Certified Financial Analyst with 15+ years of experience in capital budgeting and valuation.
The **Internal Rate of Return Calculator** determines the effective rate of return an investment is expected to yield. It is the discount rate that makes the Net Present Value (NPV) of all cash flows from a particular project equal to zero. Input any three variables (Initial Investment, Annual Cash Flow, IRR, or Project Term) to solve for the missing one, or calculate IRR if all other three are entered.
Internal Rate of Return Calculator
Internal Rate of Return (IRR) Formula
IRR is the rate ($R$) at which the Net Present Value (NPV) of a project is zero. For constant cash flows (annuity), this means:
$$C_0 = CF \times PVA_{Factor}(R, N)$$
Where $PVA_{Factor} = \left[ \frac{1 – (1 + R)^{-N}}{R} \right]$
Formula Source: Investopedia – Internal Rate of Return
Solving for the four variables (with the target of NPV=0):
C₀ (F) = CF × PVA Factor
CF (P) = C₀ ÷ PVA Factor
R (V) — Solved Iteratively (IRR)
N (Q) — Solved via Logarithms
Variables Explained
- F (Initial Investment – C₀): The cost incurred today to start the project. (Positive value).
- P (Annual Cash Flow – CF): The constant, equal cash inflow received each period.
- V (Internal Rate of Return – IRR): The calculated rate of return where the investment breaks even (NPV=0).
- Q (Project Term – N): The lifespan of the project, measured in years (periods).
Related Calculators
- Net Present Value (NPV) Calculator
- Present Value of Annuity Calculator
- Modified Internal Rate of Return Calculator
- Capital Gains Tax Calculator
What is the Internal Rate of Return (IRR)?
The **Internal Rate of Return (IRR)** is a metric used in capital budgeting to estimate the profitability of potential investments. It is a discount rate at which the Net Present Value (NPV) of all the cash flows from a particular project equals zero. In simpler terms, it represents the annualized effective compounded rate of return that an investment is expected to earn.
The decision rule based on IRR is straightforward: if the project’s IRR is greater than the company’s cost of capital (or required rate of return), the project should be accepted. If the IRR is less than the cost of capital, the project should be rejected. IRR is a widely used metric because it is intuitive, expressing profitability as a percentage rate.
How to Calculate IRR (Example)
Scenario: Initial Investment ($50,000), Annual Cash Flow ($15,000) for 5 years.
- Set the NPV to Zero:
The goal is to find $R$ such that: $$0 = -C_0 + (CF \times PVA_{Factor}(R, N))$$
- Simplify the Formula:
Rearrange to find the required PVA Factor: $$PVA_{Factor}(R, N) = C_0 \div CF$$
- Solve Iteratively (Trial and Error):
Since the $PVA_{Factor}$ formula cannot be algebraically solved for $R$, an iterative method (like bisection or binary search) is used to test different rates until one is found that yields the required $PVA_{Factor}$.
- Final Result:
In this example, the IRR is approximately 15.24%. If your cost of capital is 10%, you should accept the project.
Frequently Asked Questions (FAQ)
IRR gives you a percentage rate of return, while NPV gives you a dollar value (present value of profit). Both lead to the same accept/reject decision if the cash flows are conventional, but NPV is superior for comparing mutually exclusive projects.
When should I reject a project based on IRR?You should reject a project if its calculated IRR is lower than your company’s hurdle rate or cost of capital (the minimum required rate of return for projects of that risk level).
Can a project have multiple IRRs?Yes, projects with non-conventional cash flows (where the sign of the cash flow changes more than once, e.g., initial outflow, subsequent inflows, and a large final outflow) can have multiple IRRs. This calculator assumes conventional cash flows (initial outflow, subsequent inflows).
Is IRR the same as Annual Percentage Rate (APR)?No. APR is usually the contractual rate charged by a lender, often without considering compounding effects. IRR is a measure of the effective return of an entire investment stream over its life.