Internal Rate of Return (IRR)

# Internal Rate of Return (IRR)

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# Learn How to Calculate Your Internal Rate of Return

## IRR Helps You Compare Investment Options

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By

Dana Anspach
Updated August 17, 2018

It should be easy to calculate the rate of return (called an internal rate of return or IRR) you earned on an investment, right? You would think so, but sometimes it is more difficult than you would think.

Cash flows (deposits and withdrawals), as well as uneven timing (rarely do you invest on the first day of the year and withdraw your investment on the last day of the year), make calculating returns more complicated.

Let’s take a look at an example calculating returns using simple interest, and then we’ll look at how uneven cash flows and timing make the calculation more complex.

### Simple Interest Example

If you put \$1,000 in the bank, the bank pays you interest, and one year later you have \$1,042. In this case, it is easy to calculate the rate of return at 4.2 percent. You simply divide the gain of \$42 into your original investment of \$1,000.

### Uneven Cash Flows and Timing Make it More Difficult

When you receive an uneven series of cash flows over several years, or over an odd time period, calculating the internal rate of return becomes more difficult. Suppose you start a new job in the middle of the year.

You may invest in your 401(k) through payroll deductions so every month money goes to work for you. To accurately calculate the IRR you would need to know the date and amount of each deposit and the ending balance.

To do this type of calculation you need to use software, or a financial calculator, that allows you to input the varied cash flows at differing intervals. Below are a few resources that can help.

• Try this free online internal rate of return calculator that allows for up to fifteen years of cash flow entries.
• You can also download a Microsoft Excel  internal rate of return spreadsheet template , which explains how the IRR function in Excel works and allows you to input cash flows to see how it works.
• For those of you who like online tutorials, this ​ video shows you how to calculate IRR on an HP12(c) calculator .​

### Why Calculate Internal Rate of Return?

It is important to calculate the expected internal rate of return so you may adequately compare investment alternatives.

For example, by comparing the estimated internal rate of return on an investment property to that of an annuity payment to that of a portfolio of index funds, you can more effectively weigh out the various risks along with the potential returns – and thus more easily make an investment decision you feel comfortable with.

Expected return is not the only thing to look at; also consider the level of risk that different investments are exposed to. Higher returns come with higher risks. One type of risk is liquidity risk. Some investments pay higher returns in exchange for less liquidity, for example, a longer term CD or bond pays a higher interest rate or coupon rate than shorter-term options because you have committed your funds for a longer time frame.

Businesses use internal rate of return calculations to compare one potential investment to another. Investors should use them in the same way. In retirement planning, we calculate the minimum return you need to achieve to meet your goals and this can help assess whether the goal is realistic or not.

### Internal Rate of Return Is Not the Same as Time Weighted Return

Most mutual funds and other investments that report returns report something called a Time Weighted Return (TWRR). This shows how one dollar invested at the beginning of the reporting period would have performed.

For example, if it was a five-year return ending in 2015, it would show the results of investing on January 1, 2001, through December 31, 2015. How many of you invest a single sum on the first of each year?

Because most people do not invest this way there can be a large discrepancy between investment returns (those published by the company) and investor returns (what returns each individual investor actually earns).

As an investor, time-weighted returns do not show you what your actual account performance has been unless you had no deposits or withdrawals over the time period shown. This is why the internal rate of return becomes a more accurate measure of your results when you are investing or withdrawing cash flows over varying time frames.

# Internal Rate of Return (IRR)

The Internal Rate of Return is a good way of judging an investment. The bigger the better!

The Internal Rate of Return is the interest rate
that
makes the Net Present Value zero

OK, that needs some explaining, right?

It is an Interest Rate.

We find it by first guessing what it might be (say 10%), then work out the Net Present Value.

The Net Present Value is how much the investment is worth in today’s money
(we find how to calculate it later)

Then keep guessing (maybe 8%? 9%?) and calculating, until we get a Net Present Value of zero.

### Example: Sam is going to start a small bakery!

Sam estimates all the costs and earnings for the next 2 years, and calculates the Net Present Value:

At 6% Sam gets a Net Present Value of \$2000

But the Net Present Value should be zero, so Sam tries 8% interest:

At 8% Sam gets a Net Present Value of −\$1600

Now it’s negative! So Sam tries once more, but with 7% interest:

At 7% Sam gets a Net Present Value of \$15

Close enough to zero, Sam doesn’t want to calculate any more.

The Internal Rate of Return (IRR) is about 7%

So the key to the whole thing is … calculating the Net Present Value!

Read Net Present Value … or this quick summary:

An investment has money going out (invested or spent), and money coming in (profits, dividends etc). We hope more comes in than goes out, and we make a profit!

To get the Net Present Value:

Add what comes in and subtract what goes out,
but future values must be brought back to today’s values.

Why?

Because money now is more valuable than money later on.

### Example: Let us say you can get 10% interest on your money.

So \$1,000 now earns \$1,000 x 10% = \$100 in a year.

Your \$1,000 now becomes \$1,100 in a year’s time.

(In other words: \$1,100 next year is only worth \$1,000 now.)

So just work out the Present Value of every amount, then add and subtract them to get the Net Present Value.

## Present Value

So \$1,000 now is the same as \$1,100 next year (at 10% interest).

The Present Value of \$1,100 next year is \$1,000

Present Value has a detailed explanation, but let’s skip straight to the formula:

PV = FV / (1+r)n

• PV is Present Value
• FV is Future Value
• r is the interest rate (as a decimal, so 0.10, not 10%)
• n is the number of years

And let’s use the formula:

### Example: Alex promises you \$900 in 3 years, what is the Present Value (using a 10% interest rate)?

• The Future Value (FV) is \$900,
• The interest rate (r) is 10%, which is 0.10 as a decimal, and
• The number of years (n) is 3.

