Why Higher Discount Rates Lower Present Value?

Imagine you are saving up to buy a brand new gadget next year that will cost exactly one thousand dollars. That one thousand dollars is the future cash flow – the money you will receive, or in this case, need to spend, in the future. Now, think about how much you need to save today to have that one thousand dollars in a year. It seems straightforward, right? You might initially think you just need to save one thousand dollars. But let’s consider a few things.

First, think about a savings account. Banks offer interest. Let’s say your bank offers a 5% annual interest rate on savings accounts. If you deposit money today, it will grow over the year. To have one thousand dollars in a year, you actually don’t need to save the full one thousand dollars today. You need to save slightly less because your savings will earn interest and grow to that amount. In this scenario, the interest rate, 5%, acts a bit like the inverse of our discount rate. It’s the return you earn on your money.

Now, let’s flip the script and think about the discount rate. The discount rate represents the opportunity cost and risk associated with receiving money in the future rather than today. Imagine someone offered to give you one thousand dollars one year from now. Would you value that promise at exactly one thousand dollars today? Probably not. Why? Because there’s a chance things could change in a year. Maybe the person won’t be able to pay you back. Maybe you could use that money today for something really important or beneficial. This uncertainty, this risk, is factored into the discount rate.

Think of the discount rate as a measure of how much less valuable future money is to you compared to money in hand right now. A higher discount rate means you perceive future money as significantly less valuable today. Conversely, a lower discount rate means you see future money as almost as valuable as money today.

Let’s go back to our future gadget costing one thousand dollars. Instead of a savings account, let’s imagine you have other investment options. Suppose you could invest in a relatively safe venture that promises a 10% annual return. This 10% now becomes your discount rate, or at least a part of it. It represents what you could potentially earn if you had the money today and invested it elsewhere.

If your discount rate is 10%, how much would you be willing to pay today for the promise of receiving one thousand dollars in a year? You would calculate the present value. To find the present value, you essentially reverse the process of compounding interest. Instead of adding interest, you are discounting the future value back to the present.

With a 10% discount rate, the present value of one thousand dollars received in one year is calculated by dividing one thousand dollars by one plus the discount rate, which is 1.10. This calculation gives you approximately 909 dollars and 9 cents. This means that receiving 909 dollars and 9 cents today, and investing it at 10%, would grow to approximately one thousand dollars in a year. Therefore, the present value of that future one thousand dollars, with a 10% discount rate, is about 909 dollars.

Now, what if the discount rate was higher, say 20%? This higher rate could reflect a riskier investment environment or a greater opportunity cost. Using a 20% discount rate, you would divide one thousand dollars by one plus 20%, which is 1.20. This calculation gives you approximately 833 dollars and 33 cents. Notice that the present value has decreased to about 833 dollars.

As you can see, when the discount rate increased from 10% to 20%, the present value of the future one thousand dollars decreased from approximately 909 dollars to about 833 dollars. This is because a higher discount rate implies that future money is considered less valuable today. It reflects a greater demand for return, perhaps because of higher perceived risk or more attractive alternative investment opportunities. Essentially, to compensate for the higher risk or opportunity cost, the present value needs to be lower.

In simpler terms, think of the discount rate as a hurdle. The higher the hurdle, the less attractive the future cash flow becomes in today’s terms. You need to discount it more heavily to account for that higher hurdle of risk or opportunity cost. Therefore, as the discount rate increases, the present value of a future cash flow decreases, reflecting the diminished value of that future money in today’s context.