### Calculating stock returns - dividend discount model (DDM)

 The main benefit in owning stocks is the dividends that the company pays to its shareholders. Other than the dividends, being share holder does not provide any perks to speak of (the “free” coffee at the annual shareholders meeting does not count). Given that dividends are the only reason to own the stocks, valuing the price of the stock is relatively straightforward: one only has to figure out how much the future dividends are worth. This is the beauty of KISS investing; the investing decisions boil down to a simple arithmetic calculation.So how much should we pay for a company that pays \$10 dividend every year until the earth comes to an end?  If you guessed anything over \$1,000, you are not seeing the big picture (=The only thing certain in life is death. Or do you really think that you will be here after 100 years (100 x \$10 = \$1,000) to collect the dividend?) More to the point, having the \$10 is more valuable now than next year as we could invest the money. For example, we could put the \$10 on a bank CD that has the interest rate of r = 4% and have (1+r)·\$10 = (1+0.04)·\$10 =\$10.40. The interest rate that we expect to earn is called the discount rate and we denote that with the symbol r. Given the discount rate r = 4%, the value of \$10 next year is equivalent of \$10/(1+0.04) = \$9.62 today.­ In finance terms, the net present value (NPV) of the \$10 is \$9.62. Similarly, the NPV of the \$10 dividend that we get after two years is \$10/(1+0.04)2 = \$9.25 and the NPV of the \$10 dividend that we get after 100 years is mere \$10/(1+0.04)100 = \$0.20. The net present value of all the future dividends is obtained by summing them discounted to the present value:Here D0 is the annual dividend and r is our discount rate. Equation (1) is quite cumbersome but in this case the infinite series can be simplified significantly toEquation (2) assumes constant dividends. Fortunately for investors, the dividends tend to grow over time as the company earnings increase. The NPV of dividends with growth rate g is Equation (3) is known as the dividend discount model and it is ­the key to KISS investing. We will use it to value the future dividends. If the NPV of future dividends is more than the stock price, we will buy the stock; conversely, if the value of future dividends is less than the stock price, we will not buy the stock (and if we own it, we should consider selling it). To use Equation (3), we need two additional pieces of information: dividend growth rate g and the discount rate r. The discount rate we get to choose but it should be realistic or we cannot find safe investment opportunities. In investing, it is slow and steady that wins the day! Based on the history of stock market, r = 8% is reasonable expectation for long term total return in large stocks. Similarly, the large gap stocks have historically had a growth rate of g = 5%. For example, in 2011 HJ Heinz Co. (HNZ) has the annual dividend of \$1.80. With r = 8% and g = 5%, we have NPV = \$1.80/(0.08-0.05) = ­\$60.00. At the beginning of 2011, Heinz was trading for about \$50.00 which means that the company is a good buy for an investor seeking an annualized return of 8%. And since this return is in form of dividends, the stock price after buying the stock is irrelevant – the 8% annual return accounts only for the dividends. No need to worry about the price drops/market crashes/position of the moon! This is why the ­KISS investor sleeps well.