 # Discounted Payback Period Formula – With Examples

The discounted payback period formula is the same as that simple payback period method (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 their present value.

We can calculate the payback period or the time that it takes for a project to break even. We can account 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 four years and will bring the following profits during each of these years:

• First Year =  \$7,000
• Second Year =  \$9,000
• Third Year =  \$4,000
• Forth Year = \$12,000

The company believes that the cost of capital 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 we will undertake.

## 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 – Discounted Cash Flow

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 four years, so n spans from zero to four).

### Second Step – Cumulative Discounted Cash Flow

Calculate the cumulative discounted cash flows until we get a cumulative cash flow number greater than zero.

### Third Step – First Positive Number

When we get the first positive number, we know that the project has started bringing profits. From this point, we can calculate the discounted payback period. We then work out how many months from this last period we need to add to reach zero. We are trying to find the point where there is zero profit (neither a loss nor a profit).

### Payback Period Example

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

TimeCash FlowDiscounted 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

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

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, three years and five 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 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 benefits:

• 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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