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Regular and Nine-Period Discounted Payback

Compare simple recovery, analytic discounted recovery, and the first interpolated recovery among nine entered cash flows.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Use the result with context

Results are estimates for planning and education. Confirm rates, taxes, fees, and legal requirements with the relevant institution or a qualified professional before making a financial decision.

Formula and method

An investment of 1,000 with annual cash flow of 1,100 has simple payback of about 10.91 months. At a 10-percent discount rate, both the constant-flow model and the entered first-year cash flow recover the investment in 12 months.

Simple recovery = investment/periodic cash flow. Discounted irregular recovery is the first period whose discounted cumulative cash flow covers the investment, interpolated within that period.

Worked example

Enter these known values and leave the other values blank.

Initial investment
1000 USD
Annual cash flow
1100 USD
Discount rate
10 %
Year 1
1100 USD
Payback period
0:10.91 yrs / mos
Discounted payback period
1:0 yrs / mos
Discounted payback period
1:0 yrs / mos

Assumptions and limitations

  • Cash-flow periods are equal years. Regular discounted recovery assumes the entered constant cash flow continues indefinitely; its discounted perpetuity must exceed the investment.
  • The irregular branch searches only the first nine periods and interpolates uniformly within the crossing period. When no recovery occurs within that horizon, the recovery field is hidden and a no-recovery message is shown.
  • Keep monetary inputs in one currency. Currency conversion factors are a captured snapshot rather than current quotes.
  • Clear the unknown numeric field before solving a supported inverse.

Common questions

What does this scenario assume?

Cash-flow periods are equal years. Regular discounted recovery assumes the entered constant cash flow continues indefinitely; its discounted perpetuity must exceed the investment.

What does the result leave out?

The irregular branch searches only the first nine periods and interpolates uniformly within the crossing period. When no recovery occurs within that horizon, the recovery field is hidden and a no-recovery message is shown.

References

Reviewed local arithmetic: Simple recovery = investment/periodic cash flow. Discounted irregular recovery is the first period whose discounted cumulative cash flow covers the investment, interpolated within that period. Model input requirements: Regular cash flow must support finite discounted recovery. Use a positive discount rate for this analytic model.

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