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:

DIV_{1} = expected dividend, P_{0} = current share price, P_{1} = end of year price. DIV_{1} = DIV_{0} + (1 x g) while “g” is the growth of dividend. If ABC Company stock is selling for $200/share (P_{o} = $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.

P_{0} = (DIV_{1} + P_{1}) / (1 + r)

P_{0 }= ($10 + $215) / (1 + 12.5%)

P_{0 }= $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:

P_{0} = DIV_{1} / r

P_{0} = $10 / 12.5%

P_{0} = $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:

P_{0} = DIV_{1} / r

P_{0} = [$10 x (1 + 5%)] / (12.5% – 5%)

P_{0} = $10.5 / 7.5%

P_{0} = $140

If we want to compute the expected return (r), the formula is:

Dividend Yield = DIV_{1} / P_{0}

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:

DIV_{1} = DIV_{0} x (1 + g) = $10 x (1 + 7%) = $10.7

DIV_{2} = DIV_{1} x (1 + g) = $10.7 x (1 + 6%) = $11.34

DIV_{3} = DIV_{2} x (1 + g) = $11.34 x (1 + 5%) = $11.91

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

P_{3} = DIV_{3} x (1 + g) / r – g

P_{3} = 11.91 x (1 + 5%) / (12.5% – 5%)

P_{3} = $166,74

Then we can compute the P0 now:

P_{0} = [$10.7 / (1 + 12.5%)^{1}] + [$11.34 / (1 + 12.5%)^{2}] + [($11.91+$166.74) / (1 + 12.5%)^{3}]

P_{0} = $9.51 + $8.96 + $125.47

P_{0} = $143.94