How book value per share works

Book value per share is book equity divided by the share count:

$$\text{BVPS} = \frac{E}{N}$$

On $2,000,000,000 of book and 100,000,000 shares, BVPS is $20. Price over that BVPS is P/B. A $50 share on $20 is 2.50 times. Market capitalisation over book equity is the same 2.50: $5,000,000,000 / $2,000,000,000.

The two routes are the same identity. Multiplying price and BVPS by the share count cancels, so market cap over book equity cannot disagree with price over BVPS unless one of the three inputs is from a different date than the others.

The price to book calculator on this page works both routes from one set of figures. How price to book works is the multiple. This page is the $20 in the denominator.

Keep the $50 price and 100,000,000 shares. Raise BVPS to $50. Book equity is $5,000,000,000, equal to market cap. P/B is 1.

The share did not get cheaper. Book caught up. A BVPS of $50 matching a $50 price is the accounting residual matching the market residual on this sheet, not a floor under the price, and not what a break-up would raise. The first sheet's $20 of BVPS was the same price on a thinner book pile. The per-share residual moved. The market residual did not.

How price to book works is the multiple that follows that catch-up. This page is the $50 in the denominator.

Price $80, BVPS $40, shares 50,000,000. Book equity is $2,000,000,000. Market cap is $4,000,000,000. P/B is 2.

The same $40 of BVPS on half the first sheet's shares is a smaller book pile. BVPS hides scale the way P/B does. Put the share count back in before lining two names up.

P/E against P/B is the earnings multiple against the book multiple. This page is the book per share those two both need in the background.

Do not paste this $2,000,000,000 of book onto the DuPont teaching equity. Different sheet, different firm.

It is not a market price. It is not tangible book. Identifiable intangibles stay in this residual. Banks sometimes quote tangible BVPS. Type the book your sheet is using.

It is not a liquidation bid. Specialised plant and in-house brands do not sit at sale value on the balance sheet.

It is not EPS. Earnings per share is a year's profit cut into shares. BVPS is the residual claim cut into shares. A profitable firm with thin book can print a high EPS and a modest BVPS at once.

When book equity is zero or negative, BVPS is zero or negative and P/B stops working. This calculator prints no P/B in that case rather than a nonsense figure. Negative book is a description of the residual claim, not a per-share asset anyone can spend. You can still write the residual as a loss per share. That is a description of the claim. It is not a book value you can take to a buyer.

A BVPS above the price is common in asset-heavy sectors after a mark against the book. It is not, on its own, a bargain. Compare it with the same firm over time, or with a rival doing the same work.

It is not a break-up model, not tangible book, and not a P/B screen. The three sheets are $20 of BVPS on $2,000,000,000 of book (a $50 share, P/B 2.50), $50 of BVPS when book equals the $5,000,000,000 cap (P/B 1), and $40 of BVPS on 50,000,000 shares (book $2,000,000,000, cap $4,000,000,000). This is educational material, not financial advice.