Internal rate of return (IRR) is a measure of the profitability of an investment, taking into account the time value of money. It is the discount rate that makes the net present value (NPV) of an investment equal to zero.

To calculate the IRR of an investment, you need to know the expected cash flows from the investment and the initial cost of the investment. You can then use the IRR formula to determine the discount rate that would make the NPV of the investment equal to zero.

Here is the formula for calculating IRR:

IRR = discount rate that makes NPV = 0

NPV = -initial investment + (expected cash flow / (1 + discount rate)^1) + (expected cash flow / (1 + discount rate)^2) + … + (expected cash flow / (1 + discount rate)^n)

Where “discount rate” is the IRR, “initial investment” is the cost of the investment, and “expected cash flow” is the amount of cash that is expected to be received from the investment in each period. “n” is the number of periods over which the cash flows are expected to occur.

To calculate IRR, you can use the formula above and solve for the discount rate that makes the NPV equal to zero. You can also use a financial calculator or spreadsheet software to solve for IRR.

Here is an example of how to calculate the internal rate of return (IRR) of an investment:

Imagine that you are considering investing in a project that requires an initial investment of $100,000 and is expected to generate cash flows of $40,000 in year 1, $50,000 in year 2, and $60,000 in year 3. You can use the IRR formula to determine the profitability of this investment.

First, you need to determine the NPV of the investment by discounting the expected cash flows to their present value using a discount rate. Let’s assume that you are using a discount rate of 10%. The NPV of the investment would be calculated as follows:

NPV = -$100,000 + ($40,000 / (1 + 10%)^1) + ($50,000 / (1 + 10%)^2) + ($60,000 / (1 + 10%)^3)

= -$100,000 + $36,364 + $30,303 + $21,212

= $87,878

Next, you can use the IRR formula to solve for the discount rate that makes the NPV equal to zero:

IRR = discount rate that makes NPV = 0

NPV = -$100,000 + ($40,000 / (1 + discount rate)^1) + ($50,000 / (1 + discount rate)^2) + ($60,000 / (1 + discount rate)^3)

Solving for the discount rate that makes the NPV equal to zero, we find that the IRR of this investment is approximately 21%.

This means that if you invested $100,000 in this project, you would expect to earn a return of 21% per year, taking into account the time value of money.

You can use this IRR to compare the profitability of this investment to other potential investments and to determine whether it is a good fit for your portfolio. However, it is important to note that the IRR calculation is based on certain assumptions, such as constant cash flows, and the actual return may differ from the calculated IRR.

Ultimately IRR is used to evaluate the profitability of an investment by taking into account the time value of money. It is a useful measure because it allows you to compare investments with different cash flow patterns and holding periods on a common basis. However, IRR has some limitations, such as the assumption of constant cash flows and the sensitivity of the result to changes in the expected cash flows.