What is a rate of return? In the world of money, when we hear that word, what does it mean? Like many things in life, there is no simple answer. If you had to boil it down to the simplest attributes, we could say that a rate of return usually has these properties: it is measured in terms of percentage, it is often expressed in annual terms and, needless to say, when it comes to investing, we always prefer a positive return over a negative one.

With courses in university math departments titled Theory of Interest and Financial Mathematics, the sky is the limit when it comes to complexity. Nonetheless, when we hear the term ‘rate of return,’ it helps to think of it as a broad group of terms, rather than any single defining methodology. With many variations out there, here are some of the most commonly applied definitions, as well as the nine most common key terms of finance.

**1. Holding Period Rate of Return**

This one is simple: it is your total money back, divided by the capital you put in, over any period of time. In the exempt world, a really good example may be a land banking product; money in - wait - money out. If you got a $1.50 back for your dollar invested six years prior, your holding period rate of return is 50%. The focus is on the raw return, and less so on the time frame invested.

**2. Simple Interest**

This term is often used with the bond component of certain exempt products, or when calculating hurdle rates. It certainly makes for easy math and it is measured in annual terms. If you’re getting 10% simple interest, 3 years later, you can expect a total of 30% on your money.

**3. Compounding Interest**

This term is often referenced when speaking to the ugly side of debt, or the good side of letting investments grow over many years. Here, the name of the game is growth. Like simple interest, this is measured in annual terms. But the key difference when compared to simple interest is that it has an exponential component to it. In math, we call this a higher order function. It means the growth in one period compounds based on what happened in the prior period. Investments offering a DRIP (dividend reinvestment program) will show graphs illustrating this form of interest. When doing financial planning, growth is what really matters and thus, compounding interest is used. It is also known as the compounding annual growth rate (CAGR) or the geometric return, with all 3 versions having the same mathematical equivalence.

**4. Annual Percentage Rate (APR) vs Effective Annual Rate (EAR)**

If you look at mortgage documents, you will often see the acronyms APR and EAR. The APR is simply the annual rate the bank will charge you. What you, as the consumer should really care about is the EAR, which will reflect the true economic burden in annual percent terms. What does the EAR do? It recognizes the number of compounding periods in a year which is being applied to the APR. The more compounding periods there are in a year, the higher the EAR will be. With most Canadian mortgages being semiannually compounded, one way to battle this is by increasing the payment frequency.

**5. Internal Rate of Return (IRR)**

If you invest in years 1, 3 and 5, and see money back in years 7, 9, and lastly 12, how do you calculate a rate of return? Through the wonders of iterative calculations (think trial and error), computers, and less preferably, humans, one can calculate an IRR. Like most rates of returns, it is again a way to tell you how hard your money is working. Here, the focus is on the timing of cash flows, and whether they are positive or negative. While it is not precisely the same as compounding interest, in simple cases, the 2 will yield the same answer. Again, compounding interest is all about growth, and while an IRR does focus on the same, it will also capture the scope and timing of cash flows. The formal definition of an IRR is the discount rate (see below) which makes a NPV (see below) equal to zero. IRR’s are especially useful for cases such as investment projects with staggered exits, pension products, insurance tools, and flow throughs, especially if tax savings, and their timing, are being accounted for. IRR’s are also useful for products with return of capital built into their returns, as often the cash flows back to the investor are laddered over time.

**6. Expected Future Value**

This is the amount you expect at some point in the future. Give someone $1000 today and they will give you 10% and your money back in a year. What do you expect? Easy, right? $1000 x (1+10%) = $1100. You expect a future value of $1100. Expectations must be set accordingly in the investor’s mind, which reinforces the role of good advising from a DR (dealing representative). Expectations are fundamentally a hope with some degree of risk tolerance. When something is guaranteed, there is still a degree of risk, no matter how small. Even with statisticians, when something is considered 100% certain, they will always say ‘the probability converges to 100%’; this means it can get very, very close, but never truly hits 100%.

**7. Discount Rate**

Would you hire childcare for $20/hour so you can make $100/hour at work? While there could be many factors at play, from a sheer economic standpoint, you will likely hire the care provider. This is because you discount your time at $100/hour. In finance, when analyzing investments, one must always recognize what they can discount their money at. That is, what else could they do with their money if they did not make the investment being considered. The discount rate selected will vary depending on the investment and its risks. For example, you may discount your money for making a very safe GIC investment at the rate the other banks are offering for similar GICs. If it is a risky investment, you may discount your money at 20% per annum for example.

**8. Net Present Value (NPV)**

IRRs and NPVs are staples to finance. Take the above example with the $1000. We know the future value is $1100, in one year, and you began with $1000 today. If you assume that you can get 10% (the discount rate) on your money with other investments of equal risk, and you are promised $1100 in one year, what is the present value (PV) of the $1100 offer? It is $1000; $1100/(1+10%). Note how this is the opposite of the calculation two paragraphs above. You are bringing the future value to what the value would be today. A present value is basically what a decision is worth today at some assumed discount rate; that discount rate should match the return profiles of similar investment options with similar risks, liquidity and tax efficiency. A NPV is a present value, but it will take into account both positive and negative cash flows, ‘netting’ them out. An IRR will tell you how hard your money is working, while a NPV will tell you what that decision is worth today. This very phrase fundamentally will dictate multibillion dollar decisions. For those who may enjoy Excel a little too much, this powerful tool can compute many of the above listed measures.

**9. Cost of Capital**

This is simply the cost to get money and to fund its use. For most people, it will be interest costs if the funds are borrowed. For companies and exempt products, it can be both debt costs, and the costs of equity (the return which equity holders are expecting from their investment). If there is idle cash to use for the investment, there is technically no cost of capital. That being said, there is still an opportunity cost, which means something was theoretically given up to deploy that cash and use it. It is interesting to note that a cost of capital is a finance term, while an opportunity cost is an economic concept. Typically, financial projections of an exempt offering will focus on costs of capital (like a mortgage on a real estate project, or what investors are being paid in a mortgage pool), as this is specific to the project. An investor’s job is to think about their specific cost of capital (like their line of credit), if applicable, and any opportunity cost (if its cash), as this is specific to them and their circumstances.

As far as math lessons go, numbers may help explain, as much as they may confuse a client. With the above explanations there are 3 main takeaways for a dealing representative: there are many ways to understand and compute how hard money is working; it is important to project what an investment will be worth tomorrow; and it can help to know what any decision is worth today. The key takeaways for a client are that they understand the investment’s risks and its application. If a DR communicates and plans well for the client, the numbers will take care of themselves!

*Please note this article was originally published in Exempt Edge Magazine and updated for Educate & Explore.*