MIRR, payback and profitability index in practice
Beyond the NPV/IRR duo: how a finance-reinvestment MIRR fixes the reinvestment flaw, what discounted payback really measures, and why PI is NPV in disguise.
NPV and IRR answer is this project good? — but managers ask follow-up questions: how fast does cash come back, what if reinvestment happens at a different rate, how much bang per unit of capital? MIRR, the two paybacks and the profitability index exist for exactly these follow-ups, and all five live together on the FinScope cash-flow worksheet.
MIRR: fixing IRR's reinvestment fantasy
IRR quietly assumes every interim cash flow is reinvested at the IRR itself — flattering for a 19% project, absurd for a 60% one. MIRR replaces that assumption with two explicit rates: negative flows are financed at the finance rate and positive flows are rolled forward at the reinvestment rate, then a single rate connects the compounded outflows to the compounded inflows.
- Enter the flow −1000, 300, 500, 500, 200 on the cash-flow worksheet.
- Set finance rate = 10% and reinvestment rate = 12%.
- The engine compounds outflows to t=0 at 10% and inflows to the horizon at 12%.
- Result — engine-verified: MIRR = 15.9686%, sitting between the two input rates, below IRR's optimistic 19.0862%.
- For the classic flow −1000, 500, 400, 300, 100 the same rates give MIRR = 13.1686%.
Payback and discounted payback
Payback is the time until cumulative undiscounted flows recover the outlay; discounted payback applies the same idea after discounting each flow. For the verified flow the plain payback is 2.4 periods and the discounted payback is 2.836 periods — always longer, because discounting shrinks the far flows. If a rate is high enough that the project never recovers on a discounted basis, the metric honestly returns 'never' rather than a fake number.
| Metric | Value | Answers | Blind spot |
|---|---|---|---|
| MIRR (f10 / r12) | 15.9686% | true annual return with realistic reinvestment | needs two rate estimates |
| Payback | 2.4 periods | how fast cash returns | ignores time value and later flows |
| Discounted payback | 2.836 periods | breakeven in present-value terms | ignores flows after recovery |
| Profitability index | 1.1982 | value created per unit of capital | scale-blind across projects |
Profitability index: NPV wearing a ratio
PI is defined as the present value of inflows divided by the absolute initial investment. Its charm is the algebra: PI = 1 + NPV / |CF₀|. The verified example gives PI = 1.198211 — and indeed 1 + 198.2105/1000 = 1.198. A PI above 1 accepts, below 1 rejects; it is the cleanest way to ration capital across many small projects when the budget is fixed.
A sane workflow
- Compute NPV at your true cost of capital — the accept/reject gate.
- Read discounted payback for liquidity and risk budgeting, not for value.
- Report MIRR alongside IRR whenever flows are unconventional or IRR looks inflated.
- Use PI only when capital is rationed across small, comparable projects.
Frequently asked questions
When is MIRR better than IRR?
Whenever interim cash flows realistically cannot be reinvested at the IRR itself — i.e., almost always. MIRR lets you state the finance cost and the reinvestment rate explicitly; for the verified flow it returns 15.9686% instead of IRR's 19.0862%, and unlike IRR it stays unique even when flows change sign more than once.
Why is discounted payback always longer than plain payback?
Because each flow is shrunk by discounting before it is added to the recovery pile, so the same cumulative target takes more periods to reach. In the verified example the plain payback is 2.4 while the discounted payback is 2.836 periods at a 10% discount rate.
How is the profitability index related to NPV?
Directly: PI = 1 + NPV / initial investment. The verified project's PI of 1.198211 is exactly 1 + 198.2105/1000. So PI never says anything NPV cannot — it merely rescales value per unit of capital, which is why it is most useful for rationing a fixed budget.
Practice it live
Open the matching worksheet and reproduce every number in this article.
Open calculator