# What is Internal Rate of Return

Internal Rate of Return (IRR), also known as “Economic Rate of Return,” “Rate of Return,” or “Discounted Cash Flow Rate of Return” is a measure of worth of an investment. It refers to the expected rate of returns generated by an investment, based on internal factors and without considering environmental factors such as interest rates or inflation.

Internal Rate of Return (IRR) is an indicator of the efficiency, quality, or yield of an investment.

An investment becomes acceptable for investors or business owners when its internal rate of return is greater than an established minimum acceptable rate of return or cost of capital. For instance, comparing the IRR the investment against prevailing rates of return in the securities market determines whether the project is worth its while or whether the money would generate better returns in the securities market. Similarly, comparing IRRs of various projects help determine the most attractive project among the lot.

Other uses of IRR include comparing the profitability of investments. The higher a project’s internal rate of return, the more attractive such investment become for investors.

The Internal Rate of Returns however does not consider the risk factors or other costs resultant from the returns, and this remains the biggest limitation in applying Internal Rate of Return.

*Image Credit: Wikimedia Commons*

## Methodology

The Internal Rate of Return of an investment is the interest rate at which the net present value of the investment’s income stream becomes zero, or the rate at which the net present value of costs or negative cash flows of the investment equal the net present value of the benefits or positive cash flows of the investment.

For investments such as bank accounts, calculating the internal rate of return is straightforward and the bank reveals the same. For instance, a savings account offering 5 percent simple interest payable annually has an internal rate of return of 5 percent as well. Calculating the Internal Rate of Returns for other investments or projects with irregular cash flows however remains complex.

There are many methods to calculate Internal Rate of Returns. One simple method is to perform the following steps using a spreadsheet based calculator:

- express the cash flow of the investment as an income stream by listing the years, months or other periodic units of measurement, and the money added to the investment or the returns generated during the period
- calculate the net present value of future returns from the investment
- identify the internal rate of return as the percentage of discounted interest at which the net present value of the total returns from the investment becomes zero.

## Example

How to calculate IRR manually?

Consider an investment of $5000 in a savings bank offering 5 percent interest, payable annually, with the investor taking out the interest at the end of every year. The income stream lists out as follows:

- Year 0: $-5000 (investment)
- Year 1: $250 (5 percent of $5000 interest, withdrawn)
- Year 2: $250 (5 percent of $5000 interest, withdrawn)
- Year 3: $250 (5 percent of $5000 interest, withdrawn)
- Year 4: $250 (5 percent of $5000 interest, withdrawn)
- Year 5 : $5250 (end of investment, with the entire amount withdrawn)

Now consider this investment of $5000 in a bottling plant machinery, with the following income stream:

- Year 0: $-5000 (cost of establishing the plant)
- Year 1: $300 (profits)
- Year 2: $800 (profits)
- Year 3: $1500 (profits)
- Year 4: $1600 (profits)
- Year 5: $1800 (profits)

At the end of year 5, the machinery has no value owing to wear and obsolesce.

Adding up the income stream, the total returns of $5000 invested in a savings account is $1250, whereas the total returns for the same amount invested in the bottling plant is $1000

The investment in bank account provides more returns than investment in the bottling plant, but the investment in the bank account need not be better than the investment in the bottling plant. This is because of investment in the bottling plant provides greater returns earlier, and the present value of income in the distant future is far less than present value of income in near future.

The present value of a future amount of income = (Future Value)/(1 + Interest Rate)^n, where the exponential “n” is the number of years or in the future after which the future value will materialize.

Using this formula, the future value of the investment in the bottling plant at 5 percent interest rate available in the savings bank, the alternative investment possible is as follows:

- Year 0: $-5000
- Year 1: $1800 = (300)/(1 + 5%)^1 = 300/1.0500 = 285.71
- Year 2: $2100 = (800)/(1+ 5%)^2 = 800/1.1025 = 725.62
- Year 3: $2100 = (1500)/(1+ 5%)^3 = 1500/1.1576 = 1295.76
- Year 4: $2100 = (1600)/(1+ 5%)^4 = 1600/1.2155 =1316.32
- Year 5: $2100 = (1800)/(1+ 5%)^5 = 1800/1.2763 =1410.35

Total = -5000+285.71+725.62+1295.76+1316.32+1410.35 = 33.76

Thus, although the returns are more from the bank account, the considerations of present value of money makes investment in the bottling plant more worthwhile by $33.76.

The internal rate of return for the bottling machine is the discount rate that makes the present value of the machine’s income stream total zero, or the rate of returns generated by an alternative investment at which the difference between the net present value of returns from the bottling machinery investment and the other investment is zero.

Now replace the discount rate of 5 percent with 5.2 percent.

- Year 0 = -5000
- Year 1: $1800 = (300)/(1 + 5.2%)^1 = 300/1.0502 = 285.17
- Year 2: $2100 = (800)/(1+ 5.2%)^2 = 800/1.1067 = 722.87
- Year 3: $2100 = (1500)/(1+ 5.2%)^3 = 1500/1.1643 = 1288.38
- Year 4: $2100 = (1600)/(1+ 5.2%)^4 = 1600/1.2248 =1306.34
- Year 5: $2100 = (1800)/(1+ 5.2%)^5 = 1800/1.2885 =1396.99

Total -5000+285.17+722.87+1288.38+1306.34+1396.99 = 0

Thus, the Internal Rate of Return of the investment in bottling plant is 5.2 percent.

The calculation to determine the rate of discount at where the net present value becomes zero is best done using an excel sheet.

*Image Credit: flickr.com/Kevinzhengli*

## References

- Baker, Samuel, L. “The Internal Rate of Return.” University of South Carolina. Retrieved from https://hadm.sph.sc.edu/courses/econ/irr/irr.html on 10 November 2010
- Sigman, Karl. “Internal rate of return, bonds, yields.” Retrieved from https://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-bonds.pdf on 11 November 2010.