Interest Rates Impact on Perpetuity Value: The Inverse Relationship

Imagine you’ve discovered a magical money tree. This tree gives you a fixed amount of cash every single year, and it will keep doing so forever. This, in a simplified way, is similar to a financial concept called a perpetuity. A perpetuity is essentially an investment that promises to pay you a consistent stream of income indefinitely. Think of it as receiving a fixed payment, say $100, every year, from now until the end of time.

Now, let’s consider how the value of this magical money tree, or our perpetuity, changes when interest rates in the wider economy fluctuate. Interest rates are a bit like the pulse of the financial world. They represent the cost of borrowing money, but also the return you can expect to get on your savings or investments in general. When interest rates change, it affects the perceived value of future money.

Let’s say you’re considering buying our magical money tree that pays $100 a year. To figure out what it’s worth to you today, you need to consider what else you could do with your money. If you put your money in a regular savings account and earn interest, you could be making money that way too. The prevailing interest rate gives you a benchmark, a standard return you could achieve elsewhere.

Suppose interest rates are currently at 5 percent per year. This means if you invested $100 in a typical investment earning 5 percent, you would get $5 in return each year. Now, to receive $100 annually from our magical money tree, how much would you be willing to pay for it upfront? You would want to pay an amount that makes the money tree’s return competitive with other investment options earning 5 percent.

In this case, the value of the perpetuity, or our money tree, would be $2000. Why $2000? Because if you invested $2000 at a 5 percent interest rate, you would earn exactly $100 per year, just like the money tree provides. Essentially, the value of the perpetuity is calculated by dividing the annual payment by the interest rate. So, $100 divided by 0.05 equals $2000.

Now, let’s see what happens if interest rates rise. Imagine the central bank decides to increase interest rates, and suddenly, the standard rate becomes 10 percent per year. This means you can now get a 10 percent return on your investments elsewhere. If you can get a 10 percent return easily, is our money tree still worth $2000? Probably not.

To get $100 a year now with a 10 percent interest rate, you only need to invest $1000 in a regular investment. $1000 invested at 10 percent yields $100 annually. Therefore, in this new higher interest rate environment, the magical money tree, still paying $100 a year, is now worth only $1000. Notice how the value of the perpetuity decreased when interest rates went up.

Conversely, what if interest rates fall? Let’s say interest rates drop to 2 percent. Now, getting a decent return on your money becomes harder in regular investments. To earn $100 a year at a 2 percent interest rate, you would need to invest a much larger sum. Specifically, you would need to invest $5000 to get $100 annually at 2 percent interest. $100 divided by 0.02 equals $5000.

In this low interest rate environment, our magical money tree, still paying $100 per year, suddenly becomes more valuable. Its value increases to $5000. This demonstrates that when interest rates decrease, the value of a perpetuity increases.

So, the relationship between interest rates and the value of a perpetuity is inverse. When interest rates rise, the value of a perpetuity falls. When interest rates fall, the value of a perpetuity rises. This is because the value of the perpetuity is essentially the present value of all those future payments, discounted back to today. Higher interest rates mean future payments are discounted more heavily, making the perpetuity less valuable today. Lower interest rates mean future payments are discounted less, making the perpetuity more valuable today. Understanding this inverse relationship is crucial for anyone considering investments that provide a stream of income over time, especially those that are designed to last indefinitely.