Yes, taxation of dividends could affect things, depending on Jane's situation. For simplicity I'll assume Jane pays no taxes on the dividend.
For growth, if we assume
- equal $/share increases, e.g., $10/share
- the short term market value is greater for the dividend ($115) than the buyback ($110) but the long term values are equal ($1,814).
- equal market caps ($6,000,000) after the events
- both the short term ($115 vs. $113) and long term ($1,814 vs. $1,790) favor the dividend.
In all cases Mary's stock options are far better due to the higher share price after the buyback - is that what you see also?
Regarding the options contracts, that's not a fundamental difference between dividends and buybacks. Mary prefers a buyback solely because her contracts specify a fixed strike value, but the board could have drafted those contracts differently to adjust the strike price based on the number of shares outstanding, or any number of other possible versions of the contracts. In fact, there could be a term in the contract providing that if the company ever does a buyback, then Mary's options becomes wholly worthless.
As far the other scenarios, only the first one seems logical to me (what you describe as equal dollar share increase). This is consistent with my previous post. The way I see it, there are two logical ways that the market could apply your hypothetical 20% growth factor.
The first way would be for the market to apply the 20% growth
before considering the corporate action. In this method, the market value of the company before the announcement is $10 million and then after the announcement, the market revises its valuation to $12 million. With 100,000 shares outstanding, the market value of each share will increase by $20, regardless of whether the subsequent return to shareholders is through a dividend or buyback. Consistent with your model, we can assume that the increase is gradual and that the corporate action will take place in the middle of it, but either way, it will be the same dollar value in either case, because it was calculated by the market
before considering the corporate action.
The second way the market could react would be to apply the 20%
after considering the corporate action. In this method, the market value of the company before the announcement is $10 million, but the market is going to subtract the amount of the upcoming cash expenditure before applying the 20% factor, because the market reasons that the cash that is about to be ejected is not available for compounding. With a cash expenditure of $5 million (for the $50 special dividend per share or equivalent buyback), the market would calculate the 20% growth per share as 20%*($5 million)/100,000=$10. In this case, the market value of each share will increase by $10, regardless of whether the subsequent return to shareholders is through a dividend or buyback. Consistent with your model, we can assume that the increase is gradual and that the corporate action will take place in the middle of it, but either way, it will be the same dollar value in either case, because it was calculated by the market
after considering the corporate action.
In summary, if the 20% growth factor is applied in a logically consistent fashion, then it does not appear to be relevant to the long-term analysis. It only seems to make a difference in the long-term if you apply the growth factor in a manner that seems irrational to me, whereupon you assume that the fact that a buyback is being used rather than a dividend causes the shares to increase by more.
My analysis here (and in my previous post) is equivalent to the analysis in brooklynguy's post, but I thought this way of phrasing it was easier to agree with, but I may have been wrong about that.
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The other point is this. My analysis does not assume that the market is inefficient. The large gap between the market and intrinsic value could be due to something that is unknowable to the market, not something that the market has irrationally failed to incorporate into the price despite knowledge of same. For instance, the management of Q might be sitting on an invention that they know will radically alter the world, but they haven't announced it yet and won't announce it until it's done in 2025. In this case, an insider of Q would know that Q is seriously underpriced, but the market has no way of knowing that, so the gross mispricing of Q is not inconsistent with most versions of the efficient market hypothesis.