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

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