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Discounted Payback Period Calculator.

Calculates the number of years it takes for an investment's discounted cash flows to recover the initial outlay, accounting for the time value of money.

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Your inputs

How it works

  1. 1

    Convert the discount rate to a decimal by dividing by 100.

  2. 2

    Calculate the present value factor for each year: 1 / (1 + r)^n.

  3. 3

    Sum the discounted cash flows year by year until the cumulative sum equals or exceeds the initial investment.

  4. 4

    The payback period is the number of years needed to reach that point.

ceil(log(1 / (1 - (initial_investment * (discount_rate/100) / annual_cash_flow))) / log(1 + (discount_rate/100)))

Frequently asked questions

What is the difference between payback period and discounted payback period?

The regular payback period ignores the time value of money, while the discounted payback period discounts future cash flows to present value, giving a more accurate measure of investment recovery.

What if the annual cash flow is not constant?

This calculator assumes a constant annual cash flow. For variable cash flows, you would need to sum the discounted cash flows individually each year.

What does a discounted payback period of 0 mean?

It means the initial investment is recovered immediately, which is unlikely unless the investment generates cash flow in the first period that exceeds the initial outlay.

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Results

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Discounted Payback Period

6years

Cumulative Discounted Cash Flow at Payback108 881,52$
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Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Calculates the number of years it takes for an investment's discounted cash flows to recover the initial outlay, accounting for the time value of money.

  1. Convert the discount rate to a decimal by dividing by 100.
  2. Calculate the present value factor for each year: 1 / (1 + r)^n.
  3. Sum the discounted cash flows year by year until the cumulative sum equals or exceeds the initial investment.
  4. The payback period is the number of years needed to reach that point.

Formulas

The math behind this calculator, written out so you can verify the result.

Discounted Payback Period (constant cash flow)

n = ln(1 / (1 - (I * r) / CF)) / ln(1 + r)

This formula solves for the number of periods n when the present value of an annuity equals the initial investment I, given a discount rate r and constant cash flow CF.

Example:

Input: I = 100,000, CF = 25,000, r = 10%

Calculation: n = ln(1 / (1 - (100000 * 0.10) / 25000)) / ln(1.10)

Result: ≈ 5.36 years, so about 6 years

Real-world use cases

Where this calculation shows up in everyday life.

Capital budgeting

Compare investment projects by how quickly they recover their cost in present value terms.

Example: Choosing between two machines with different costs and cash flows.

Risk assessment

A shorter discounted payback period indicates lower risk because the investment is recovered sooner.

Example: Evaluating a startup vs. a stable business investment.

Liquidity planning

Helps firms understand when they will have their capital back for other uses.

Example: Planning for reinvestment after a project's payback.

Tips and common mistakes

Tips

  • Use a realistic discount rate that reflects the opportunity cost of capital.
  • For projects with uneven cash flows, use a spreadsheet to calculate the exact payback period.
  • Compare the discounted payback period with the project's expected life to ensure recovery within the useful life.
  • Remember that the discounted payback period is always longer than the simple payback period when the discount rate is positive.

Common Mistakes to Avoid

  • Using the nominal cash flows without discounting them.
  • Ignoring the time value of money when comparing projects.
  • Assuming the payback period is the same as the project's break-even point in accounting terms.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.