## Monday, December 05, 2005

### The mathematics of splits/bonus/rights issues 7 comments

(P.S: Sorry for any disturbances the advertisements above may have caused you)
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?

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12/06/2005 9:24 AM
Anonymous said...

Re: Let Y be the ex-rights share price:
(1250)Y - 250(0.04)=1000(0.45) -> Y=0.368 >0.36

I think it's not so straightforward. By paying \$40 for 1,000 rights, a shareholder gets 1,000 warrants of Asia Water. The warrants now trades at \$200 per 1,000 warrants. If the paper profit from the warrants is imputed, the the ex-rights price of Asia Water should be much lower than 36.8 cents.

12/25/2005 11:53 PM
DanielXX said...

Yes I agree that the market value of the warrant would be another guide. Based on that:
Value after = Value before
1000(Y)+250(0.2-0.04)=1000(0.45)
-->Y=\$0.41 ie. not necessarily lower, as you said.

I think we're basing on two different scenarios: my scenario (Case 1) was that the scripholder keeps his rights and converts them to full shares. Your scenario (Case 2) is that he sells the rights on the market.

In fact, based on our results, it appears that it may be better to hold the rights and convert them to shares, because the fair value Y for mother share price is much lower for Case 1 ie. one can reap a better profit converting the rights to shares, and selling them off at a market price above its fair value, all things being equal.

12/26/2005 7:36 PM
Anonymous said...

I'm looking at this linkage from the SAY post you made on 20-Sep-06 09:21 am Latest on Dividend / Bonus shares

They are offering a 2 for 1 bonus and I think then that this is equivalent to a 2 for 1 split - except that they will not change the price from \$40 to \$20... however, as in MSFT's \$3 dividend last year, the price immediately dropped from \$27 to \$24, and subsequently laid lower into the \$22-23 range.

My question to you is do you think that will happen here? That when they issue the 2 for 1 will the price immediately devalue to \$20 form \$40.

Question 2 is do you think it'll drive lower as a result as in the case of MSFT.

Thanks

9/20/2006 11:51 AM
DanielXX said...

Hi anonymous,
If you consider that nothing has changed about the company before and after the issue of the bonus shares, it makes sense that the market value of the company must remain the same.

Market value is of course, equal to Shares outstanding X Price per share. You can use it to reason out how much that the share price should adjust downwards by when shares outstanding increases by say, 1.5 (ie. a 1-for-2 bonus). The share price will adjust downwards correspondingly such that market value remains the same.

That is the theoretical situation. As for dividends, using the same principle that nothing has changed before or after, share price before = share price after + dividend issued.

9/20/2006 5:47 PM
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11/23/2010 11:39 PM