Who will decide the face value of the company and on what basis face value will be decided?

face value is fixed by the company in the primary market it’s not changed any time

Present trading price at secondary markets like NSE AND BSE it is fluctuating according to the demand and supply forces at the market level.& its based up on the company performance investors are interested to buy that shares on stock exchange that rate is decided by the demand / Supply

source: http://in.finance.yahoo.com/

Face value is calculated by the issuer, i.e. the company which collects funds, by means of an IPO Initial Public Offering.

For collecting 100 rupees fund with 20 shares, each share will have a face value of Rs.5.

It is the value that is the share initially worth for. When it is listed in normal market (secondary market) teh value of the share is changed by trading it in the market by traders and investors, In case of company closing down/shutting down its operation, the company is obligated to pay the face value back to the shareholder.

Book value is a different thing, dont get confused with that. Usually the market price is higher than book value (value what the company is worth).

Face value will be only a fraction of share price once it is traded in regular manner.

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I think in case the company is shutting down, they will have to give the book value to the shareholders…

I still feel its the face value, under legal obligation, the company will return for retail investors.
For preference share holders it could be higher based on liquidated assets.
Request some seniors to clarify this.
Thanks for your input trade100
Edit:
http://tradingqna.com/697/what-happens-to-my-holdings-if-the-share-company-is-suspended
Have a look at this too