Why Gordon Growth Valuation Does Not Add a Separate Sale Option
Summary
The document asks whether a stock’s dividend value under a Gordon-style discounted cash-flow model should include an additional option to sell when its market price exceeds the present value of future dividends. It frames the ability to liquidate before an investment horizon as an American-style option and proposes adding that option value to the dividend valuation.
The response argues that if the Gordon model is assumed to correctly value the company, the stock price at a future time already equals the present value of the remaining dividends. Under that assumption, the proposed exercise condition creates no additional option value. The answer points toward real-options theory and notes that the Gordon model has limitations, but does not develop a fuller valuation framework or assess behavioral-finance effects. The conclusion therefore depends on accepting the model’s assumptions; it is not a general claim that selling flexibility is never valuable.
Key ideas
- The proposed valuation adds a sale option to the present value of expected dividends.
- Under the assumed Gordon valuation, the future stock price equals the value of remaining dividends.
- That equality makes the proposed option valueless within the model’s own assumptions.
- The question connects to real-options theory, while the answer cautions that the Gordon model has limitations.
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Full text
# Gordon's dividend valuation model: Ignoring optionality
# 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 $t<T$, 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 by skoestlmeier (score 1)
https://quant.stackexchange.com/a/42354
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.