What is an IRR?

What is an IRR, how is it calculated and when is it used?

Updated over a week ago

IRR stands for Internal Rate of Return. It is a way to show your overall effective rate of return for a particular investment. An IRR is also often referred to as the ‘yield to maturity’ for an investment, particularly a bond.

Although it is less familiar than other terms or ways of showing your return, such as a simple annual interest rate or Annual Equivalent Rate (AER), an IRR is a useful way of comparing returns on different investments. In particular, an IRR is useful for comparing investments that pay back your capital and interest at different times over the life of the investment, or where the amounts vary over time.

Any investment, bond or loan can be represented as an IRR. The calculation of an investment’s IRR simply takes the amount you invested at the start, and the dates and amounts of what you get paid back over the investment’s term.

An IRR also takes into account the time value of money - this is the concept that money in your pocket today is more valuable than money you receive tomorrow because of the opportunity to do something else with it (whether that is reinvesting it or just spending it). IRR is therefore useful as it takes into consideration not just how much you get back, but also when it is paid.

The IRR for a particular investment will increase the more money you are due to get back, but also the quicker you get that money back. Take a look at the different examples below to help understand how an IRR works.

# Example 1

In this example, we look at how two investments that have the same term length (how long they are) and pay out the same total amount, can have different IRRs.

Investment A

• Investment amount: £1,000

• Date of investment: 1 January 2020

• Term period: 2 years

• Rate of return: 8% per year - paid annually

• Capital repayment: Lump sum at maturity

• Total returned: £1,160

• IRR: 8%

 Date 1 Jan 2020 31 Dec 2020 31 Dec 2021 Investment - £1,000 - - Capital repayment - - £1,000 Interest - £80 £80 Total - £1,000 £80 £1,080

Investment B

• Investment amount: £1,000

• Date of investment: 1 January 2020

• Term period: 2 years

• Rate of return: 8% per year - paid at maturity

• Capital repayment: Lump sum at maturity

• Total returned: £1,160

• IRR: 7.7%

 Date 1 Jan 2020 31 Dec 2020 31 Dec 2021 Investment - £1,000 - - Capital repayment - - £1,000 Interest - - £160 Total - £1,000 - £1,160

In the above examples, both investments are for 2 years, you earn 8% a year in interest, and it repays your invested capital at the maturity date (31 December 2022). In total you receive back £1,160 from both investments.

However in the case of Investment A you receive interest annually, whereas Investment B pays the interest all at the end. As an IRR takes into consideration when you receive money back, and not just how much, we can use the IRR for each investment to compare them.

Investment A has an IRR of 8% (you’ll notice that this is the same as the simple annual interest rate, 8% p.a) whereas Investment B has an IRR of 7.7%. As you have to wait a bit longer to receive your interest compared to Investment A, the IRR is lower for Investment B.

# Example 2

In this example we look at how an IRR can be useful to compare investments that pay out different amounts in total and at different times.

Investment A

• Investment amount: £1,000

• Date of investment: 1 January 2020

• Term period: 4 years

• Rate of return: (As you receive your capital back in equal instalments, it’s not possible to provide the rate of return as a single percentage per year figure)

• Capital repayment: Equal instalments

• Total returned: £1,160

• IRR: 6.2%

 Date 1 Jan 20 31 Dec 20 31 Dec 21 31 Dec 22 31 Dec 23 Investment - £1,000 - - - - Capital repayment - £250 £250 £250 £250 Interest - £40 £40 £40 £40 Total - £1,000 £290 £290 £290 £290

Investment B

• Investment amount: £1,000

• Date of investment: 1 January 2020

• Term period: 4 years

• Rate of return: 5% per year - paid annually

• Capital repayment: Lump sum at maturity

• Total returned: £1,200

• IRR: 5.0%

 Date 01 Jan 20 31 Dec 20 31 Dec 21 31 Dec 22 31 Dec 23 Investment - £1,000 - - - - Capital repayment - £0 £0 £0 £1,000 Interest - £50 £50 £50 £50 Total - £1,000 £50 £50 £50 £1,050

In this example, you’ll see that both investments are for 4 years, but they pay different amounts of interest. Also, Investment A repays your capital in equal annual instalments and Investment B is a bullet repayment (repays your capital in one lump sum at maturity).

Investment B returns more money in total, £1,200 compared to £1,160 for Investment A, but due to the different repayment structures, it can be harder to compare the overall return if you held each investment for the full term. That’s where an IRR can be useful.

Investment A has an IRR of 6.2% and Investment B has an IRR of 5.0%. While Investment B does pay back more in total in interest, more of your money is tied up over the life of the investment, whereas Investment A pays money back sooner.

## Example 3

Another benefit of using an IRR to show an investment’s overall return is it allows you to compare the return based on paying a different price for the same investment. The higher the price (in £GBP) an investor wants for a particular investment they are selling, the lower the return will be as an IRR for the buyer. You can read more about the marketplace and the price of investments here.

Here's a simple example of how the price you pay for an investment on the marketplace can affect the effective rate of return (IRR) you would receive.

Investment A

• Investment amount: £1,000

• Date of investment: 1 January 2020

• Term period: 2 years

• Rate of return: 6% per year - paid annually

• Capital repayment: Lump sum at maturity

• Total returned: £1,120

• IRR: 6.0%

 Date 1 Jan 20 31 Dec 20 31 Dec 21 Investment - £1,000 - - Capital repayment - - £1,000 Interest - £60 £60 Total - £1,000 £60 £1,060

Let's assume that the seller decides they want to sell the investment on 1 July 2020, 6 months into the first year of the investment. The table below shows the different IRRs a potential buyer would receive based on different prices.

 Price IRR £950 12.1% £1,000 8.2% £1,030 6.0% £1,050 4.6%

As you might expect, the higher the price paid, the lower the effective rate of return (IRR) for the buyer - as the investment pays a fixed amount of interest, a buyer will be paying more to get back the same amount of interest.

If the seller wants to sell the investment at a price equal to the amount they originally invested, £1,000, you'll see that the buyer's effective rate of return is actually higher than the original investment rate (8.2% compared to 6.0%). This is because the investment is now 6 months closer to the first interest payment, and an IRR takes into account not just how much you get back, but also when.

The seller may want to sell the investment for a bit more than the 'face value' of £1,000, as otherwise they would not see any return for the first 6 months that they have held the investment, as the new buyer would receive the full £60 interest payment in December. As they have held the investment for half of the year, the seller might choose to sell it for £1,030 and therefore receive back an amount equal to their original investment and half a year's worth of interest. This would also mean the buyer's effective rate of return would be the same as when the seller originally invested - 6.0% IRR. This is because although the buyer is investing £1,030, rather than the seller's original £1,000, they will receive a full year's worth of interest in December even though they will have only held it for 6 months.

# The technical detail

While an IRR can be a simple and easy metric for comparing the returns from different investments, the underlying calculation for an IRR is a bit more complex.

The IRR figure for an investment is the discount rate that makes the net present value (NPV) of all cash flows from that investment equal to zero. The formula for calculating an IRR is below, however, the nature of the formula (it’s iterative) means it is not an easy calculation to do with pen and paper. Instead, you can use a program like Excel (use the =XIRR formula) to easily calculate an IRR.

If you would like to read a bit more about Internal Rates of Return, Investopedia provides a useful article.