NPV vs payback: a worked example with two projects
One project returns the initial cash sooner. Another produces more value over four years. Compare both measures on the same cash flows, then change the discount rate.
Payback measures how long a project takes to recover its initial investment from net cash inflows. Net present value (NPV) discounts future cash flows to today's value and subtracts the investment. They answer different questions, so they can favour different projects.
An operations team has two proposals, each costing €40,000 upfront. The first returns cash quickly. The second takes longer, but keeps producing larger inflows later.
If the approval pack shows only payback, that later value disappears from the comparison. The four-year cash flows below show the difference.
NPV vs payback: the main differences
| Measure | Question | What it leaves out |
|---|---|---|
| Simple payback | When does cumulative undiscounted net cash recover the investment? | Time value of money and cash after recovery |
| Discounted payback | When does cumulative discounted net cash recover it? | Cash after discounted recovery |
| NPV | What is the net present value of all included cash flows? | Anything missing or wrong in those cash flows or the rate |
ACCA's payback explanation distinguishes the first two methods and their limits. Payback remains useful for discussing cash recovery, especially when funding is tight. It cannot describe the whole investment on its own.
Worked example: use the same four-year horizon
The two fictional projects are alternative ways to improve one operation. Assume the organisation can choose at most one. The table shows the extra net cash each project would generate, after its additional operating costs, in thousands of euros.
| Time | Project A: earlier inflows | Project B: later inflows |
|---|---|---|
| Today, year 0 | −40 | −40 |
| End of year 1 | +25 | +10 |
| End of year 2 | +20 | +15 |
| End of year 3 | +5 | +20 |
| End of year 4 | +5 | +25 |
| Total undiscounted net cash | +15 | +30 |
Assume no residual value or further cash flows after year 4. The example is in constant purchasing-power euros with an illustrative real discount rate of 8%. Tax, financing and working-capital changes are excluded.
In a real appraisal, include relevant future incremental cash flows and keep cash assumptions consistent with the discount rate. ACCA's investment-appraisal guidance explains those choices.
Calculate payback before discounting
Project A is still €15,000 short after year 1. Its year-2 inflow takes cumulative net cash to +€5,000, so simple payback occurs at the end of year 2.
Project B is €15,000 short after year 2. Its year-3 inflow takes cumulative net cash to +€5,000, so it pays back at the end of year 3.
All inflows arrive at year-end here, so payback occurs at a year-end too. Cash arriving throughout the year would need different timing.
A has faster simple payback. We still need to value the rest of the cash flows.
Calculate NPV and inspect the timing
For each future inflow, divide by (1 + r) raised to its year number, where r is the annual discount rate. Add those present values to the negative year-0 investment.
Project A at 8%, in €000
NPV = −40 + 25/1.08 + 20/1.08² + 5/1.08³ + 5/1.08⁴
NPV ≈ 7.939, or €7,939
Project B's NPV is approximately €16,372 at the same rate. B pays back later and has the higher NPV under these assumptions.
Four-year horizon / cash arrives at year-end
Early recovery and later value can disagree
Present-value contribution in €000 at 8%. Graphite: A. Rust: B. The initial investment is negative; future inflows are positive.
Scroll sideways for all five dates. Exact contributions and cumulative balances are in the table.
Project A NPV / 8%€7,939Simple payback: year 2Discounted payback: year 2
Project B NPV / 8%€16,372Simple payback: year 3Discounted payback: year 4
Project B has the higher NPV under these inputs.
| Year | A cash | B cash | A PV | B PV | A cumulative PV | B cumulative PV |
|---|---|---|---|---|---|---|
| 0 | −€40,000 | −€40,000 | −€40,000 | −€40,000 | −€40,000 | −€40,000 |
| 1 | €25,000 | €10,000 | €23,148 | €9,259 | −€16,852 | −€30,741 |
| 2 | €20,000 | €15,000 | €17,147 | €12,860 | €295 | −€17,881 |
| 3 | €5,000 | €20,000 | €3,969 | €15,877 | €4,264 | −€2,004 |
| 4 | €5,000 | €25,000 | €3,675 | €18,376 | €7,939 | €16,372 |
Cash and rate assumptions
Choose at most one project. Both have four-year lives with no residual value or later cash flows. The amounts are additional net cash after operating costs, with inflation removed. Use the slider to test different illustrative real rates. Tax, financing and working capital are excluded. NPV uses unrounded values.
NPV equals the sum of each cash flow divided by (1 + rate) to the power of its year. The ranking changes near 27.37%, where both are negative. Discounted payback is the first year-end at which cumulative discounted cash becomes non-negative; no within-year interpolation is used.
As the rate rises, later cash receives a larger discount. The NPV ranking crosses at about 27.37% for these exact cash flows. At that rate, both NPVs are already negative. A higher relative NPV does not make either proposal worthwhile under the model.
Use the control to see how the chosen rate affects the ranking. The example does not select a company's rate or assess the projects' risks.
Check what could change the investment decision
Before selecting B, examine whether its larger late inflows are credible. A delayed launch, lower volume or higher support bill could change the result. Update the underlying cash forecast rather than using an unexplained rate increase to cover every uncertainty.
Check funding and non-financial requirements separately. A higher-NPV proposal may still be unaffordable in the required period or fail an essential operating constraint.
The automation-selection note connects the process choice to a business case. The build vs buy example compares the cash costs of obtaining software. NPV adds a consistent treatment of timing to that discussion.
Keep the cash forecast connected to delivery
Once a project is approved, assign an owner to each expected cash change and record when it should occur. Time released from a task is not automatically a reduction in payroll payments.
The benefits realisation note follows that distinction after go-live. Compare the forecast with actual results as they arrive, including changes to operating costs.
Put payback and NPV next to each other in the decision pack. Then show the cash flows behind them. Readers should be able to explain why the measures disagree before choosing which trade-off they can accept.
Sources and example notes
- ACCA. Payback and discounted payback, timing and limitations.
- ACCA. Investment appraisal, relevant cash flows and consistent inflation treatment.
Cash flows and rates are fictional. Both projects have an assumed four-year life and no residual value; 8% is an illustrative real rate, not a recommended company rate.