"Book value" is how much you would get (per share) if you shut down a company NOW, sold all their assets, paid off their debts, and divided whatever cash you had left by the number of outstanding shares....

If your corporation is making a healthy profit, why on EARTH would you DO such a thing?

(I suspect your understanding of Mathematics is somewhat flawed)...

Mathematics tells you that? Only if you have no ide on how the stock market works. Or for that matter, anything else that's bought or sold. "Book value" is irrelevant - what matters is what the owner is willing to sell it for and what a buyer is willing to pay for it.

Mathematics will tell. You that the intrinsic value behind each common share is the book value per share.

What are reasons for a share to trade above book value apart from company hype, growth, and stability of earnings/business ?

Also, is it always a good idea to buy when the share is trading below a book value for a cyclical business ?