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Edlintics

Tasa Interna de Retorno (TIR)

Calcula la tasa de descuento a la que el VAN de un proyecto es exactamente cero.

The IRR calculator solves for the discount rate at which a series of cash flows has a net present value of exactly zero — the break-even rate of return a project delivers.

ByHoang Truong

Separa los valores con una coma o un salto de línea

El primer valor es la inversión inicial (negativo); cada valor siguiente es el flujo neto de ese período.

Tasa interna de retorno10,0 %

Ejemplo resuelto

Usando los valores anteriores:

Flujos de caja
-1000 €, 100 €, 100 €, 1100 €
Tasa interna de retorno10,0 %

The formula

LaTeX
0=∑t=0nCFt(1+IRR)t0 = \sum_{t=0}^{n} \dfrac{CF_t}{(1+IRR)^t}

Variables

Cash flow at period t (€)
Internal rate of return (solved) (%)
Period number (0, 1, 2, …)
Final period

What internal rate of return means

Internal rate of return (IRR) answers a slightly different question than NPV: instead of telling you how much value a project creates at a discount rate you supply, it solves for the discount rate at which the project's NPV is exactly zero. That rate is the project's own break-even rate of return — the effective annual return the cash flows deliver on the money invested.

IRR is popular precisely because it collapses a whole stream of cash flows into one comparable percentage: "this project returns 14%" is an easy number to hold up against a hurdle rate or against another project's IRR, without needing to pick a discount rate first.

How to calculate it

There's no algebraic shortcut — IRR is found by trial and error (the calculator does this with an iterative numerical solver):

  1. Guess a rate and compute NPV at that rate using the same formula as the NPV calculator.
  2. If NPV is positive, the true IRR is higher than your guess (a higher rate discounts the future cash flows down further); if NPV is negative, IRR is lower. Adjust the guess and repeat.
  3. Keep refining the guess until NPV is close enough to zero — that rate is the IRR.
  • IRR only exists where the cash flows change sign at least once (an outflow followed by inflows, typically).
  • Compare IRR against your hurdle rate or cost of capital: IRR above the hurdle means the project clears your required return.
  • IRR and NPV will always agree on accept/reject for a single conventional project, evaluated at the same rate.

A worked example

Take a project needing €1,000 upfront that returns €100 at the end of each of the first two years and €1,100 (a final €100 return plus €1,000 principal back) at the end of year three — the same shape as a three-year bond priced at par with a 10% coupon. Checking NPV at 10%: €100 ÷ 1.10 + €100 ÷ 1.10² + €1,100 ÷ 1.10³ ≈ €90.91 + €82.64 + €826.45 = €1,000.00, which exactly offsets the €1,000 investment. NPV is zero at 10%, so the IRR is exactly 10%.

Limitations to know

IRR assumes any cash flow received partway through the project can be reinvested at the IRR itself, which can overstate returns for very high-IRR projects where that reinvestment rate isn't realistic. Cash flows that change sign more than once can also produce more than one mathematically valid IRR, making the number ambiguous — NPV at a chosen rate is the more reliable metric in that situation. IRR also can't be compared directly between two projects of very different size or duration without also checking NPV.

Preguntas frecuentes

IRR is the discount rate at which a project’s NPV is exactly zero. It uses the same cash flows and the same formula as NPV, just solved for the rate instead of the euro value — so IRR and NPV should always agree on whether a project clears your required return.