Place the amounts on the timeline
The purchase happens now, at time zero. The receipts happen one, two and three years later. Unequal amounts are compatible with regular annual intervals: the amounts need not be equal for the timing convention to be consistent.
Calculate and sum the present values
The time-zero amount stays −1,000. Discount each later receipt by the appropriate power of 1.10. The present values of the receipts sum to approximately 978.9624, slightly below the amount paid today.
| Time | Cash flow | Discount factor | Present value |
|---|---|---|---|
| 0 | -1000 | 1 | -1,000 |
| 1 | 300 | 0.9091 | 272.7273 |
| 2 | 400 | 0.8264 | 330.5785 |
| 3 | 500 | 0.7513 | 375.6574 |
Explain the difference
The undiscounted net amount is 200, but NPV is negative at the chosen 10% rate. Discounting has reduced the value of the later receipts. Including the initial outflow in the cash-flow sequence and then subtracting it again would double-count the cost.