Wondering about growth rates? Do the math

When you study companies as possible investments, a little math is involved. Fortunately, it’s not rocket-science math. Here’s a short lesson on calculating growth rates. Imagine Buzzy’s Broccoli Beer (ticker: BRRRP), with sales of $12 million in 2002 and $48 million in 2005. If you have a slightly fancy calculator, it might sport a feature that calculates growth rates for you. If not, here’s what to do.

Divide $48 million by $12 million, and you’ll get 4. This means that sales quadrupled, or increased by a growth multiple of 4. That doesn’t translate to a gain of 400 percent, though. (After all, if something doubles, it increases by 100 percent, not 200 percent.) To get the percentage, you need to take the growth multiple, subtract 1, multiply by 100, and then tack on a percentage sign. So 4 minus 1 equals 3. And 3 times 100 is — bingo! — 300 percent.

Another way to approach it is to take the $48 million and subtract the $12 million, getting $36 million, which represents the growth. Divide $36 million by $12 million, and you’ll get 3. Multiply that by 100, and you have 300 percent. Same answer.

One last valuable step is to annualize the growth rate, figuring out by how much Buzzy’s sales are growing each year. To do this, we first need to determine the time period involved. From 2002 to 2005 is three years, so we’ll be taking the third, or cube, root of the growth multiple, raising it to the 1/3 power.

You’ll need either a computer with a spreadsheet program or a calculator with a “^” button — one that raises numbers to various powers. Raise the growth multiple of 4 to the 1/3 power, and you’ll get 1.59 (4 ^ 1/3 equals 1.59). Now subtract 1, multiply by 100, and you have 59 percent as the approximate average annual growth rate. (If the time period had been five years, you’d raise the multiple to the 1/5 power. For 8.4 years, it would be the 1/8.4 power.)

This math can prove profitable, after a little practice.

Ask the Fool

Q: How much risk should I, as a teenager, take when investing? — P.R., Macon, Ga.

A: First off, kudos to you for learning about investing at your age!

You’re right to think about risk in relation to age. People near retirement, for example, should be more conservative in their investing, because they may be relying on their investments for critical income and because they may not have the luxury of being able to wait out market downturns.

If you’re 15, though, and the stock market swoons, you can just be patient. In fact, you’d be smart to keep buying stocks when their prices are depressed. (If the money you’re investing is for college, stocks aren’t a good idea, as the market could drop in the short term. Short-term investors should stick to safer plays, like money market funds and CDs.)

Young people investing for the long haul are in the best position. Let’s say you invest $750 and it earns the historical average annual market return of around 10 percent. In 30 years, when you’re only 45, it’ll become $13,000. Sock it away until retirement at 65, and it’ll top $88,000. Add to it over the years, and you’re looking at early retirement!

Learn more at www.fool.com/teens and in our book “The Motley Fool Investment Guide for Teens” by David and Tom Gardner with Selena Maranjian (Fireside, $14).

Q: I hold some stock certificates and want to sell the stock. How can I do so? — M.C., Morganton, N.C.

A: Hand-deliver or mail the certificates to your brokerage, which can then sell them for you. If you don’t have a brokerage, you can open an account with one and then hand over the certificates.

My dumbest investment

In a graduate class on real estate, my professor said that the dumbest thing one could do was to make a real estate decision where the numbers came together because of tax considerations, since tax laws could change overnight. I never violated that rule in real estate, but I did invest in an oil partnership where the only benefit was the favorable tax treatment. Luckily, my loss wasn’t too big. I have many friends who lost their shirts and some who went through Chapter 7 bankruptcy proceedings when they invested in real estate and oil deals — all because the tax laws did change. No investment decision should be based on tax considerations. Taxes should be considered only after you decide that the investment is sound. At that point it’s fine to seek the best short-term tax treatment for the investment. Never count on a favorable tax treatment over the long haul, even on IRAs, 401(k)s, etc. I am old enough to remember the promise that monthly Social Security payments “will never be taxed.” — M.S., Dallas

The Fool Responds: Amen.