# What is a Discounted Payback Period?

The term "discounted payback period" refers to a method used in capital budgeting to determine the profitability of a project. Managers of a firm can use it to make a decision regarding whether to take on a certain project. It basically calculates the time it would take for a project to generate enough cash inflow to break even, taking the time value of money into consideration.

A simple payback period calculates the time it would take for a project to break even from the moment the firm undertakes the initial expenditure. For example, a company pays $10,000 US Dollars (USD) at the outset of a project that is predicted to produce the following annual cash inflows in its first five years: $2,000 USD, $2,500 USD, $3,000 USD, $3,500 USD and $4,000 USD. At the end of the third year, the project will have generated $7,500 USD. It takes 0.71 year to recover the last $2,500 USD (because $2,500 USD / $3,500 USD = 0.71), so the payback period of this project is 3.71 years.

The simple payback period, while useful, has the problem of ignoring the time value of money. The concept of time value of money dictates that a certain amount of money is more valuable today than the same amount of money in the future because of inflation and the possibility of investing the money today to generate a larger amount of money in the future. The discounted payback period solves this problem by discounting the future cash inflows to calculate their present values before determining the payback period.

Assume that the required return of the project is 12 percent, so each cash flow is discounted by 12 percent a year. The project's predicted cash flows have the following present values: $1,785.71 USD (from $2,000/1.12), $1,992.98 USD (from $2,500 USD/1.12^{2}), $2,135.34 USD (from $3,000 USD/1.12^{3}), $2,224.31 USD (from $3,500 USD/1.12^{4}) and $2,269.71 USD (from $4,000 USD/1.12^{5}). At the end of the fourth year, the project will have generated $8,138.34. The project will have recovered the rest of the initial expenditure in 0.82 year (because $1,861.66 USD / $ 2,269.71 USD = 0.82), so the discounted present value for this project is 4.82.

Discounted cash flows are always smaller than non-discounted cash flows, so discounted payback period is always longer than simple payback period. Discounted payback period solves one problem with simple payback period, but it still has a problem. It ignores cash flows beyond the payback period, so a manager might reject long-term projects that are profitable in later years if he or she uses discounted payback period as a basis for his or her decision.

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