Gordon's dividend valuation model: Ignoring optionality

Question

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 $t<T$, 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).

Answer 1

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.

Be aware of some problems with the model and consider other approaches in asset pricing: Your question somehow points to the field of real options, so let me recommend you this paper, which matches behavioral finance with the theory of real options.