ComCom - The Condition, one Example and some notes
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the condition holding for Common Company (ComCom):

  • If:
    • $i$ indicates the number of Issued shares for ALL the company;
    • $c$ indicates the number of ALL Common shareholders, being the shareholders owning shares in all its Common portion; and
    • $d$ indicates the Decentralizing property of the company,
      • where $0 <= d <= 1$ and $d$ equals the proration of its Common portion, in which
        • EACH shareholder, being a common shareholder, owns equal number of shares and the number $=( i * d ) / c$,
      • where $d$ may be set, or reset form zero, only once in the lifetime of the company,
        • of which each shareholder shall be either a Common, or a Private, shareholder, never both,
      • where $i * d$ indicates the number of ALL issued shares for the Common Portion and
      • where the proration of the Private portion $= 1 - d$,
      • such that
        • if $d = 0$, then the company is Private and shall not be a Common Shareholder of any other Common Company,
        • otherwise the company is a Common Company and the bigger is $d$ the more Decentralized is the Common company,
  • Then
    • Common companies may be formed by an agreement between its shareholders, where this agreement is prior to any other agreement with other potential such shareholders and where the agreement sets
      • $( i *d ) / ( c * ( c + x ) )$ to be the number of shares of EACH Common Shareholder, which shall be
        • either decreased with each entry of a new Common Shareholder, as $x = 1$,
        • or increased with each departing of a current Common Shareholder, as $x = -1$.
  • Hence:
    • When considering the market forces upon the Share price of each Common Company,
    • If $t$ indicates the price of all Shares in the company, which is the estimated Total value of the company, then
      • $t / i$ indicates one Share price being an estimated value of EACH share in the company;
      • $t * d$ indicates ALL the estimated value of its Common portion;
      • $t * ( 1 - d )$ indicates ALL the estimated value of its Private portion; and
      • $v = ( t * d ) / c$, indicating the value owned by EACH Common shareholder, reflects the value of
        • the number $=( i * d ) / c$ of shares owned by that Common Shareholder,
      • such that, as $0 < d <= 1$,
        • $t * d = v * c$ (or $v / d = v + ( 1 - d ) * ( t / c )$) and each Share price $=t/i=(v*c)/(d*i)$,
    • where $t / i >=1$ cent and where $c <= i * d$,
      • so that each share price is at least one cent and each Common Shareholder owns at least one share,
        • hence for satisfying this requirement, more or less shares may be issued .

Here is a an example demonstrating what happened to the v being the value held by EACH common shareholder, where

  • c increases from zero;
  • $d=0.8$;
  • $i=500$;
  • and v is stable, despite (or exactly when) the n (number of shares of EACH Common shareholder) is reduced
$c=$ number of Common Shareholders $v=(t*d)/c=$ the value owned by EACH Common shareholder $t=(v*c)/d=$ the value the company $t/i=$ the value of one share $t*d=v*c=$ the value of the common portion $(i*d)/c=$ the number of shares owned by EACH common shareholder $t*(1-d)=$ the value of the private portion
$0$ - $12.5=v/d$ $0.025=12.5/500$ $0$ - $12.5$
$(+=1)$ $(+=0)$ $(+=12.5=v/d)$ $$(+=0.025=v/(d*i))$ $(+=10=v)$ $(-=(i*d)/(c*c(c+1))$ $(+=2.5)$
$1$ $10$ $12.5$ $0.025=12.5/500$ $10$ $400= 0.8*i=(4/5)*i$ $2.5$
$2$ $10$ $25$ $0.05=25/500$ $20$ $200=0.4*i =(4/10)*i$ $5$
$3$ $10$ $37.5$ $0.075=37.5/500$ $30$ $133.333=0.266'*i=(4/15)*i$ $7.5$
$4$ $10$ $50$ $0.10=50/500$ $40$ $100=0.2*i =(4/20)*i$ $10$
$5$ $10$ $62.5$ $0.125=62.5/500$ $50$ $80=0.16*i=(4/25)*i$ $12.5$
$6$ $10$ $75$ $0.15=75/500$ $60$ $66.667=0.133'*i =(4/30)*i$ $15$
$7$ $10$ $87.5$ $0.175=87.5/500$ $70$ $57.1428= 0.1142857*i =(4/35)*i$ $17.5$
$8$ $10$ $100$ $0.20=100/500$ $80$ $50=0.1*i =(4/40)*i$ $20$
Now, one private shareholder buy $10$ percents of the company, or half of its private portion, for value of $20$ (double price), hence $v$ now is doubled: $v=20$
$8$ $20$ $200$ $0.40=200/500$ $160$ $50=0.1*i =(4/40)*i$ $40$
$(+=1)$ $(+=0)$ $(+=25)$ $(+=0.05)$ $(+=20)$ $(-=(i*d)/(c*c(c+1))$ $(+=5)$
$9$ $20$ $225$ $0.45=225/500$ $180$ $44.44'=0.088'*i =(4/45)*i$ $45$
$10$ $20$ $250$ $0.50=250/500$ $200$ $40=0.08*i =(4/50)*i$ $50$

Conclusion:

As $d$ is a nonzero and constant and the projected value of all the company is $$t=i*s$,where $i$ is the number of all shared issued and $s$ is the price of each such share,

  • the equivalent for calculating number of shares multiplied share price,
    • per each Common shareholder is $v=(t*d)/c$,
      • which is reflected ONLY from $t$ and $$c$ being the number of all Common shareholders
    • and per each Private Shareholder is $(t*(1-d))* x$, where $x$ is the share/portion of the private shareholder in the Private portion of the company.

Note that:

  • The equality of the value held by EACH common shareholder can be (and is normally) kept not only between the exiting ones, but also between the entering and departing ones, until private shareholders change the share price. This equality enables stabilizing the business plan of the company and it kept by having the price of shares increased by $v/(d*i)$ for matching $(v*c)/(d*i)$, or by increasing $t$ by $v/d$, with each entry of new common shareholder. This increase of the share price offsets the decrement by $(-=(i*d)/(c*c(c+1))$ of the number of shares held by each Common shareholder and is generally explained by involvement of more them, when the common shareholders are to be the clients/contributers supporting the growth of the company (which as shareholder are expected to be more loyal and having benefit in bringing more like them etc).

See also:

Common shareholders in ComCom are like citizens in a state as it is defined in the suggested constitution of its citizens.

@bring back@

By namzezamnamzezam, on 25 May 2007 21:46 history Tags:

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