Book value is the value of an asset on the balance sheet minus total depreciation, depletion, or amortization. For an entire company, it is often viewed as total assets minus total liabilities, often stated on a per-share basis. In this case, it is also known as shareholder's equity.
When an asset is purchased, the cost of that asset is recorded or "booked" on the balance sheet. As time passes and the asset is used or consumed, the asset's "carrying value" is reduced by the accounting expenses of depreciation, depletion, and amortization. A truck used to make deliveries has its value reduced via depreciation or a mine's value is reduced via depletion (gold removed, for example). As the asset is used up, it is worth less and less to the company, so its book value declines over time.
However, just because an asset has been used up from an accounting point of view (had it's book value reduced to zero or some minimum), that doesn't mean the asset is still not useful to the company. It can keep the truck in service and making deliveries, for instance. Another example is Sears, which had a lot of land carried on its books at book value (the original cost), even though the price for land had risen. Eddie Lampert saw that this value could be unlocked by selling the land for a profit.
Corporate book value and valuation
From the basic rule of accounting, Assets = Liabilities + Equity, the book value of all the assets minus the liabilities is what shareholders have invested in the company. This is called the "Net Asset Value" and is often called the book value of the company.
This is one way to value a company, although some consider it to be of little use when looking at tech companies that are heavy on intellectual property and the like, and light on assets such as factories and heavy equipment. So they might go to the next level and refine it to tangible book value, which takes out things like goodwill.
Price-to-book value is one metric investors use when investigating a company. It tells you what you are paying for a company's net assets. Stocks trading at a P/B ratio of less than 1 are often considered undervalued, though this depends on the industry.
Of course, book value changes all the time as a company acquires or sells assets, and as depreciation is taken into account. Book value won't equate exactly to market value.
And plenty of companies trade below book value, which can make for a compelling investment if the value is really there, if it can be unlocked. Value can be a subjective measure -- especially with the intangible assets -- and the market isn't always rational.
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