Net present value is the most reliable way to judge an investment, but managers often want quick answers to simpler questions: How long until we get our money back? How much value do we get for each unit invested? The payback period, discounted payback period and profitability index (PI) answer those questions. They are best used alongside NPV and IRR, not instead of them.
What you will learn
- Calculate simple and discounted payback periods
- Calculate the profitability index and use it under capital rationing
- Explain the strengths and weaknesses of each measure
- Choose the right measure for the decision at hand
The payback period
The payback period is the time it takes for a project’s cumulative cash inflows to recover the initial investment.
Payback period
With even annual cash flows: Payback = Initial investment ÷ Annual cash inflow
With uneven cash flows: Payback = Years before full recovery + Unrecovered amount at start of the recovery year ÷ Cash flow in that year
Worked example: simple payback
A project costs 100,000 and returns 40,000, 45,000 and 50,000 at the end of years 1, 2 and 3.
| Year | Cash flow | Cumulative |
|---|---|---|
| 0 | −100,000 | −100,000 |
| 1 | 40,000 | −60,000 |
| 2 | 45,000 | −15,000 |
| 3 | 50,000 | 35,000 |
The investment is recovered during year 3. Unrecovered at the start of year 3: 15,000. Payback = 2 + 15,000 ÷ 50,000 = 2.3 years (assuming cash arrives evenly through the year). The payback calculator produces the same result.
Decision rule: accept projects whose payback is shorter than a maximum period set by management.
The discounted payback period
Simple payback ignores the time value of money. The discounted payback uses present values instead.
Worked example: discounted payback at 10%
Using the same project and a 10% discount rate:
| Year | Cash flow | Present value at 10% | Cumulative PV |
|---|---|---|---|
| 0 | −100,000 | −100,000.00 | −100,000.00 |
| 1 | 40,000 | 36,363.64 | −63,636.36 |
| 2 | 45,000 | 37,190.08 | −26,446.28 |
| 3 | 50,000 | 37,565.74 | 11,119.46 |
Discounted payback = 2 + 26,446.28 ÷ 37,565.74 = 2.70 years. The final cumulative figure, 11,119.46, is the project’s NPV.
Discounted payback is always longer than simple payback for a project with positive cash flows, because each inflow is worth less in present value terms. If the discounted payback is reached within the project’s life, the NPV is positive.
Strengths and weaknesses of payback
Strengths
- Simple to calculate and explain.
- A rough measure of liquidity and risk: a short payback means money returns quickly, which matters for cash-constrained firms or in uncertain markets (rapid technological change, political risk).
Weaknesses
- Ignores cash flows after the payback point. A project that pays back in two years and then ends can look better than one paying back in three years that goes on generating cash for twenty.
- Simple payback ignores the time value of money.
- The cut-off period is arbitrary.
- It does not measure value created.
The profitability index
The profitability index compares the present value of future cash flows with the initial investment.
Profitability index
PI = Present value of future cash flows ÷ Initial investment
equivalently PI = 1 + NPV ÷ Initial investment
For the example project, the present value of inflows is 36,363.64 + 37,190.08 + 37,565.74 = 111,119.46, so PI = 111,119.46 ÷ 100,000 = 1.11. Every 1 invested returns 1.11 in present value terms.
Decision rule: accept projects with PI > 1, which is the same as NPV > 0.
Using PI under capital rationing
When a company has more positive-NPV projects than funds — capital rationing — it should choose the combination that gives the highest total NPV within the budget. For divisible projects and a single-period budget limit, ranking by PI does exactly that.
Worked example: choosing projects with a limited budget
A company has 300,000 to invest this year and four divisible projects (illustrative figures):
| Project | Investment | NPV | PI | Rank by PI |
|---|---|---|---|---|
| A | 100,000 | 11,000 | 1.11 | 3 |
| B | 150,000 | 30,000 | 1.20 | 1 |
| C | 120,000 | 18,000 | 1.15 | 2 |
| D | 80,000 | 6,400 | 1.08 | 4 |
- Fund B in full: 150,000 used, NPV 30,000.
- Fund C in full: 270,000 used, NPV 48,000.
- The remaining 30,000 goes to A, the next by PI: 30% of A gives NPV 0.3 × 11,000 = 3,300.
- Total NPV: 51,300 from 300,000.
Ranking by NPV alone would start with B and then C as well, but in other cases it can pick large projects that use up the budget inefficiently.
PI ranking has limits: it does not work well when projects are indivisible (you must take all or nothing), when budget limits apply in several years, or when projects are mutually exclusive. In those cases, compare the total NPV of feasible combinations directly.
Which measure to use
| Question | Best measure |
|---|---|
| Does this project create value? | NPV |
| What return does it earn? | IRR (with care) |
| How quickly is cash recovered? | Payback or discounted payback |
| Which projects to fund with limited capital? | Profitability index (divisible projects) or total NPV of combinations |
Most companies report several measures together. A project with a positive NPV but a very long payback may be rejected if the company is short of cash or the forecasts are highly uncertain; that is a legitimate judgement, as long as it is made consciously.
Common mistakes
- Using payback as the only criterion and rejecting valuable long-term projects.
- Forgetting that payback assumes cash flows arrive evenly within the year.
- Ranking mutually exclusive projects by PI instead of NPV.
- Treating a PI just above 1 as safe without testing how sensitive it is to the forecasts.
Key terms
- Payback period — time needed to recover the initial investment from cash inflows.
- Discounted payback — payback calculated using present values of cash flows.
- Profitability index — present value of future cash flows divided by the initial investment.
- Capital rationing — a limit on the funds available for investment.
- Cut-off period — the maximum acceptable payback set by management.
Frequently asked questions
Why do businesses still use payback if it ignores later cash flows?
It is a simple liquidity and risk screen. Firms with limited cash or in fast-changing industries value recovering their investment quickly.
Can a project with a long payback have a high NPV?
Yes. Infrastructure and other long-life projects often have long paybacks but create substantial value over decades.
When does PI give a different answer from NPV?
For accept-or-reject decisions they agree. They can rank projects differently because PI measures value per unit invested while NPV measures total value.
Key takeaways
- Payback measures how quickly an investment is recovered; discounted payback adds the time value of money.
- Both ignore cash flows after the payback point and do not measure value created.
- PI = PV of future cash flows ÷ investment; PI > 1 is equivalent to NPV > 0.
- Under capital rationing with divisible projects, ranking by PI maximises total NPV.