# Discounted Payback Period Method – Calculation with Examples

The discounted payback period method is exactly the same as that simple payback period method (which was explained in a different  post) apart from one thing. The discounted payback period method accounts for the time value of money. In other words, it allows us to discount the future cash inflows (or outflows) and calculate the present the value of them.

By doing that, we can calculate the payback period or the time that it takes for a project to break even by correctly accounting for the fact that having \$1 now does not have the same value as having \$1 in 5 years from now.

## Discounted Payback Period Formula & Calculation

As explained above, the discounted payback period is used to calculate the time that it takes for a project to bring in enough profits to cover the initial investment (and other subsequent costs) or put it differently, how many years it takes to break even and recoup the initial investment.

Trying to give a single formula will complicate things but an example will help us understand how the payback period is calculated. Let’s assume that company ABC has the option to invest in a project that will initially cost \$20,000. The project will run for 4 years and will bring the following profits during each one of these four years.

Year 1 =  \$7,000

Year 2=  \$9,000

Year 3=  \$4,000

Year 4= \$12,000

The company believes that the cost of capital that should be used to discount these cash flows is 10% since that’s the interest rate the bank charges Company ABC for the loan facility.

Company ABC uses the discounted payback period method (among other methods) to rank potential projects and choose the ones that will be undertaken.

## Discounted Payback Period Example

Using the example explained above, we will need to perform the following steps to calculate the discounted payback period.

-First Step : Calculate the discounted cash flow for each period by using the following formula :

Discounted Cash flows =  (Cash flows)/ (1+r)^n

where r is the cost of capital or 10% and n is the time (for this example we have 4 years so n spans from zero to four).

-Second Step: Calculate the cumulative discounted cash flows until we get a cumulative cash flow number that is greater than zero

-Third Step: When we get the first positive number we know that the project has started bringing profits so the discounted payback period can be now calculated. What we need to do is workout how many months from this last period we need to add in order for the project to make zero profit (neither a loss nor a profit).

Let’s see the above steps by using the example already provided.

Time Cash Flow Discounted Cash FlowsCumulative Cash flows
Period 0(\$20,000)(\$20,000)(\$20,000)
Period 1\$7,000\$6,364

(\$13,636)
Period 2\$9,000\$7,438
(\$6,198)
Period 3\$4,000\$3,005(\$3,193)
Period 4\$12,000\$8,196\$5,003

What we can see from the table above is that during the last period the cumulative cash flows become positive. We therefore know that the discounted payback period is somewhere between the third and the fourth period.

In order to find exactly what’s the discounted payback period is, we do the following simple math:

Discounted Cash flows for Last period = \$8,196

Cumulative Cash flows for last period with negative number = \$3,193

We will need the following number of months from the last period to break even:

Number of months = (3,193)/(8,196/12)= around 5 months. The discounted payback period is therefore 3 years and 5 months.

## Discounted Payback Period vs Simple Payback Period

As already noted, the difference between the discounted payback period method and the simple payback method is the fact that we can discount the cash flows and account for the time value of money which as explained above is the fact that having one dollar today is not the same as having one dollar in one year from now.

Apart from that, these two methods are exactly the same and have the same advantages and disadvantages.

## Advantages of the Discounted Payback Period

In line with the advantages of the simple payback period, the discounted payback period has the following advantages:

• It is an enhancement when compared to the simple payback period method since it accounts for the time value money
• It’s a simple and easy way to screen a large number of projects and discard projects that take time to bring in some profits.

## Disadvantages of the Discounted Payback Period

• The discounted payback period also ignores what happens after the project has broken even. There is therefore a risk that we will reject projects that take more time to recoup our investment but will have significantly positive cash inflows after that.
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