# Dividend Discount Model

Dividend discount model is a model to valuing stock’s price by discounting expected dividend to the present value. Having a company’s stock, shareholders will received dividend payment and capital gain or losses if the stocks is sold.

And how to calculate the expected return for having a stock? The rate of return that shareholders or investors expect from having the share can be calculated as follow: DIV1 = expected dividend, P0 = current share price, P1 = end of year price. DIV1 = DIV0 + (1 x g) while “g” is the growth of dividend. If ABC Company stock is selling for \$200/share (Po = \$200), expected cash dividend is \$10, the expected sell price is \$215, then the expected return would be:

r = (\$10 + \$215 – \$200) / \$200 = 12.5%

What if you want to compute the current price? As stated before, shareholders will received cash dividends and capital gain or losses.

P0 = (DIV1 + P1) / (1 + r)
P= (\$10 + \$215) / (1 + 12.5%)
P= \$225 / 1.125 = \$200

Generally, there are 3 variations in valuing dividend:

No Growth Dividend: the value of stock with no dividend growth would be dividend divided by expected return. If the ABC Company pay dividend \$10 per share with no growth and the expected return is 12.5%, the price would be:

P0 = DIV1 / r
P0 = \$10 / 12.5%
P0 = \$80

Stable Growth Dividend: the value of stock with stable dividend growth would be dividend divided by expected return minus the dividend growth. If the ABC Company currently pay dividend \$10 per share with 5% growth next year and the expected return is 12.5%, the price would be:

P0 = DIV1 / r
P0 = [\$10 x (1 + 5%)] / (12.5% – 5%)
P0 = \$10.5 / 7.5%
P0 = \$140

If we want to compute the expected return (r), the formula is: Dividend Yield = DIV1 / P0

Using the data given before and we want to compute the expected return:

r = \$10.5 / \$140 + 5%
r = 12.5%

Supernormal Growth Dividend: the value of stock with different dividend growth in some years and followed by constant growth (for example). If the ABC Company currently pay dividend \$10 per share with 7% growth next year, 6% in the second year, and growing stable by 5% per year, the expected return is 12.5%, the price would be: DIV1 = DIV0 x (1 + g) = \$10 x (1 + 7%) = \$10.7
DIV2 = DIV1 x (1 + g) = \$10.7 x (1 + 6%) = \$11.34
DIV3 = DIV2 x (1 + g) = \$11.34 x (1 + 5%) = \$11.91

We can use the constant growth formula to compute the P3:

P3 = DIV3 x (1 + g) / r – g
P3 = 11.91 x (1 + 5%) / (12.5% – 5%)
P3 = \$166,74

Then we can compute the P0 now:

P0 = [\$10.7 / (1 + 12.5%)1] + [\$11.34 / (1 + 12.5%)2] + [(\$11.91+\$166.74) / (1 + 12.5%)3]
P0 = \$9.51 + \$8.96 + \$125.47
P0 = \$143.94