Dividend Discount Model (DDM) - Part One

A security with a greater risk must potentially pay a greater rate of return to induce investors to buy the security. The required rate of return (aka capitalization rate) is the rate of return required by investors to compensate them for the risk of owning the security.

This capitalization rate can be used to price a stock as the sum of its present values of its future cash flows in the same way that interest rates are used to price bonds in terms of its cash flows. The price of a bond is the sum of the present value of its future interest payments discounted by the market interest rate. Similarly, the dividend discount model (aka DDM, dividend valuation model, DVM) prices a stock by the sum of its future cash flows discounted by the required rate of return that an investor demands for the risk of owning the stock. Future cash flows include dividends and the sale price of the stock when it is sold. This DDM price is the intrinsic value of the stock. If the stock pays no dividend, then the expected future cash flow is the sale price of the stock.

Intrinsic Value = Sum of Present Value of Future Cash Flows

Intrinsic Value = Sum of Present Value of Dividends + Present Value of Stock Sale Price

Formula for Calculating a Stock's Intrinsic Value
Stock Intrinsic Value = D1 + D2 + ... + Dn + P (1+k)1 (1+k)2 (1+k)n (1+k)n	P = Selling Price of Stock D = Annual Dividend Payment k = Capitalization Rate n = Number of Years until Stock is Sold; Present Value of Stock Sale Proceeds

In the above equation, it is assumed that 1 dividend is paid at the end of each year and that the stock is sold at the end of the n^th year. This is done so that the capitalization rate (k) is an annual rate, since most rates of return are presented as annual rates, and simplifies the discussion. We are only interested in the equation's pedagogical value rather than specific results.

Note that if the stock is never sold, then it is essentially a perpetuity, and its price is equal to the sum of the present value of its dividends. Since the DDM considers the current sale price of the stock to be equal to its future cash flows, then it must also be true that the future sale price of the stock is equal to the sum of the cash flows subsequent to the sale discounted by the capitalization rate.

In an efficient market, the market price of a stock is considered to be equal to the intrinsic value of the stock, where the capitalization rate is equal to the market capitalization rate, the average capitalization rate of all market participants.

There are 3 models used in the dividend discount model:

1. zero-growth, which assumes that all dividends paid by a stock remain the same;
2. the constant-growth model, which assumes that dividends grow by a specific percent annually;
3. and the variable-growth model, which typically divides growth into 3 phases: a fast initial phase, then a slower transition phase that ultimately ends with a lower rate that is sustainable over a long period.