Accounting
Payback, IRR or NPV: Which One Answers Your Question
- A case where all three disagree
- Why they disagree
- A practical decision rule
- Three traps worth knowing
- Run your own numbers
- Reproducing these figures
If you appraise the same investment three ways you can get three different verdicts. That is not a sign that one of the methods is broken. Each answers a different question, and the trouble starts when you ask a method a question it was never designed to answer.
Here is the short version. Payback answers “how long until I get my money back”. IRR answers “what rate of return does this earn”. NPV answers “how much wealth does this create”. When they conflict, NPV is usually the one to follow, and the rest of this explains when that rule bends.
A case where all three disagree
A manufacturer has ₹20,00,000 available and two proposals on the table.
Project A, a machine upgrade. Costs ₹5,00,000. Saves labour and scrap immediately, with the benefit tapering as the older line is retired.
Project B, a new production line. Costs ₹20,00,000. Slow to commission, then builds.
| Year | Project A | Project B |
|---|---|---|
| 0 | (₹5,00,000) | (₹20,00,000) |
| 1 | ₹3,00,000 | ₹3,00,000 |
| 2 | ₹2,50,000 | ₹5,00,000 |
| 3 | ₹1,50,000 | ₹7,00,000 |
| 4 | ₹50,000 | ₹9,00,000 |
| 5 | — | ₹11,00,000 |
Assumptions. Cash flows are after tax and arrive at the end of each year. The cost of capital is 12%. Neither project has a terminal value. Both are accepted or rejected as a whole.
The three answers
| Measure | Project A | Project B | Prefers |
|---|---|---|---|
| Payback period | 1.80 years | 3.56 years | A |
| IRR | 24.6% | 17.7% | A |
| NPV at 12% | ₹1,05,699 | ₹3,60,836 | B |
| Profitability index at 12% | 1.21 | 1.18 | A |
Three of the four measures point at A. The one that points at B is the one that measures how much richer the company ends up. Project B creates ₹3,60,836 of value against Project A’s ₹1,05,699, which is roughly three and a half times as much.
Why they disagree
Payback ignores everything after the payback date
Project A returns its ₹5,00,000 in 1.80 years and then produces ₹2,50,000 more in total. Project B takes 3.56 years and then produces ₹15,00,000 more. Payback cannot see the difference because it stops counting the moment the original outlay is recovered.
Payback also ignores the time value of money entirely. A rupee in year three counts the same as a rupee in year one.
None of that makes payback useless. It is a liquidity measure, and liquidity is a real constraint. If the business genuinely cannot survive a four year wait, Project B is unaffordable regardless of what NPV says. Use payback as a screen, not as a ranking.
IRR ignores scale
IRR is a percentage, and a percentage has no size. Earning 24.6% on ₹5,00,000 is a better rate than 17.7% on ₹20,00,000, and a worse outcome in rupees.
This is the most common appraisal error in practice. A small project with a spectacular rate gets funded ahead of a large project with a merely good one, and the business ends up with a portfolio of excellent percentages and not much money.
The profitability index has the same blind spot, which is why it also prefers A. It is a ratio, so it too is scale free.
NPV depends on the discount rate, and that changes the answer
The preference for B is not permanent. It depends on the cost of capital:
| Discount rate | NPV, Project A | NPV, Project B | Higher |
|---|---|---|---|
| 8% | ₹1,47,939 | ₹6,72,298 | B |
| 10% | ₹1,26,187 | ₹5,09,596 | B |
| 12% | ₹1,05,699 | ₹3,60,836 | B |
| 15% | ₹77,121 | ₹1,60,675 | B |
| 18% | ₹50,867 | (₹15,599) | A |
| 20% | ₹34,529 | (₹1,21,592) | A |
| 25% | (₹2,720) | (₹3,52,512) | A |
Somewhere between 15% and 18% the ranking flips. That is the crossover rate, and it exists because B’s cash flows are further out and therefore more sensitive to discounting.
Above about 17.7%, Project B destroys value outright. Its NPV turns negative because 17.7% is its IRR, and the IRR is by definition the rate at which NPV hits zero.
So the discount rate is not a technicality. If your genuine cost of capital is 12%, take B. If borrowing costs 18%, take A. Getting the rate roughly right matters more than which method you use.
A practical decision rule
- Screen on payback against whatever recovery period the business can actually survive. This is a constraint, not a preference.
- Rank on NPV at an honest cost of capital, when projects compete for the same money.
- Use IRR to communicate, because a percentage travels well in a meeting, and to see how much room you have before the project stops being worth doing.
- Use the profitability index when capital is genuinely rationed and you are choosing a basket of projects rather than one, because then value per rupee invested is the binding question.
Three traps worth knowing
IRR can have more than one answer. If the cash flow signs change more than once, say an outlay, then inflows, then a large closure or replacement cost, the equation can have multiple roots. Spreadsheets will report one of them without warning you. NPV has no such problem.
IRR assumes you can reinvest at the IRR. A project showing 24.6% implicitly assumes its interim cash flows also earn 24.6%. If your actual reinvestment rate is 12%, the true return is lower than advertised.
Discounted payback fixes only half the problem. Discounting the cash flows before computing payback handles the time value of money, but it still ignores everything after the cutoff.
Run your own numbers
Two worked decisions that use the same thinking: the return on a ₹50,000 marketing spend and whether you can afford to hire.
If the cash flows themselves are the uncertain part, which is usually the case, start with a 13 week cash flow forecast before appraising anything.
Reproducing these figures
Every number above comes from the two cash flow columns, discounted at the stated rate. NPV is the sum of each flow divided by (1 + r) raised to the year. IRR is the r where that sum is zero. Payback is the point where the running total crosses zero, interpolated within the year. Nothing is estimated and nothing is taken from another source, so you can rebuild the whole table in a spreadsheet and check it.