Calculate simple and discounted payback periods for capital investments with uneven cash flows and cumulative cash flow charting.
This calculator takes an initial investment amount and a year-by-year list of cash inflows, which don't need to be equal, and walks the cumulative balance forward until it crosses zero. It reports both the simple payback period and, if you supply a discount rate, the discounted payback period, which present-values each cash flow before accumulating it. The interpolation within the crossing year assumes cash arrives evenly across that period, so the fractional-year figure is an approximation, not an exact date. Users are often surprised that discounted payback is always longer than simple payback for any positive discount rate, since discounting shrinks every future inflow.
A concrete input and expected output from the current implementation.
Input
Initial investment: $10,000. Annual cash flows: Year 1 $3,000, Year 2 $4,000, Year 3 $5,000, Year 4 $2,000. Discount rate: 10%.
Expected output
Simple payback period: 2.60 years. Discounted payback period: 3.15 years.
The cumulative undiscounted balance turns positive during year 3 (-3,000 + 5,000, crossing at 0.60 of the year). Discounted at 10%, the same cash flows present-value to 2,727.27, 3,305.79, 3,756.57 and 1,366.01; the cumulative balance stays negative until partway through year 4 (-210.37 of 1,366.01, or 0.15 of the year), giving 3.15 years.
The tool subtracts the initial investment at period 0, then adds each period's cash flow in sequence, tracking the running total. The payback period equals the number of full periods before the running total turns positive, plus a fractional period computed as the remaining negative balance divided by the cash flow of the crossing period.
When a discount rate is entered, each period's cash flow is divided by (1+r)^t before being added to the cumulative total, producing present-value cash flows. Because discounting reduces later cash flows more than earlier ones, the discounted payback period is always equal to or longer than the simple payback period for the same cash flow stream.
This is expected for any discount rate above zero. Discounting reduces the present value of every future cash flow, so it takes more nominal cash to reach the same present-value breakeven, which pushes the discounted payback period later than the simple one for the same cash flow stream.
The tool doesn't recommend one; you supply it. Most users enter their company's weighted average cost of capital or a required rate of return set by an investment committee. If you're unsure, discounted payback with an approximate rate is still more informative than none, but the result is only as sound as the rate you choose.
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