Investment appraisal calculator
Judge an investment project on NPV, IRR, MIRR, the profitability index and the payback period, with your own cash flows, charts and every step explained.
What is investment appraisal?
Investment appraisal answers one question: is this project worth putting money into? Rather than one number it answers from several angles: how much the project earns above the return you require (NPV), what return the project itself achieves (IRR and MIRR), what each euro invested returns (the profitability index), and how long the outlay takes to come back.
Every measure is built from one series of cash flows: the investment is a negative flow in year 0 and the receipts are positive flows in later years. Each flow is converted to today's value at the discount rate, and their sum is the NPV. Look instead for the rate at which NPV comes out zero and you have the IRR. The payback period is read straight off the running total.
Why one number is not enough
Picture two projects. The first costs €1,000 and returns €1,500 in a year. The second costs €100,000 and returns €130,000 in a year. The first returns 50%, the second only 30% and yet the second earns €30,000 instead of €500.
That is the whole reason an investment is not judged on a single number. Percentage measures (IRR, MIRR, the profitability index) say how efficient the project is. Absolute measures (NPV) say how much money it brings. Time measures (the payback period) say how long your money is tied up and what risk that carries.
When the measures contradict each other, and on projects of different sizes they often do, the NPV decides. It is the only one measuring what ultimately reaches the account: euro.
The formulas and where they come from
It all rests on a single series of cash flows. The investment is a negative flow in year 0, the income positive flows in later years. Each flow is restated in today's money and added up:
The internal rate of return is the discount rate at which the NPV equals zero. It cannot be written as a formula: it is found numerically, by narrowing an interval step by step, exactly as the calculator above does:
MIRR corrects the assumption that every inflow is reinvested at the IRR. The inflows are instead compounded forward to the end of the project at the reinvestment rate, the outflows discounted back to the start at the finance rate, and the return that implies is worked out:
The profitability index is a simple ratio: the present value of what the project brings, divided by the present value of what it costs:
What each variable means
The most common mistake is in the units: the rate must be a decimal and the years must match the order of the flows. Year 0 is today and is not discounted.
| Symbol | Name | Jednotka |
|---|---|---|
| Net present value | € | |
| Initial investment | € | |
| The cash flow in year t | € | |
| Discount rate | ||
| Year | years | |
| Project length | years | |
| Internal rate of return | ||
| Modified internal rate of return | ||
| Profitability index |
A worked example
How to read each measure
A positive NPV means the project earns more than the return you require, by that many euro in today's money. An IRR above the discount rate says the same thing in another language. A profitability index above 1 confirms it and, on top of that, lets projects of different sizes be compared. Where these measures disagree, which typically happens when two projects are compared, NPV decides: it is the only one measuring the absolute gain in euro.
- NPV: net present value
- The only measure that counts the benefit in euro. A positive NPV means the project earns more than the return required: by exactly that many euro in today's money. When the measures conflict, the NPV decides.
- IRR: internal rate of return
- The return of the project itself, independent of what you require. If the IRR exceeds the discount rate, the NPV is positive: they say the same thing in different languages. With unconventional flows, though, an IRR may not exist, or there may be several.
- MIRR: modified rate of return
- A correction to the IRR's strongest assumption. The IRR quietly assumes every inflow is reinvested at the IRR itself; the MIRR asks at what rate you actually would. It is therefore usually lower and more realistic.
- PI: profitability index
- How many euro of present value one euro invested returns. Above 1 means a worthwhile project. Useful on a limited budget, when projects of different sizes have to be compared.
- The payback period
- When the outlay comes back. The simple version ignores the time value of money, the discounted one accounts for it and is therefore always longer. Neither says anything about what happens afterwards, which is why neither decides on its own.
Common mistakes
Related calculators
Related terms
Every term used in this calculator has its own encyclopedia entry with a detailed explanation and derivation.
Related topics
Terms that come up in this calculation
- Present value (PV)What a future sum of money is worth today. It answers the question "how much would I have to have now for it to grow into that".
- DiscountingConverting a future sum into its value today: the opposite of compounding. It shows how much you would need to have now to reach a given future amount in a given time.
- ReturnThe amount or the percentage by which an investment has earned. It can be expressed in euro or in percent and only after deducting inflation does it tell you how much more you can buy.
- RiskThe degree of uncertainty about how an investment will turn out. A higher possible return usually comes with higher risk, but that is a possibility, not a promise.
- InflationThe general rise in prices across an economy, which gradually erodes the purchasing power of money: the same sum buys less in a few years than it does today.
Calculators that follow on from this one
- DiscountingWork out the present value of future cash flows, with the discount factor, a year-by-year breakdown, the effect of inflation and the whole method explained.
- Compound interestWork out how an investment grows under compound interest, including regular contributions, the effect of inflation, and a year-by-year breakdown.
- FIREFind out when you reach financial independence, with your FIRE number, a year-by-year portfolio projection, the passive income and scenarios side by side.