Did you pay attention in Arithmetic class?

Stocks had a rough session, giving up ground as investors ponder the next big driver of the next big move. There are still plenty of job openings according to the latest numbers from the Bureau of Labor Statistics.

I know the math. Another day of confused looks and “what’s going on with this market” questions at the water cooler. If you want to look less confused or know the answer to that time-old question, you are looking at the wrong market.

I graduated with an undergraduate degree in Economics with a sharp focus on Finance in 1989. That was a long time ago. You have to trust me when I tell you that there are a few things that I remember quite well from my undergraduate training, chief amongst them is the formula for present value. It has been such an integral part of my career that I even remember the class, the professor, and the classroom I learned it in. I have lost count of the number of times that I have used the formula since I learned it. Indeed, even after many, many graduate courses later, the formula still stands. One can safely say that I am, in fact, well versed in the use of present value calculations.

Being a present value blackbelt, the toughest lesson that I learned was that the results of formula must be taken in context. When I was still a green belt in present value (graduate school), I remember using it to come up with the theoretical value of a stock… um, the same bottom-up method used by blue chip analysts today. There was something wrong, though. My carefully vetted model showed that the company’s stock price should be around $2.00 and yet it was trading at $22.00. I checked my math again and again. I even gave the company the benefit of the doubt when it came to my projections for earnings over the 3 upcoming years, ignoring those published by Zacks Investment Research, the GO TO company for that at the time. What was I missing?

It is a simple formula, but it relies heavily on a few things. Of course, you have to have some solid cash flow projections for the foreseeable future… um, 2 to 3 years. You can spend weeks just on those projections alone. Once you are done with those, you have to pop those into the equation, come up with some sort of market interest rate and you can see what those 3 years of cash flows are worth in today’s dollars. That should be the value of the stock, right? Wrong! What about all the future cash flows beyond 3 years? How do we account for those? We use what is referred to in finance as a terminal value. That is where everything gets turned on its head. Many analysts assume that the company will just keep growing at the same pace… forever… and ever… and ever. We call that a growing perpetuity. Don’t get caught up in the theory, it’s too early in the week for that. The formula for a growing perpetuity is as follows:

Notice how interest rate and growth are in the denominator (the bottom 😉) of the equation. Because there is a minus sign in front of the expected perpetual growth (g), the bigger it gets, the smaller the amount of the denominator, which means the terminal value gets bigger as growth gets bigger. That is why companies that have great future growth prospects have really high terminal values. Notice the keyword “growth”… as in growth companies… as in Microsoft, NVIDIA, Amazon, Alphabet, Tesla, Apple, and Meta, AKA The Magnificent 7.  So, we have established that growth is important for the value of a… growth company. What about the interest rate (r)? That too, is in the denominator, but in this case, as it gets larger, so does the denominator, which means the terminal value gets lower. There are many ways to come up with that r in the equation. The most common one is to tie it to prevailing yields in Treasuries. Has the light bulb gone off yet? If Treasury yields, interest rates, or whatever are going up, the theoretical value of a stock goes… down. Have you noticed that yields have gone up in the past few days? I didn’t even mention that those expected cash flows over the next few years are discounted with that same r in their denominators, meaning that as it goes up, those cash flows are worth less, in today’s dollars. If all this was a bit confusing, don’t worry, I will sum it up for you. If yields go higher, the theoretical, intrinsic, value of a stock goes down. It’s just math.

Remember how I said this needs to be taken in context? Sure, that math suggests that a stock is worth less if interest rates are going higher, but is a +15 basis-point gain in 10-year Treasury yields a reason to sell a stock? I will let you decide. It would seem to me that the most important thing to focus on would be the prospect of future growth… um, g, if you like. Has that changed for your favorite growth stock over the past 2 days? That company the younger version of me was trying to value was Microsoft. My math showed that it was highly overvalued, trading in the $20s. You see, the market was assuming great growth for Microsoft in the future, which I didn’t account for. It’s too bad, because grow it certainly did, and if I understood the math better, I could have made +1,431% return. But I didn’t. It’s just math, stupid.



  • ADP Employment Change (March) is expected to show that +150k new jobs were created for the month, slightly higher than February’s +140 new hires.
  • ISM Services Index (March) may come in at 51.7, same as in February.
  • Pay attention to Chairman Powell, who will speak at 12:10 Wall Street Time.
  • Other Fed speakers today: Bostic, Bowman, Goolsbee, Barr, and Kugler. Your ears will hurt by the end of the day.


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