# Math For Investors 101

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The baseball world uses a lot of mathematical equations to describe exploits on the field. One of them is batting average which is calculated by dividing the number of hits by the number of at-bats. A player with 100 hits and 380 at-bats has an average of .263.

The investing world is also ruled by equations. Study hard. There will a quiz at the end.

One of the most important is the one used for calculating the current value of an investment based upon compounded interest: Current value = Initial Value*(1+i)^n where i is the effective interest rate, n is the time period involved and the "^" symbol means raised to the power of.

As an example, the current value of an initial \$10,000 investment accumulating 9% per year for 30 years can be calculated using [\$10,000*(1.09)^30]. The answer is \$132,677.

The 9% rate of return is the average gain per year for the S&P500 index over the last 30 years. Could you have done better? Yes, probably. If you bought and held the right stocks over the long haul.

Investing in a basket of quality stocks (don't forget to diversify with some bonds and cash too) in different market sectors and averaging a return of say 10% per year would have equated to a current value of \$174,494. A "small" difference in the average rate of return (10% vs. 9%) makes a big difference in total value (\$41,817).

Looking at companies with the potential to outperform the market (and their competitors) gives you a good chance for better performance. That's like trading for the improving .333 hitter and getting rid of the declining .251 hitter currently on the team. You want to be able to beat the league average.

International Business Machines (NYSE: IBM) at one time made personal computers, in fact inventing the IBM-compatible PC in the early 80's. Before the computer industry declined IBM transformed itself into a provider of services to other businesses. That's a sign of good management. IBM has plenty of cash, increasing free cash flow 33% from 2007 to 2011 to about \$12B, and has one of the best known brands in the world. Who doesn't know of IBM? The stock has performed well, increasing by 65% over the last 5 years. That equates to a 10.5% return per year. The S&P500 declined about 5% over the same period. IBM would be that .333 hitter.

In contrast, Dell Computers ﻿(NASDAQ: DELL), which took over the title as world's biggest computer maker, has not adapted and transformed itself. Management is not performing well. Although free cash flow has increased by the same amount as IBM's (33%) from 2007 to 2011 to about \$4.5B, the stock has declined by 64%, and has not recovered from the 2008 financial crisis. Dell is the declining .251 hitter that needs to be traded for the .333 hitter. It would not give you that "slight" advantage.

Another equation is the one used for price earnings ratio (P/E). It is calculated by dividing the stock price by the earnings per share over the previous year. For a \$100 stock that had \$10 of earnings the P/E would be 10. When compared to others in the industry, sector or entire market or previous values for the stock it provides a quick snapshot as to the underlying value of a company. In general those with lower P/E's have greater value than one with higher P/E's. The caveat is that P/E is usually calculated for past earnings performance and it will not necessarily provide an indication of value going forward unless earnings estimates are accurate.

The chart below provides a historical summary of P/E calculated for the trailing twelve months (TTM) for the S&P500:

Microsoft Corp. (NASDAQ: MSFT) stock was priced at \$58.38 and had a P/E of about 42, well above the S&P500 aggregate of 27, on 12/31/99. Since then the stock has declined by about 47% to \$30.82. Current P/E is 15.2, just slightly below the market. It would appear Microsoft was overvalued in the late 1990's and priced just about right today in comparison to the overall market.

A third equation used in the investment world is the one for dividend yield. It is calculated by dividing the dividend amount by the stock price. A \$100 stock paying \$2.50 per share per year has a 2.5% yield.

McDonalds Corp (NYSE: MCD) currently pays \$2.80 per share. With a stock price of \$89.49 the yield is 3.1%. A much better return than you could find at your local bank. McDonald's is a member of the Dividend Aristocrats which are companies that have been increasing dividend payouts for 25 consecutive years or more. The company has averaged a 21% dividend growth rate since 1976 and it has plenty of cash to keep paying a dividend.

Stocks from the mortgage real estate investment trust (mREIT) industry are required by law to pay out most of their earnings as dividends and subsequently have a high yield. For example, Annaly Capital Management, Inc. (NYSE: NLY) currently has a yield of 12.7% based upon a stock price of \$17.31 and a dividend of \$2.20. However, the payout has been declining over the past few years. In Sept. 2010 the quarterly payout was \$0.68 per share. Today it is \$0.55 per share.

So in wrapping up your math lesson today please take the following quiz:

1. Calculate the effective rate of return when a \$10,000 investment grows to \$20,000 after 10 years. Would that have beaten the average return for the S&P500?

2. What is the P/E ratio for a \$200 stock with \$12.50 of earnings last year? How does that compare to the overall market?

3. What is the yield on a \$50 stock that pays a \$2.50 dividend? Is that competitive with other forms of investments?

If you know the answers you are ready for Math for Investors 201.

Mark Morelli owns shares of McDonald's and International Business Machines. The Motley Fool owns shares of International Business Machines, McDonald's, Microsoft, and Annaly Capital Management. Motley Fool newsletter services recommend McDonald's. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.If you have questions about this post or the Fool’s blog network, click here for information.