Track recovery without confusing it with profit
Payback measures how long receipts take to recover spending. It describes liquidity and exposure, not the total economic value of a project.
Period 0: −$10,000.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
Simple payback is reached. Discounted payback ≈ 4.263 years. Fractional interpolation assumes uniform receipt within the recovery year.
Accumulate net receipts without interest for simple payback.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
What the model means
Simple payback sums undiscounted net cash flows. Discounted payback sums cash flows discounted at the chosen rate. For constant annual receipts, simple recovery time is I/A, but only meaningful as a within-life recovery if it lies inside the project horizon.
Build the calculation
When cumulative recovery crosses zero between years k−1 and k, interpolation gives (k−1)+unrecovered amount/receipt in year k. This assumes receipts spread within that year. With strict year-end cash flows, the first complete recovery is at the integer year-end. A later negative cash flow can erase an earlier recovery.
Set up. Calculate. Explain.
Rebuild the starting scenario
Initial investment: 10000 $; Annual net receipt: 3000 $/year; Discount rate: 10 % per year; Number of years: 6 years. Calculate the interpolated simple payback period.
Setup hint
Accumulate net receipts without interest for simple payback.
Open the visual solution
- Accumulate net receipts without interest for simple payback.
- For discounted payback, discount each annual net receipt before accumulating.
- With strictly end-of-year receipts, recovery occurs at the first nonnegative integer year. Both payback measures ignore receipts after recovery and are not worth maximization.
Period 0: −$10,000.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
Simple payback is reached. Discounted payback ≈ 4.263 years. Fractional interpolation assumes uniform receipt within the recovery year.
Accumulate net receipts without interest for simple payback.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Transfer the idea to a new scenario
An investment of $14,000 generates $4,000/year for six years, discount rate 12%. Find interpolated simple payback, then inspect discounted recovery.
Setup hint
Accumulate net receipts without interest for simple payback.
Open the visual solution
- Accumulate net receipts without interest for simple payback.
- For discounted payback, discount each annual net receipt before accumulating.
- With strictly end-of-year receipts, recovery occurs at the first nonnegative integer year. Both payback measures ignore receipts after recovery and are not worth maximization.
Period 0: −$14,000.00. This is the time-zero cash flow. Periods use the payment interval stated in the model.
Simple payback is reached. Discounted payback ≈ 4.815 years. Fractional interpolation assumes uniform receipt within the recovery year.
Accumulate net receipts without interest for simple payback.
Cash-flow dates and signs are part of the answer. Model values retain precision; displays round money to cents. Illustrative assumptions exclude taxes and inflation unless stated.
Checks allow 0.1% numerical rounding (minimum $0.05 or 0.001 in the stated nonmonetary unit). Interpolated factors and rates are approximations; keep table precision consistent.
Why can a payback policy reject a positive-PW project?
Can you defend your setup?
Can you place each amount on the timeline, match the interest period, calculate the equivalent quantity, and state the decision or limitation?
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