June 01, 2016

## Applied Game Theory or How to Pay a Dividend without Paying a Dividend

Koninklijke Boskalis Westminster lets its shareholders choose whether they want to receive their yearly dividend in cash or in the form of newly created shares, creating a paradox in which everyone gets less by choosing more.

When opting for cash, the Dutch government takes a tax of 15%. If you opt for the shares, you get the equivalent amount in shares tax-free. This creates an interesting situation: it makes sense for each individual shareholder to opt for the shares and to unlock the cash by selling the newly received ones, thereby saving the taxes and getting strictly more value than when opting for cash. However, if every shareholder does so, Boskalis does not need to distribute a single cent. Instead, it can just issue a few new shares to its shareholders, which makes the whole operation a de facto stock split instead of a dividend payment. Nothing of value leaves the company and the intrinsic value of the company stays the same.

That’s how Boskalis can pay a dividend, without actually paying a dividend.

**Addendum: Theoretical foundations**

This post has sparked a lively discussion on hackernews, with some commentors doubting that there is much game theory at work here. The argumentation above is admittedly sloppy and not 100% watertight, in particular regarding the “everyone gets less part”. However, under the right assumptions, this can indeed be seen as a prisoner’s dilemma in which chosing the share dividend will make the shareholders collectively worse off, at least in the short run with mark-to-market accounting.

Let’s assume a share price of 100€ and a dividend of 5%, so the price will drop 5% on dividend day. Otherwise, there would be an arbitrage opportunity. So after dividend day, a share will trade at 95€. Let’s further assume that buying or selling large quantities of shares has an impact on price. This is the boldest assumption, as it violates the efficient market hypothesis. (One paper that spontaneously comes to my mind that supports my assumption is this one by Lilienfeld-Toal and Schnitzler, see figures 3 and 4.) In particular, I assume that selling 5% of the outstanding shares will push the price down from p to s*p. For s=0.97, the price would go down 3%. Similarly, t=0.85 reflects taxes on dividends of 15%.

This leads to the following prisoner’s dilemma situation, illustrated as a game theoretic decision table (only showing what you get):

everyone else |
||||
---|---|---|---|---|

cash | shares | |||

cash | 95+5t | 95s+5t | ||

you |
||||

shares | 95+5 | 95s+5 |

If you own exactly one share and choose cash, dividend day will change your holdings from one share worth 100€ to one share worth 95€ and 4.25€ in cash after taxes (95+5t). But if you opt for the stock dividend, you will own about 1.05 shares worth 100€ in total after dividend day. Selling 0.05 shares will not measurably impact the market price and bring your wealth to 1 share worth 95€ and 5€ in cash (95+5), making you strictly better off than when opting for cash as you save the taxes. However, if everyone does that, the resulting mass selling of 5% of all outstanding shares will push down the price by say 3%, making you end up with one share worth 92€ and 5€ in cash (95s+5), which is worse than before and also worse than the initial scenario when everyone chose cash. Now you are stuck, because switching back to cash would make you even worse off (95s+5t). That’s a classic prisoners dilemma.