# Discounted Payback Period

The discounted payback period is referred to the time it takes to recoup an investment from the revenue or free cash flow it generates by using the value of those cash flows in today's currency by discounting them using an appropriate discount rate.

In some instances analysts and operation managers prefer to use the discounted payback period as a more accurate measure as this discounts the revenue or free cash flows to current value, this is especially useful when the payback period is longer and there are many cash flows out in future years or cash flows are irregular throughout the years.

Just like the regular payback period, this is a common investment evaluation and ranking measure used to gauge how quickly plant and equipment or assets purchased by businesses can repay themselves.

### Discounted present value formula

The following formula allows us to discount an amount of money that will be received in the future to today's currency value.**PV = FV / (1+r)**

^{n}Formula legend:

**PV:**present value of money

**FV:**future value of money

**r:**discount rate yearly

**n:**Number of years out in the future

### Example of calculating payback

As an example a company is looking to purchase a piece of plant for US$500 000 which will add production capacity and create the following additional cash flows:Discounting the original figures (FV) at a discount rate of 10% using the formula above we obtain the figures on the right (PV):

**FV Year1:**$50 000,

**PV=**$45 454

**FV Year 2:**$200 000,

**PV=**$165 289

**FV Year 3:**$200 000,

**PV=**$150 262

**FV Year4:**$250 000,

**PV=**$170 753

In this example the payback period is 3.81 years, calculated by adding up the Present value (PV) revenues from year one to year three this totals: US$361 005, This means that by the end of year three US$361 005 has been recouped and somewhere in the fourth year the investment is fully paid back. At the start of the fourth year US$138 995 is left to recoup the investment, to find out at what point in the fourth year the investment is fully paid off you divided US$138 995 by US$170 753 and this is 0.81, thus the payback period is 3.81

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