I know, this sounds complicated. Well it isn't; just keep reading for a couple minutes. Start with the concept of present value. Actually, it is easier to understand if we start with the opposite, the future value of money. Let's say you have $1000, and along comes Bill Gates who asks you to lend him the money so he can cover his rent this month. In return he agrees to pay you an annual interest rate of 10%. One year later he pays you back, $1000, plus the extra $100 in interest (1000 * 10%), for a total of $1100. This $1100 is the future value of $1000 one year from now at an interest rate of 10%. Now turn it around, $1000 is the present value of one payment of $1100, one year from now, discounted at an interest rate of 10%. In words, present value is the amount of money that must be invested today, at a given interest rate, to produce the desired amount after a specified amount of time. Take another example; you are eyeing a new house in a development project that will be finished in six years, and you know you will need $100,000 to purchase the house outright. You also know you can get an investment that pays twelve percent per year. How much do you need to invest now? Well as a quick approximation, using the rule of 72, in six years, at 12 percent, your money will double. Thus, you need to invest $50,000 now. This $50,000 is the present value of $100,000 six years from now at 12%.

Now, take a closer look at what bonds and stocks are from the point of view of an investor. A stock or bond is simply a series of payments, either dividends or coupon payments. When you buy a security you pay for the rights to all future payments for that security. If you later decide to sell it, you simply transfer the remaining payments to someone else. Thus, the price you pay for a stock or bond is the present value of all remaining payments. The question then becomes, what interest rate to use to discount the payments. This is the second part of the equation.

Suppose that when you buy a stock, along with the certificate, they give you a table of all future payments, and the dates when they will be paid out. This takes the uncertainty out and essentially makes the payments certain and guaranteed, like a guaranteed loan. In this case, the interest rate is simply the cost of borrowing money, the compensation for not being able to use your money for something else, like going to the movies. Supply and demand of loanable funds determines this rate, called the risk free interest rate, as measurable by short-term treasury notes. Unfortunately, a stock does not come with a table listing the payments. In the future anything can happen to a company, and so risk replaces guarantees. Therefore, we introduce a second component into the interest rate equation. By examining credit cards, a familiar institution of American life, we can solve the puzzle. When you purchase an item on a credit card, they loan you the money in exchange for a series of future payments. These payments are calculated at a certain interest rate. In fact, out of my mail, lets take a look at the fine print on a credit card application (who here reads the fine print?). "The rate is determined by adding 9.9 percentage points to the highest Prime Rate published in The Wall Street Journal..." Here the Prime Rate represents the rate charged by banks to their most credible customers, analogous to the risk free interest rate for investments. The later part, the 9.9%, represents the risk spread between the most credible customers and you. The worse your credit worthiness, the higher the interest rate becomes. Thus, the rate is composed of two parts, compensation for using their money, and compensation for the possibility of you defaulting. In conclusion, the second part in the interest rate equation is the composition for the uncertainty of future payments, that is the amount the security must pay you so that they can rip up that table. So a stock must pay an "interest rate" equal to the risk free rate plus a premium to compensate for the possibility that future dividends will not materialize, or will be less than expected. The same goes for a bond.

Now you have the tools to understand the equation put forth before. The price of a security equals the sum of the present value of all expected future payments, discounted using the composite interest rate discussed above.

Now the actual price of a security comes into play. Start out with stock in a company that just discovered a new high tech gadget that will revolutionize some product. They are destined to make a fortune, and so the risk factor of future dividends has gone way down. Therefore, in accordance with the theory just developed, the stock should pay a lower interest rate. So how does this happen? Investors seeing the good news will step in and buy the security, driving up the price. In effect this makes the dividends less valuable, as you have to pay more now to obtain the same dividend in the future, thereby reducing the effective interest rate. This inverse relationship between the relative value of dividends and the price of a security is important. To examine this feature, we turn our attention to the yield of a security. The yield is the interest rate at which all future payments are discounted at to arrive at a present value equal to the current price of the security. For this reason, investors use the yield as a measure of expected return if the security is held indefinitely. Obviously, if the price of the security goes up, the yield of the security goes down. That is, you are paying more for the same future payments, thus making the expected return lower. This inverse relationship allows markets to adjust for new developments in a security. So, if a new piece of information makes future dividends more secure, the price will increase in order to reduce the yield, thereby reflecting the decrease in risk premium. Please note that the term yield is often applied to stocks as a measure of current dividends. This yield, divides the current annual dividend for a stock by the price to obtain the current return.

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