Internal rate of return

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Internal Rate of Return (IRR) is a financial metric used in capital budgeting to estimate the profitability of potential investments. It is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. The IRR is used to evaluate the attractiveness of a project or investment.

Calculation

The IRR is calculated by solving the equation for the discount rate that sets the NPV of all cash flows (both incoming and outgoing) to zero. The formula for NPV is:

\[ NPV = \sum \frac{C_t}{(1 + r)^t} \]

where:

• \( C_t \) = net cash inflow during the period t
• \( r \) = discount rate (IRR)
• \( t \) = number of time periods

The IRR is the value of \( r \) that makes the NPV equal to zero.

Interpretation

The IRR is used to evaluate the desirability of an investment or project. If the IRR of a new project exceeds a company's required rate of return, that project is desirable. If the IRR falls below the required rate of return, the project should be rejected.

Comparison with Other Metrics

The IRR is often compared with the net present value (NPV) and the payback period. While NPV provides the value of an investment in terms of currency, IRR provides the rate of return expected from the investment. The payback period, on the other hand, measures the time required to recover the initial investment.

Advantages and Disadvantages

Advantages

• The IRR provides a clear percentage return expected from an investment.
• It considers the time value of money, making it a more accurate measure than the payback period.

Disadvantages

• The IRR can be misleading if used to compare projects of different durations or sizes.
• It assumes that all interim cash flows are reinvested at the same rate as the IRR, which may not be realistic.

Applications

The IRR is widely used in various fields, including corporate finance, private equity, and real estate development. It helps in making decisions about whether to proceed with a project, compare the profitability of different projects, and allocate resources efficiently.

See Also

• Net present value
• Payback period
• Discounted cash flow
• Capital budgeting
• Return on investment