So the Present Value of \$900 in 3 years is:

PV = FV / (1+r)n
PV = \$900 / (1 + 0.10)3
PV = \$900 / 1.103
PV = \$676.18 (to nearest cent)

Notice that \$676.18 is a lot less than \$900.

It is saying that \$676.18 now is as valuable as \$900 in 3 years (at 10%).

### Example: try that again, but use an interest rate of 6%

The interest rate (r) is now 6%, which is 0.06 as a decimal:

PV = FV / (1+r)n
PV = \$900 / (1 + 0.06)3
PV = \$900 / 1.063
PV = \$755.66 (to nearest cent)

When we only get 6% interest, then \$755.66 now is as valuable as \$900 in 3 years.

## Net Present Value (NPV)

Now we are equipped to calculate the Net Present Value.

For each amount (either coming in, or going out) work out its Present Value, then:

• Subtract the Present Values you pay

Like this:

### Example: You invest \$500 now, and get back \$570 next year. Use an Interest Rate of 10% to work out the NPV.

Money Out: \$500 now

You invest \$500 now, so PV = −\$500.00

Money In: \$570 next year

PV = \$570 / (1+0.10)1 = \$570 / 1.10
PV = \$518.18 (to nearest cent)

And the Net Amount is:

Net Present Value = \$518.18 − \$500.00 = \$18.18

So, at 10% interest, that investment has NPV = \$18.18

But your choice of interest rate can change things!

### Example: Same investment, but work out the NPV using an Interest Rate of 15%

Money Out: \$500 now

You invest \$500 now, so PV = -\$500.00

Money In: \$570 next year:

PV = \$570 / (1+0.15)1 = \$570 / 1.15
PV = \$495.65 (to nearest cent)

Work out the Net Amount:

Net Present Value = \$495.65 – \$500.00 = -\$4.35

So, at 15% interest, that investment has NPV = -\$4.35

It has gone negative!

Now it gets interesting … what Interest Rate can make the NPV exactly zero? Let’s try 14%:

### Example: Try again, but the interest Rate is 14%

Money Out: \$500 now

You invest \$500 now, so PV = -\$500.00

Money In: \$570 next year:

PV = \$570 / (1+0.14)1 = \$570 / 1.14
PV = \$500 (exactly)

Work out the Net Amount:

Net Present Value = \$500 − \$500.00 = \$0

Exactly zero!

At 14% interest NPV = \$0

And we have discovered the Internal Rate of Return … it is 14% for that investment.

Because 14% made the NPV zero.

## Internal Rate of Return

So the Internal Rate of Return is the interest rate that makes the Net Present Value zero.

And that "guess and check" method is the common way to find it (though in that simple case it could have been worked out directly).

Let’s try a bigger example:

### Example: Invest \$2,000 now, receive 3 yearly payments of \$100 each, plus \$2,500 in the 3rd year.

Let us try 10% interest:

• Now: PV = -\$2,000
• Year 1: PV = \$100 / 1.10 = \$90.91
• Year 2: PV = \$100 / 1.102 = \$82.64
• Year 3: PV = \$100 / 1.103 = \$75.13
• Year 3 (final payment): PV = \$2,500 / 1.103 = \$1,878.29

NPV = -\$2,000 + \$90.91 + \$82.64 + \$75.13 + \$1,878.29 = \$126.97

Let’s try a better guess, say 12% interest rate:

### Example: (continued) at 12% interest rate

• Now: PV = -\$2,000
• Year 1: PV = \$100 / 1.12 = \$89.29
• Year 2: PV = \$100 / 1.122 = \$79.72
• Year 3: PV = \$100 / 1.123 = \$71.18
• Year 3 (final payment): PV = \$2,500 / 1.123 = \$1,779.45

NPV = -\$2,000 + \$89.29 + \$79.72 + \$71.18 + \$1,779.45 = \$19.64

Ooh .. so close. Maybe 12.4% ?

### Example: (continued) at 12.4% interest rate

• Now: PV = -\$2,000
• Year 1: PV = \$100 / 1.124 = \$88.97
• Year 2: PV = \$100 / 1.1242 = \$79.15
• Year 3: PV = \$100 / 1.1243 = \$70.42
• Year 3 (final payment): PV = \$2,500 / 1.1243 = \$1,760.52

NPV = -\$2,000 + \$88.97 + \$79.15 + \$70.42 + \$1,760.52 = -\$0.94

That is good enough! Let us stop there and say the Internal Rate of Return is 12.4%

In a way it is saying "this investment could earn 12.4%" (assuming it all goes according to plan!).

## Using the Internal Rate of Return (IRR)

The IRR is a good way of judging different investments.

First of all, the IRR should be higher than the cost of funds. If it costs you 8% to borrow money, then an IRR of only 6% is not good enough!

It is also useful when investments are quite different.

• Maybe the amounts involved are quite different.
• Or maybe one has high costs at the start, and another has many small costs over time.
• etc…

### Example: instead of investing \$2,000 like above, you could also invest 3 yearly sums of \$1,000 to gain \$4,000 in the 4th year … should you do that instead?

I did this one in a spreadsheet, and found that 10% was pretty close:

At 10% interest rate NPV = -\$3.48

So the Internal Rate of Return is about 10%

And so the other investment (where the IRR was 12.4%) is better.

Doing your calculations in a spreadsheet is great as you can easily change the interest rate until the NPV is zero.

You also get to see the influence of all the values, and how sensitive the results are to changes (which is called "sensitivity analysis").

Present Value
Net Present Value
Investment/Loan Graph
Investing (Introduction)
Money Index