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Internal Rate of Return

Concept

Internal Rate of Return (IRR) is a concept in finance that refers to the discount rate that makes the Net Present Value (NPV) of all cash flows from a particular project equal to zero. IRR calculations rely on the same formula as NPV does. It's used in capital budgeting to rank different investments of equal size. As the name suggests, IRR is expressed in the form of a rate.

Formula​

While there's no specific formula for calculating IRR, it's defined by the following equation which sets the Net Present Value (NPV) equal to zero:

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

Where:

  • CFtCF_t is the net cash inflow during the period tt.
  • IRR\text{IRR} is the internal rate of return.
  • tt is the number of time periods.

Calculating Internal Rate of Return​

Calculating IRR can't be done through simple algebra. It requires trial-and-error or financial calculators/software. Here's a simple step-by-step guide on how to calculate IRR:

  1. Estimate the IRR. Set it as rr in the NPV formula and calculate the NPV.
  2. If NPV is close to zero, the estimated IRR is accurate.
  3. If NPV is not close to zero, adjust the IRR estimate and repeat the calculation until the NPV is zero.

Practical Example​

Suppose you invest $1,000 at the beginning of the year and receive $550 at the end of the year 1 and $800 at the end of the year 2. What is the IRR of this investment?

In your case:

  • CF0CF_0 = $1,000 (the initial investment)
  • CF1CF_1 = $550 (the return in year 1)
  • CF2CF_2 = $800 (the return in year 2)

You need to solve for IRR in the following equation:

0=−$1,000+$5501+IRR+$800(1+IRR)20 = -\$1{,}000 + \frac{\$550}{1 + IRR} + \frac{\$800}{(1 + IRR)^2}

By trial-and-error, or using a financial calculator or software, you'd find that the IRR is approximately 21.07%.

Takeaway

Remember, the IRR is the discount rate that makes the NPV of the cash flows equal to zero. It's a commonly used metric for estimating the profitability of potential investments. Always make sure to consider other factors such as risk, inflation, and your financial goals when making investment decisions.