Stop thinking about the $2 paid up capital as anything to do with the value of the company and you will be less confused.
Ignore the $2 paid up capital for the time being.
There are many ways to value a company. People may use earnings and future earnings to value a company. People may use Net Asset Value to value a company (Total Assets - Total Liabilities). Market Value/ market capitalisation (value of shares), etc etc.
Depending on your purpose, you will use different methods of valuation. If liquidating, obviously you use NAV cause you dont care about future earnings - you just want to convert everything to cash. If an investor is looking to buy the company in a private sale of shares agreement - he will consider future earnings, etc. goodwill comes in, etc. etc. gets abit more complicated. If you are planning a takeover of a listed company, then quoted prices of shares on the exchange will be relevant....
You ask what is NAV. NAV is basically Total Assets - Total Liabilities. How to calculate this is simple. List out total assets.
This will include (but not limited to):
Cash
Book debt
Shares in other companies (this is your example)
inventory
equipments
land
IP rights
List out all the liabilities of the company, which may include:
Bank borrowings
Salary owing
current liabilities (book debts owing to other ppl).
Take aggregate of total assets minus aggregate of total liabilties, and you will get NAV.
Remember this is only 1 way of valuing a company.
What i shared are the basics..
You may be confused because you confused equity and paid up capital.
equity = Assets - Liabilities.
But note that equity is NOT equal to paid up capital.
Paid up capital, technically speaking, is whatever amount funded by the shareholders. or to be more specific, amount paid up for the sale of that company's shares. If the company was set up to have 2 shares and they were sold for $1 each, paid up capital is $2.
That doesnt mean the company's value is $2. Capital is made up of shareholder's equity (the paid up capital) and other forms of capital - shareholder loans, bank borrowings, etc etc.
sorry for rambling. i dont teach, so apologies if i didnt explain it well.