# Essential Basic Math for Investors

The fundamental essence of investing in stocks is to buy a share in a company and make an acceptable return over a holding period through a combination of dividends and capital gains.

True investing requires a planned holding period of at least one year although in many cases you may plan to hold the stock indefinitely for many years.

A planned holding period of less than one year is an operation in pure speculation or gambling, rather than investing.

An acceptable company for investment should have a high probability of making a positive return and only a very small probability of incurring a significant loss if held for several years.

Returns on a stock will come from: 1. Dividends collected over the holding period and 2. The (hoped for) capital gain on ultimate sale of the stock.

The capital gain is fueled by two things, first the growth in earnings. For example, if a stock is bought at a P/E of 12 and its earnings double over a five year period, then the stock will yield a capital gain of 100% if the P/E remains at 12.

The second driver of the capital gain or loss is the change in the P/E ratio. If you buy a stock with a P/E of 12 and the P/E changes by 50% to 18, over any period of time, then this yields a 50% capital gain, assuming earnings are unchanged.

The P/E is fueled by investor outlook for earnings growth and the general market sentiment. Changes in the P/E account for most day to day stock volatility.

But, ultimately over longer periods of time earnings growth will determine the capital gain since earnings growth produces capital gains at a constant P/E and is also the main driver of changes in the P/E.

Therefore, investors should be very concerned about the expected growth in earnings per share (“EPS”).

Growth in EPS is the buoyancy force that drives up the value of a stock. Your goal should be to buy companies with strong EPS growth potential AND IMPORTANTLY to buy them at prices that reflect a lower EPS growth. For example, if a stock price is implicitly pricing in 20% EPS growth, then you can expect to lose money if the EPS ultimate grows at “only” 15%. You must seek to buy stocks that will grow EPS at a higher rate than the growth that you are implicitly paying for when you buy the stock. This is a fundamental concept that most investors (and even most advisors) simply do not understand. You are ahead of the game if you understand this.

Any dividends and growth in dividends are also buoyancy forces that drive stock values up.

The required rate of return on investment is a gravitational force that pulls stock values down.

Investors require a return on investment. If you require a 5% return on your investment then you should be willing to pay up to \$7.84 today for a guaranteed payment of \$10.00 five years from now. However, if you require a 10% return (perhaps because you have alternative uses for the money that will return 10%) then you would now be willing to pay no more than \$6.21 today for that same guaranteed \$10.00 payment in five years. Your higher required return has acted as a gravitational force pulling down the value of the investment. The impact of a higher required return becomes very dramatic over longer periods of time.

The result is some interesting and surprising results.

A stock that pays no dividends MUST grow its earnings at at least the same rate as your required return. (Assumes no change in the P/E).

If you want to make a 9% return on a non-dividend paying stock, then that company MUST grow EPS at at least 9%. Often such a company would brag if earnings grew at 8%, but the fact is that this is a losing investment for you.

Surprisingly, if you must make 9% on your money and the non-dividend paying company can only grow earnings at 8%, then the stock is ultimately worthless to you!

Consider a non-dividend paying company that is selling at \$12.00 and earning \$1.00 per share and therefore selling at a P/E of 12. Now imagine that the earnings will remain at \$1.00 per share for ten years (because management keeps investing the earnings in bad projects). If the P/E stays at 12 then this company will still be selling for \$12.00 per share in ten years. If you could forecast all of this and your required rate of return was 9%, what is the value of that share to you today? The surprising answer is that it is worth \$5.07 today. That means this stock with zero growth and zero dividend should only be selling at a P/E of 5! And if it is assumed to keep on making a \$1.00 per share forever but with no growth and no dividend then in the very long term, it is actually exactly worthless!

Investors should be aware of the concepts of growth as buoyancy force and required return as a gravitational force or at least find an advisor who understands this.

Shawn Allen, CFA, CMA, MBA, P.Eng.

March 7, 2003 (last revised March 15, 2003)