# Discounted Payback Period

Discounted payback period is a variation of payback period which uses discounted cash flows while calculating the time an investment takes to pay back its initial cash outflow. One of the major disadvantages of simple payback period is that it ignores the time value of money. To counter this limitation, discounted payback period was devised, and it accounts for the time value of money by discounting the cash inflows of the project for each period at a suitable discount rate.

## Calculation

In discounted payback period we have to calculate the present value of each cash inflow. For this purpose the management has to set a suitable discount rate which is usually the company's cost of capital . The discounted cash inflow for each period is then calculated using the formula:

 Discounted Cash Inflow = Actual Cash Inflow (1 + i)n

Where,
i is the discount rate; and
n is the period to which the cash inflow relates.

Sometimes, the above formula may be split into two components which are: actual cash inflow and present value factor i.e. 1 / (1 + i)n. Discounted cash flow is then the product of actual cash flow and the present value factor.

The rest of the procedure is similar to the calculation of simple payback period except that we have to use the discounted cash flows as calculated above instead of nominal cash flows. Also, the cumulative cash flow is replaced by cumulative discounted cash flow.

 Discounted Payback Period = A + B C

Where,
A = Last period with a negative discounted cumulative cash flow;
B = Absolute value of discounted cumulative cash flow at the end of the period A; and
C = Discounted cash flow during the period after A.

Note: In the calculation of simple payback period, we could use an alternative formula for situations where all the cash inflows were even. That formula is not applicable here since it is extremely unlikely that discounted cash inflows will be even.

%
periods

The calculation method is illustrated through the example given below.

## Decision Rule

A shorter discounted payback period indicates lower risk. Given a choice between two investments having similar returns, the one with shorter payback period should be chosen. Management might also set a target payback period beyond which projects are generally rejected due to high risk and uncertainty.

Often, the decision may not be an easy one though. For example, where a project with higher return has a longer payback period thus higher risk and an alternate project having low risk but also lower return. In such cases the decision mostly rests on management's judgment and their risk appetite.

## Example

An initial investment of \$2,324,000 is expected to generate \$600,000 per year for 6 years. Calculate the discounted payback period of the investment if the discount rate is 11%.

### Solution

Prepare a table to calculate discounted cash flow of each period by multiplying the actual cash flows by present value factor. Create a cumulative discounted cash flow column.

 Yearn Cash FlowCF Present ValueFactorPV\$1=1/(1+i)n DiscountedCash FlowCF×PV\$1 CumulativeDiscountedCash Flow 0 -2,324,000 1.0000 -2,324,000 -2,324,000 1 600,000 0.9009 540,541 -1,783,459 2 600,000 0.8116 486,973 -1,296,486 3 600,000 0.7312 438,715 -857,771 4 600,000 0.6587 395,239 -462,533 5 600,000 0.5935 356,071 -106,462 6 600,000 0.5346 320,785 214,323

Discounted Payback Period
= 5 + |-106,462| ÷ 320,785
= 5 + 106,462 ÷ 320,785
≈ 5 + 0.33
≈ 5.33 years

Advantage: Discounted payback period is more reliable than simple payback period since it accounts for time value of money. It is interesting to note that if a project has negative net present value it won't pay back the initial investment.

Disadvantage: It ignores the cash inflows from project after the payback period. An attractive project having lower initial inflows but higher terminal cash flows might be rejected.