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Price to book vs price to sales

P/B and P/S can share one price and one share count. A $50 share on 100,000,000 shares is a P/B of 2.50 on $20 of book and a P/S of 2 on $25 of sales. Same $5,000,000,000 cap, two identities, two denominators.

 P/BP/S
FormulaPrice / BVPS, or market cap / book equity.Price / sales per share, or market cap / sales.
Shared price and countThe $50 price and 100,000,000 shares sit on this sheet too. That is the same listing, not a mashed firm.The same $50 and 100,000,000 shares. Two identities on one price and one count.
Teaching denominator$20 of book. Book equity $2,000,000,000. P/B is 2.50.$25 of sales per share. Sales $2,500,000,000. P/S is 2.
When the denominator movesRaise BVPS to $50 and P/B is 1. Book caught up with the $5,000,000,000 cap.Cut SPS to $10 and P/S is 5. Sales are $1,000,000,000. The share did not get dearer.
What it is notA sales multiple. Book $20 is not sales $25.A book multiple. Sales $25 is not book $20.

One price, one count, two denominators

P/B is the share price over book value per share. On a $50 share with $20 of BVPS, P/B is 2.50. With 100,000,000 shares, market capitalisation is $5,000,000,000 and book equity is $2,000,000,000.

P/S is the same price over sales per share. On that same $50 share with $25 of SPS, P/S is 2. Total sales are $2,500,000,000. The cap is still $5,000,000,000.

That is allowed. The P/B sheet and the P/S sheet share a price and a share count. They do not share a denominator. Book of $20 is not sales of $25. They are two identities on the same listing, not one mashed firm.

How price to book works owns the 2.50. How price to sales works owns the 2. How book value per share works owns the $20. How sales per share works owns the $25.

Each denominator can move on its own

Keep the $50 price and 100,000,000 shares. Raise BVPS to $50 and P/B is 1: book equity equals the $5,000,000,000 cap. That move does not touch sales.

Keep the same price and count. Cut SPS to $10 and P/S is 5. Sales are $1,000,000,000. That move does not touch book.

A firm can print a high P/B and a modest P/S at once when book is thin and sales are large. Those are two fractions, not a disagreement.

P/E against P/B is the earnings pair on book. P/E against P/S is the earnings pair on sales. This is educational material, not financial advice.

Worked examples

A \$50 share on \$20 of book

The share price is $50, BVPS is $20, and 100,000,000 shares are outstanding. What is P/B?

  1. P/B: 50/20=2.5050 / 20 = 2.50.
  2. Market cap: 50×100000000=500000000050 \times 100000000 = 5000000000, so $5,000,000,000.
  3. Book equity: 20×100000000=200000000020 \times 100000000 = 2000000000, so $2,000,000,000.
  4. From the totals: 5000000000/2000000000=2.505000000000 / 2000000000 = 2.50.

P/B is 2.50. Market cap is $5,000,000,000. Book equity is $2,000,000,000. BVPS is $20.

The same price and count on \$25 of sales

The same $50 price and 100,000,000 shares. Sales per share is $25. What is P/S?

  1. P/S: 50/25=250 / 25 = 2.
  2. Market cap is still $5,000,000,000.
  3. Total sales: 25×100000000=250000000025 \times 100000000 = 2500000000, so $2,500,000,000.
  4. From the totals: 5000000000/2500000000=25000000000 / 2500000000 = 2. Sales per share is $25.

P/S is 2. Market cap is $5,000,000,000. Sales are $2,500,000,000. SPS is $25. Book $20 is not this sales line.

The same price when sales per share is \$10

Keep the $50 price and 100,000,000 shares. Sales per share is now $10. What is P/S?

  1. P/S: 50/10=550 / 10 = 5.
  2. Market cap is still $5,000,000,000.
  3. Total sales: 10×100000000=100000000010 \times 100000000 = 1000000000, so $1,000,000,000.

P/S is 5. Market cap is still $5,000,000,000. Sales are $1,000,000,000. Sales per share is $10. This sales move does not rewrite the $20 book sheet.

Common questions

Are the 2.50 and the 2 the same firm?

They can be read as two identities on the same $50 price and 100,000,000 shares. Book of $20 is still not sales of $25. One denominator is the accounting residual. The other is a year's sales.

Why does a higher P/S not move P/B?

Because sales moved, not book. Cut SPS to $10 and P/S is 5 on $1,000,000,000 of sales. The $20 book sheet is a different identity.

Is a low P/S or a low P/B a bargain?

Each is a ratio on its own denominator. Thin-margin sales print a low P/S as a matter of course. A mark against book prints a low P/B. Neither is a liquidation bid.

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.