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.
- The accounting value of assets less liabilities, based on past transactions — 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.
It is a historical record. Market value reflects expectations, which is why the two routinely differ by large multiples.
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.
Each retained unit of capital earns more than shareholders require, so retained earnings add value. The premium is the capitalised economic profit.
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
Its accounting profit does not cover the cost of the capital employed. Accounting profit ignores the charge for equity capital, so a company can be profitable on that measure and still destroy value — and the discount to book is the market saying so.
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