,000 0.8696 \$4,348.00 \$4,348.00 2 \$5,000 0.7561 \$3,780.50 \$8,128.50 3 \$5,000 0.6575 \$3,287.50 \$11,416.00 4 \$5,000 0.5718 \$2,859.00 \$14,275.00 5 \$5,000 0.4972 \$2,486.00 \$16,761.00 6 \$5,000 0.4323 \$2,161.50 \$18,922.50 7 \$5,000 0.3759 \$1,879.50 \$20,802.00

Balance to be recovered in the 7th year = 20,000 - 18,922.50 = \$1077.50 Payback period = 6 years + 1,077.50 / 2,161.50 = 6.5 years.