Contrast market value with book value and link return on equity to the cost of equity
The idea
Book value of equity is a historical accounting figure; market value reflects expectations about future cash flows. The two differ because accounting records past transactions while the market prices prospects, and because most internally generated intangibles never enter the books. The bridge between them is the relationship between return on equity and the cost of equity: a company earning a return above its cost of equity creates value and trades above book, one earning below destroys value and trades below. The price-to-book ratio is therefore a statement about expected economic profit rather than about asset quality.
Formulas
Return on equity
ROE = net income ÷ average shareholders' equity
- net income
- profit after tax, for the period
- average shareholders' equity
- the opening and closing book equity averaged
Earnings measured against book value, which is why it is compared with the cost of equity: above it the company creates value by retaining earnings, below it retaining destroys value and the market price falls under book.
A practice question
What does book value of equity represent?
- The market's estimate of the company's worthWhy not: That is market capitalisation, which reflects expectations rather than recorded transactions.
- Assets less liabilities as recorded in the accounts - correct
- The amount shareholders would receive in a saleWhy not: A sale price depends on what a buyer will pay, which is rarely the accounting carrying amount.
Book value of equity is an accounting figure. Formula: Book value of equity = Total assets - Total liabilities. It is based mostly on past transactions and accounting rules. Market value reflects what investors expect in future, so the two often differ, sometimes by a large multiple. For example, a company with book equity of $500 million may have a market value of $2 billion because investors expect strong profits that the balance sheet does not record.
A harder one
A company consistently earns a return on equity above its cost of equity. How should it trade relative to book value?
- At a premium to book value - correct
- At exactly book valueWhy not: That is the case where the return on equity just equals the cost of equity, so retained capital adds nothing.
- At a discount to book valueWhy not: A discount is the market's verdict on a company expected to earn less than its cost of equity, which is the reverse of this case.
Return on equity (ROE) is profit earned on shareholders' money. Cost of equity is the return shareholders require. If ROE is above the cost of equity, each pound kept in the business earns more than investors need, so they pay more than book value. Formula: Justified P/B = (ROE - g) / (r - g), where g is growth and r is the cost of equity. With ROE 15%, r 10% and g 5%: (15 - 5) / (10 - 5) = 2.0, so about twice book value. If ROE equals r, P/B is 1.0, and if lower, below 1.0.
The hardest tier
A company trades well below book value despite reporting profits. What does this most likely indicate?
- That its assets are undervalued on the balance sheetWhy not: Undervalued assets would push the price above book, not below it.
- That its shares are illiquidWhy not: Illiquidity affects the spread and can shave the price, but it does not explain a large, persistent discount to the carrying value of the equity.
- That it earns less than its cost of equity - correct
Book value is the accounting value of shareholders' money. A price well below it means investors think that money will earn too little. Accounting profit does not subtract a charge for the cost of equity, the return shareholders require. Test: if ROE < cost of equity, then P/B < 1. So a company can report a profit and still destroy value. The discount to book is the market saying that its return is below what its capital needs to earn. Undervalued assets would push the price up, not down.
In the app: 12 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
Take the free diagnostic →