The mathematics of splits/bonus/rights issues 7 comments
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I am offering my own take on things here so those who spot any mistakes please feel free to correct me.
When companies do any of the abovementioned, I would suggest some rules to follow to obtain the theoretical ex-issue share price:
(1)Where the issue does not have an impact on net profit (total, NOT per share), or NTA (total, NOT per share), market capitalisation remains the same.
(2)Where the issue leads to a future change in total earnings or NTA, obtain theoretical value by thinking from the investor's perspective
Rule (1) is relatively easy to follow, and applies to splits and bonus issues. The abovementioned all do not increase total earnings or assets of the company, since what happens is merely a sub-division of shares for the first two and a diminution in the share base for the last. Split is the most straightforward: a 2-for-1 split means share base is doubled and hence share price must halve; that is the only way for market capitalisation to remain constant. It must be; there is no change in total earnings and hence for PE to be the same as before the market cap must remain constant. As for bonus issues, no matter what companies say about "rewarding shareholders with bonus shares" the fact is that it is just another form of stock split: there is no difference between a 1-for-2 bonus issue and a 3-for-2 split.
Rule (2) seems rather arcane; it's applicable for rights issues. Let me use an example: Asiawater recently declared a 1-for-4 rights issue for all shareholders, which means shareholders are entitled to 250 rights for every one lot of Asiawater that they own. Say Asiawater was trading at 45 cents before the rights entitlement expired. To exercise the rights (ie. convert to ordinary share) a shareholder must pay $0.04 per rights share which would obviously increase the asset base of Asiawater the company (hence Rule 2). What is the theoretical ex-rights price of an Asiawater share? It is not simply 45/(1+0.25) = 36 cents because the company asset base has increased; it must be above 36 cents. Consider the investor: theoretically his total holdings before and after should be the same monetarily. Since he effectively has to pay $0.04 per share to obtain another 250 shares, this means the pre-rights issue share price must adjust downwards by an amount such that the total monetary amount of 1,250 shares post-rights MINUS the amount needed to convert rights to shares equals the original monetary amount of 1,000 shares pre-rights ie.
Let Y be the ex-rights share price:
(1250)Y - 250(0.04)=1000(0.45) -> Y=0.368 >0.36
Thus $0.368 would be the theoretical ex-rights price from the consideration of no-loss on the side of the investor.
One would ask: why do we assume that the investor will make no money from a rights issue? Well the limiting case of a rights issue is a bonus issue, isn't it? That's when the investor does not have to recapitalise the company to obtain new shares. And since in bonus issues the market capitalisation doesn't change ie. the investor reaps no capital gains post-issue, why would he do so for a rights issue when he has to pay up to avoid being diluted?