Charles Wu is a specialist in capital budgeting and valuation, ensuring this IRR model provides reliable project assessment.
Use the authoritative **Internal Rate of Return Calculator** to find the expected compound annual rate of return for a project. This simplified model requires the **NPV Result** field to be empty or zero to solve for the IRR. Enter any three values to solve for the remaining unknown value.
Internal Rate of Return Calculator
Internal Rate of Return Formula (Annuity Model)
The IRR ($\mathbf{r}$) is the discount rate that makes $\mathbf{NPV} = 0$.
$$\mathbf{I_0} = \mathbf{CF_{avg}} \times \left[ \frac{1 – (1 + \mathbf{r})^{-n}}{\mathbf{r}} \right]$$
Where $\mathbf{I_0}$ is the absolute Initial Investment, $\mathbf{CF_{avg}}$ is the Cash Flow (P), $\mathbf{r}$ is the decimal IRR (V), and $\mathbf{n}$ is the Term (Q).
Solving for $\mathbf{r}$ (IRR) requires finding the root of the NPV function, typically achieved through iterative approximation.
Formula Source: Investopedia (IRR)Formula Variables
- F ($\mathbf{I_0}$): Initial Investment. The absolute cash outlay (use the positive value for calculation, e.g., 50,000).
- P ($\mathbf{CF_{avg}}$): Average Annual Net Cash Flow. The constant annual return expected from the project.
- V ($\mathbf{IRR}$): Internal Rate of Return. The expected compound annual rate of return (%).
- Q ($\mathbf{n}$): Project Term in Years. The expected life of the project.
Related Calculators
- Net Present Value (NPV) Calculator
- Payback Period Calculator
- Cost of Debt Calculator
- Present Value Calculator
What is 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 the discount rate at which the Net Present Value (NPV) of all the cash flows from a particular project equals zero. Essentially, the IRR is the rate of return the project is expected to yield.
The **IRR Rule** is simple: if the IRR of a project is greater than the company’s required rate of return (or cost of capital, often the Discount Rate), the project is considered worthwhile and should be accepted. Conversely, if the IRR is less than the cost of capital, the project should be rejected. The major advantage of IRR is that it presents the return as a percentage, which is often easier for managers to compare against the cost of funding the project.
How to Calculate Internal Rate of Return (Example)
Let’s find the IRR (V) given an Initial Investment ($\mathbf{I_0}$, F) of $-\$50,000$, Annual Cash Flow ($\mathbf{CF_{avg}}$, P) of $\$15,000$, and a Term ($\mathbf{n}$, Q) of 5 years.
- Step 1: Set NPV to Zero
We set the $\mathbf{NPV}=0$, meaning $\mathbf{PV_{annuity}}$ must equal the absolute value of the Initial Investment ($|\mathbf{I_0}| = \$50,000$).
- Step 2: Calculate PV Annuity Factor Required
Required PV Factor $= |\mathbf{I_0}| / \mathbf{CF_{avg}} = \$50,000 / \$15,000 \approx 3.33333$
- Step 3: Solve for $\mathbf{r}$ Iteratively
We iteratively search for the rate ($\mathbf{r}$) that results in the Annuity PV Factor of 3.33333 over 5 years.
- Step 4: Determine the IRR
The iterative solution yields an IRR ($\mathbf{r}$, V) of **15.238\%**.
Frequently Asked Questions (FAQ)
You accept a project if the calculated IRR is higher than your hurdle rate (the minimum acceptable rate of return, usually the cost of capital). If IRR > Hurdle Rate, accept. If IRR < Hurdle Rate, reject.
What is the main limitation of IRR?The main limitation is the “reinvestment assumption.” IRR assumes that all positive cash flows generated during the life of the project are reinvested at the IRR itself, which may not be a realistic rate to achieve in practice. NPV uses the cost of capital, which is generally considered more accurate.
Does this model handle unequal cash flows?No, this simplified calculator assumes a constant average annual net cash flow (an annuity) to maintain the four-variable input structure. For projects with highly variable cash flows, specialized IRR calculators (requiring multiple inputs) must be used.
Why must the Initial Investment be negative?For a standard IRR calculation to work (where the function must cross the zero axis), the cash flows must change sign—typically, a negative outflow (investment) followed by positive inflows (returns).