# Gordon's dividend valuation model: Ignoring optionality

Currently studying some papers on Behavioral Finance (the dividend puzzle), which employ some basic valuation models, calculating stock's fundamental value $$P_t$$. The most known is the discount of future cash flows(Dividends $$D$$), assuming some growth rate $$g$$. But this model totally ignores an embedded option, with reference to potential liquidation of the position:get the capital gains or continue holding stocks to get the scheduled dividends.

More formally, the Gordon model says: $$P_0=\sum_{n=1}^{\infty}\frac{D_n}{(1+r_n)^n}$$

Where $$D_n$$ and $$r_n$$ the suitable dividend and discount rate for the period (depends on the dividend payout frequency).

But, if we think about it, stock embodies an American option with maturity $$T$$, equal to the investment horizon. One should liquidate his position on time $$t, if stock price at time $$t$$, $$S_t> P_t$$, where $$P_t=\sum_{n=0}^{\infty}\frac{D_n}{(1+r_n)^n}$$, where $$P_t$$ the PV of dividends at time $$t$$.

Hence, a better valuation would be: $$P_0'=\sum_{n=1}^{\infty}\frac{D_n}{(1+r_n)^n}+P_{Call_{American}}(S_T>P_t)$$

Is there any source addressing this issue, or I have just made a huge innovation in Quantitative Finance (hehe).

• How more precisely is the stock price impacting the fundamental value of the firm in your model? – Mats Lind Oct 22 '18 at 7:39
• Fundamental value of a stock should reflect the value of all rights embodied in the share. That means the right to sell at any give moment (assuming some elementary liquidity), the right to receive a portion of profits (which translates to dividends or retained earning might lead to capital gains). – Bougias A. Oct 22 '18 at 8:25
• Wouldn't you be better off separating the fundamental value available to all stockholders from the total value available to those agents who are able to identify the fundamental value at time t and optimally excercise the call in your valuation? – Mats Lind Oct 22 '18 at 8:38

If you assume the Gordon-Model to be the correct approach for evaluating a certain company, then $$P_{Call_{American}}(S_T>P_t)$$ equals zero.
The stock price at time $$t$$ is $$P_t=\sum_{n=t+1}^{\infty}\frac{D_n}{(1+r_n)^n}=S_T$$
As $$P_t$$ equals $$S_T$$, the value of the option is zero. Hence, the Gordon-model ignores your suggested option because the assumptions make it unnecessary.