Math plays a heavy role in finance and investing, perhaps even a bigger role than in the core sciences. A key goal in raising our girls is to make sure they grow up not just math literate, but financially literate as well. Stocks, bonds, mutual funds and their derivatives are all plenty confusing when you get started. We’ve been investing for college for some time, and I’ve used that as an opportunity to explain the abstract ideas of “owning part of a company” as being equivalent to stock or “buying part of a loan” as a bond. Getting right down to the price of these market beasties is a whole other game, though. Even some adults I talk to are confused about the prices of stocks. I had a family member tell me they wouldn’t buy Google’s stock because at $600 per share it was too expensive. They only bought stocks that were $10 per share or less. It dawned on me that the connection between market capitalization and stock price (and why this had nothing to do with “expensive” or not) was something I’d need to teach my girls early in their investing careers. Just like any other big asset, a company has a value on it. This is something that’s only partially captured in the stock price because it depends not just on how each share of stock is priced, but also (importantly) on how many shares of stock are out there. Each company decides how many shares it issues, and if there are lots of them out there, then everything else being equal, each one is going to be worth less. Consider IBM which was trading for $188 a share recently. IBM has issued about 1.1 billion shares of stock, so if you multiply those numbers, you could in theory buy all of IBM for something like $200 billion. Hang on while I put away my checkbook. Now consider GE, which was trading for about $20 a share recently. GE has issued just about a ten billion shares of stock (in other words about ten for every one shares of IBM). If you multiply these figures out, you get something like $200 billion, just like IBM. So, in other words, people buying and selling shares of IBM and GE think these two companies are worth roughly the same amount of money, even though their stock prices are an order of magnitude apart. The price AND the number of shares outstanding tell you the total value of the company. Today’s share price alone doesn’t tell you if one stock is expensive compared to another stock… It only tells you how much the price might have changed recently. Reliably determining if a stock is priced reasonably is another question entirely (if you figure that out, be sure to let me know in the comments!), but plenty of people use statistics and ratios to help make better comparisons between companies. We’ll explore those in some later worksheets, and I’d like to do a ‘kid friendly’ introduction to those topic soon, but for now a good start is to learn that most of those statistics are in terms of per-share values. Understanding the value of a business itself really requires that you know what market capitalization is (number of shares x share price) and how to move between its components. Enter the market capitalization worksheets… Market Capitalization and Share Price Worksheets Hopefully these investing word problem worksheets provide a solid start to your young capitalist!