The Power of Interest: Making Informed Financial Choices
Introduction to Interest Rates
Interest rates are a fundamental concept in finance, but what exactly is an interest rate? You might think of it simply as the percentage you earn each year on your bank or investment accounts or the percentage you pay in interest on your mortgage or car loan each year. And you’re right, an interest rate is the cost of borrowing money or a reward for saving money. Think of it as the price you pay to borrow money or the money you earn for keeping your money in a bank or in investments.
But interest rates can have many different interpretations, so let me try to break down interest rates in a way that is easy to understand.
Three Interpretations of Interest Rates
Required Rate of Return: This is the minimum amount of money you expect to earn from an investment. For example, if you invest in a business, you might expect to earn at least 10% on your investment each year. You might have decided on this 10% level given your opportunity costs, which I will discuss in more detail later. What I mean by that is that if stocks over the long run have earned roughly 10-12% on average and you believe that will persist over the time horizon of your business, then you may say, “Why would I put all this time and effort into running a business that only earns me 10% per year if I think I can passively earn 10% per year in the stock market?” If the business doesn't meet this 10% return expectation, you might consider it a bad investment. Here are some other simplified examples:
Example 1: Investing in a Stock
Scenario: You are considering investing in a company's stock.
Required Rate of Return: You determine that you need to earn at least 8% per year to justify the risk of investing in this stock. There are many reasons this might be, but let’s say you feel this way because 10-year government bond yields (which are essentially a “risk-free” investment) are currently paying 3% per year. Stocks are risky, and the long-term equity risk premium, or interest rate spread over government bonds, has been roughly 5% over the long-term. If government bonds are paying 3%, then you might believe you need 5% above the 3%, or 8%, to compensate you for the additional risk you are taking by investing in a stock that is not risk-free.
Interpretation: If the stock is expected to return less than 8%, you won't invest because it doesn't meet your required rate of return.
Discount Rate: This is used to determine the present value of future cash flows. In other words, think of a discount rate as a tool to figure out how much future money is worth today. It helps us compare money today versus money at some point in the future. Imagine you have a choice between receiving $100 today or $110 a year from now. How do you decide which option is better? The discount rate helps you figure out how much that $110 in the future is worth in today’s money. If the discount rate is 10%, then $110 next year is worth $100 today. I know this may still be confusing, so let’s explore a couple more examples:
Example 1: Valuing a Future Payment
Scenario: You are offered $1,000 to be received in 3 years.
Discount Rate: You use a discount rate of 5% to determine the present value of that $1,000.
Calculation: The present value is calculated as $1,000 divided by (1+0.05)³ ≈ $863.84.
Interpretation: The $1,000 in 3 years is worth about $863.84 today if you discount it at 5%. Said differently. $863.84 today is equivalent to $1,000 in 3 years when discounted at a rate of 5%. If you can earn more than 5% per year, let’s say 7% per year, then investing $863.84 today would become $1,058.24 in 3 years and you might thus reject the offer to receive $1,000 in 3 years.
Example 2: Evaluating a Project
Scenario: A company is evaluating a project that will generate $10,000 in 5 years.
Discount Rate: The company uses a discount rate of 6% to find the present value of the future cash flow.
Calculation: The present value is $10,000 divided by (1+0.06)⁵ ≈ $7,472.58.
Interpretation: The future cash flow of $10,000 is worth about $7,472.58 today when discounted at 6%.
Opportunity Cost: This is the value of the next best alternative that you give up when you make a decision. For example, if you decide to spend $100 on a concert ticket, the opportunity cost is what you could have done with that $100 instead, like saving it in a bank and earning interest.
Example 1: Choosing Between Investments
Scenario: You have $1,000 to invest and two options: a savings account with a 2% interest rate or a stock expected to return 5%.
Opportunity Cost: If you choose the savings account, the opportunity cost is the 3% additional return you could have earned from the stock.
Interpretation: By choosing the savings account, you forgo the opportunity to earn a higher return from the stock.
Example 2: Spending vs. Saving
Scenario: You decide to spend $500 on a new gadget instead of saving it.
Opportunity Cost: The opportunity cost is the interest you could have earned by saving that $500 in a bank account with a 3% interest rate.
Interpretation: By spending the money, you miss out on the potential earnings from saving it.
Simple Example of Interest Rates
Finally, let's use a simple example to show how interest rates work with differently dated cash flows.
Imagine you have $1,000 today and you want to know how much it will be worth in one year if you invest it at an interest rate of 4.0% (roughly the average annual percentage yield for a high-yield savings account in the U.S. currently).
Here's the math:
You invest $1,000 today.
After one year, you earn 4.0% interest on $1,000.
The interest earned is $1,000 * 0.04 = $40.
So, after one year, your $1,000 investment grows to $1,040 ($1,000 + $40) before tax.
But let’s take it a step further. Let’s assume you believe high yield savings rates (which are variable in nature) will stay at roughly 4% for the next 2 years after that, or 3 years total of 4% per year on your initial investment of $1,000.
After year 1, as we already discussed, you would have $1,040. Now let’s take that $1,040 and compound it two more years forward at 4% per year. $1,040 * 1.04² = $1,124.86.
So in year 2 you earn 4% on $1,040, instead of $1,000, then in year 3 you earn 4% on $1,081.60, instead of $1,000.
This example shows how interest rates help us understand the relationship between money today and money in the future and highlights the power of “compounding” your money.
I know this may be very basic to some, but this is a very important concept and a concept that if you understand well can change your life in a significant way. I will leave you with 4 quotes on the power of compound investing over a long-term time frame:
"Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn't, pays it" - Albert Einstein
“If you understand compound interest, you basically understand the universe.” - Robert Breault
“Money makes money. And the money that money makes, makes money.” - Ben Franklin
“Understanding both the power of compound interest and the difficulty of getting it is the heart and soul of understanding a lot of things.” - Charlie Munger
Conclusion
Interest rates are a key part of finance, helping us all make decisions about saving, investing, and borrowing. By having a basic understanding of the required rate of return, discount rate, and opportunity cost, you can make better financial choices. Remember, interest rates reflect the value of money over time, helping us compare the value of cash flows at different dates. The time value of money (TVM) is a fundamental financial concept that states that money available today is worth more than the same amount in the future due to its potential earning capacity.
In future posts, I will dive deeper into the concept of time value of money with numerous examples, and I will show you how the use of a financial calculator or online calculators can help you make more informed financial decisions. Whether it be making investment decisions, loan calculations, retirement planning, or figuring out how much to pay for a business you want to buy, understanding TVM has a broad range of applications that can be crucial to making sound financial decisions and planning for the future.