I need to know what is the percentage held by shareholders after each stage:

A company starts off with 5 shareholders owning 52%, 12%, 12%, 12%  & 12%.

1) One shareholder sells back to the company their 12% share. How much do the
remaining four shareholders each own after the buyback?

2) Later, a second shareholder sells back their original 12% share.
What percentages do the remaining three shareholders each own after the
2nd buyback?

3) Even later, a third shareholder sells back what was originally a 12%
share. What percentages do the remaining two shareholders each own
after the 3rd buyback?

blue_heron...

Assuming all the remaining shareholders receive an equal split
of the buyback, the figures resulting from each buyback would 
be as follows:

1) One 12% lot of shares split 4 ways, at 3% each =
   4 shareholders owning 55%, 15%, 15%, 15% = 100%

2) One 15% lot of shares split 3 ways, at 5% each = 
   3 shareholders owning 60%, 20%, 20% = 100%

3) One 20% lot of shares split 2 ways, at 10% each =
   2 shareholders owning 70%, 30% = 100%


Please do not rate this answer until you are satisfied that
the answer cannot be improved upon by means of a dialog
established through the "Request for Clarification" process.

sublime1-ga

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Request for Answer Clarification by blue_heron-ga on 29 Oct 2003 14:04 PST

sublime1 -ga

I agree with the ac67-ga comment below- that the shares were sold back
to the company and the bought back shares should be divided amongst
the owners based on the number of shares they own.

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Clarification of Answer by sublime1-ga on 29 Oct 2003 18:23 PST

blue_heron...

I wasn't sure whether you wanted to interpret the question based
on an equal split of the buyback, or a proportional split based
on stocks owned.

Assuming a split based on currently-owned stock percentages,
I would calculate the resulting percentages in a slightly 
different manner than ac67-ga:

The 52% shareholder should receive 52/12 times the amount of
the 12% shareholders = 4.333333 times as much.

4.333333 + 1 + 1 + 1 = 7.333333

The 52% shareholders' entitlement would then be:
4.333333 / 7.333333 = 59.0909%

The 12% shareholders' entitlement would be:
13.6364%


In the next round, the 59.0909% shareholder should receive
59.0909/13.6364 times the amount of the 13.6364% holders
= 4.33332.

4.33332 + 1 + 1 = 6.33332

The 59% shareholder's entitlement would then be:
4.33332 / 6.33332 = 68.42%

The 13.6% shareholders' entitlement would be 15.79%


In the last round, the 68.42% shareholder would receive
68.42/15.79 times the amount of the 15.79% holders
= 4.33312.

4.33312 + 1 = 5.33312

The 68% shareholder's entitlement would then be:
4.33312 / 5.33312 = 81.25%

The 15.79% shareholder's entitlement would be 18.75%

A minor difference in results, but .05% of a billion dollars
is $500,000!


Best regards...

sublime1-ga

I don't think that's right.  If the shares were sold back to the
company, then the person who owns 52% of the company should get the
majority, but will still own the same percentage relative to the other
remaining holders.  So will now hold:
 52/(52+12+12+12) = 59.1% of the stock.  
The 12% holders will now hold :
12/(52+12+12+12) = 13.6% of the stock, all figures rounded to nearest
tenth.

  The next one to sell back will be selling 13.6%, so the 52% holder
will now have:
59.1/(59.1+13.6+13.6)=68.5%, and the two others will have:
13.6/(59.1+13.6+13.6)=15.8% (again rounded to nearest tenth).

  After the final sale, the two remaining will have:
68.5/(68.5+15.8)=81.3% and:
15.8/(68.5+15.8)=18.7%.  

The key is the answerer's assumption that the shares are split
equally, but they wouldn't be. Since they were sold back to the
company, the shares should be divided amongst the owners based on the
number of shares they own.

Thank you ac67-ga for your thoughts on this question. I agree with
your interpretation.

Sublime-1,
Although it looks like you used a slightly different (and more
complicated) way to figure it out, mathematically it reduces down to
the same method.  The only difference was that I rounded a little more
for sake of simplicity in illustrating the calculation.

The only time that the percentage of stock owned by an individual
would affect the amount purchasable, is if that stock had "rights"
attached to it. This is done to ensure that a shareholder cannot be
diluted by further issues of stock without an option to participate. 
However these rights also have a value and can be sold at a par value.
Typically in a buyback situation the stock would be put in a fund of
the corporations rather than automatically distributed among the
shareholders.  In a small business I would guess that the stock could
be sold to whomever the seller wishes to sell to and in whatever
quantity.  Unless there is a previous contract stating to the
contrary.
Therefore given the terms of the stock, either answer could be
perfectly acceptable.

Gentlemen,

I disagree.  The repurchase by a corporation of its own shares (a
redemption) does not change the number of share that the other
shareholders own.  The guy who owned 52 shares before the transaction,
still owns 52 shares after the transaction.  However his interest in
the entity has increased from 52/100 (52%) to 52/88 (59.09%).

The shares owned by the corporation (aka Treasury shares) cannot
typically be voted by the corporation under most state laws.  As such
the majority shareholder's voting interest in the corporate actually
increases as because of the redemption transaction.