Annual rate of return calculation

Determining your return on investment is a very important part of any investment review. Whether you're investing in savings accounts, stocks, real estate, capital upgrades, or new business ventures, estimating a return on investment will aid you in choosing among investment options.

I don't simply calculate a straight return on investment. I prefer determining an annualized rate of return that takes into consideration the timing of investments and return, as well as compounding. Most of you are probably familiar with this concept through the term Annual Percentage Yield (APY), compound annual growth rate (CAGR), or internal rate of return (IRR). Let me walk you through the steps on how you can calculate your return on investment in terms of APY:


Step 1. Calculate all the costs associated with an investment.

Ask yourself the following questions about the investment:

What are the initial upfront costs associated with the investment?
What are the maintenance costs?
Are there any fees or taxes associated with the investment?
What kind of research costs will you incur to properly evaluate (i.e. due diligence) the investment?
How much of your time will this investment consume? Your time is valuable, so a complicated project could have real opportunity costs.
Basically, don't forget the hidden costs often associated with investments. Be sure to list out all costs you can think of.

Step 2. Estimate or calculate your returns.

How much do you expect to gain from the investment?
When do you expect returns to happen?
Determine how much you expect to gain from the investment. Detail specifically all the individual returns you expect to receive from the investment.

Since returns from investments are often uncertain, you might also want to jot down what you think the probability of each return occurring when you thought they would. Be sure to also specify when these returns will occur and for how long. This will be important for the next step.

Step 3. Establish a timeline for costs and returns.

Draw a simple timeline or just list in chronological order all the costs and returns you discovered in steps 1 and 2. Costs should be listed as negative dollars and returns as positive dollars.

For example:

1/1/2006 Initial investment cost: - $100,000
9/21/2006 Sell investment: $120,000
Step 4. Calculate annualized return of investment or APY.

This is the meat of the process and the most challenging step of calculating the return on an investment. Let me explain it using a simple example that we started above.

Let's assume you made an investment on January 1, 2006. That investment cost you $100,000 including fees. Today, September 21, 2006, you decide to sell that investment and you receive $120,000 after all expenses.

Now we want to find the APY of this investment so we can compare it to other investments or even your savings account rate. In finance, this is often called calculating your internal rate of return. Technically this process involves determining a discount rate at which the present value of a series of investments is equal to the present value of the returns on those investments. (Ah, this brings back memories of economics in graduate school.) Thankfully, you don't have to fully understand the process of how this is calculated in order to use it.

For a simple situation like the example above:

APY or IRR = (Final return/Initial investment)^(365/days) - 1

In English, this means that APY equals the final dollar amount divided by the initial investment (positive number for this equation) raised to 365 divided by the number of days the investment took to complete. Then you subtract one from the number you just calculated and multiple by 100 to get your percent APY.

Too bad most investments are not this simple. You often have to pay additional capital in throughout the investment project (e.g. quarterly taxes) and your returns often come in periodically (e.g. monthly) and often with a final lump sum payout (e.g. you sell your investment to someone and get paid).

Modern spreadsheet software includes a great function to automagically find the internal rate of return (IRR), which is the same as APY. Microsoft Excel (MSFT), Open Office (SUN), and Google Spreadsheets (GOOG) include the flexible XIRR function that can take a list of investments and returns and the corresponding dates of those events and calculate the APY for that investment. This is a powerful and very useful function that I recommend everyone learn how to use and understand. The XIRR function is very flexible. You can you it for very simple investments like the example above or much more complex situations that include payments that occur regularly or even irregularly.

Let me show you a two examples:

Example #1 - Monthly returns



Example #2 - Yearly returns



View the examples using Google Spreadsheets.
View the examples using Excel spreadsheet: Annualized rate of return.xls. This spreadsheet includes the simple example from earlier in the post as well.

Notice how the return in Example #1 is much higher than that of Example #2 even though the payment amounts and total profit are the same. The key difference is the timing of the payments. Because the returns in Example #1 come monthly, the annualized rate of return or APY is much higher. In Example #2, profit dividends only come in annually. That dramatically reduces the APY. I like using annualized rates of return because they account for the time value of money.

That's it! Now you know how to properly measure your return on investments. Compare the different annualized rates of returns for your various investment options and then you can select those with the highest rates of return (assuming risk is equal among the alternatives). You can also determine your “real” return by subtracting out the average rate of inflation from the annualized rate of return. This way you can determine if you are actually building wealth with your investments.

How to calculate your return on investment

A firm's break-even point will rise if

kerat --

First, start your own thread for this new topic. This is not related to the original post, and has nothing to do with finance anyway. It also sounds like homework and therefore belongs over in the homework section.

Speaking of homework, I'm assuming that's what this is. Please see our guidelines on submitting homework:

Ask Me Help Desk - Announcements in Forum : Homework Help

Since there is more than one thing that could affect a break-even point, I'm going to assume this was a multiple choice and you left out the choices? If so, put them back in and tell us what you think the answer is and why. Then someone would be able to help you.