# Discounted Payback Period

One of the major disadvantages of simple payback period is that it ignores the time value of money. To counter this limitation, an alternative procedure called discounted payback period may be followed, which accounts for time value of money by discounting the cash inflows of the project.

## Formulas and Calculation Procedure

In discounted payback period we have to calculate the present value of each cash inflow taking the start of the first period as zero point. For this purpose the management has to set a suitable discount rate. The discounted cash inflow for each period is to be calculated using the formula:

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

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

Usually the above formula is split into two components which are actual cash inflow and present value factor ( i.e. 1 / ( 1 + i )^n ). Thus discounted cash flow is the product of actual cash flow and 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 actual cash flows. The cumulative cash flow will be 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;
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 won't be applicable here since it is extremely unlikely that discounted cash inflows will be even.

The calculation method is illustrated in the example below.

## Decision Rule

If the discounted payback period is less that the target period, accept the project. Otherwise reject.

## 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

Step 1: 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 Value FactorPV$1=1/(1+i)n Discounted Cash FlowCF×PV$1 Cumulative DiscountedCash 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

Step 2: Discounted Payback Period = 5 + |-106,462| / 320,785 ≈ 5.32 years