Book value vs market value, ROE and the cost of equity

What is the difference between book value and market value?

Book value of equity is total assets minus total liabilities as the balance sheet reports them. It reflects historical-cost accounting and grows when the company retains profits. Because management directly influences net income, and can also buy back or issue shares, it influences book value directly.

Market value of equity is what investors collectively pay, the share price times the number of shares. It reflects their expectations about the amount, timing and uncertainty of future cash flows. Management affects it only indirectly, by changing those expectations. The two values are rarely equal.

Value of a company's equitytwo answers to "what is it worth?"

• Book value Memorize assets minus liabilities, from past results
  • Management influence direct, through net income and buybacks
  • Per share book equity ÷ shares outstanding
• Market value Memorize price × shares, from expected future cash flows
  • Management influence indirect, through investors' expectations
  • Link to book price-to-book ratio

$$BVPS = \frac{BVE}{N}$$

$$MVE = P \times N$$

Book value per share divides book equity by the shares outstanding, which puts it on the same footing as the price. The ratio of the two is the price-to-book ratio.

$$P/B = \frac{P}{BVPS}$$

The price-to-book ratio above 1 signals that the market expects growth in future cash flows, or values intangible assets such as brands and software that accounting leaves out. Compare it only across companies in the same industry, because the industry’s growth outlook is built into it.

How do you calculate return on equity?

Return on equity (ROE) measures how much accounting profit a company earns on the equity capital shareholders have supplied. It is net income available to common shareholders (after any preference dividends) divided by average book equity.

$$ROE_t = \frac{NI_t}{(BVE_{t-1} + BVE_t)\,/\,2}$$

Some sources divide by beginning equity instead, on the view that only the equity in place at the start generated the year’s income.

$$ROE_t = \frac{NI_t}{BVE_{t-1}}$$

Both are acceptable if used consistently. Beginning equity suits stable book values, or tracking one company year after year. Average equity suits volatile year-end values or an industry that uses it. Exam questions usually say which one to use; if one does not, use average equity, the main formula.

A rising ROE is not always good news. It also rises if equity shrinks faster than profits, for example after losses or a debt-financed share buyback, and then the extra return comes from more leverage and risk. Different accounting choices, such as depreciation or inventory methods, change both net income and equity, so ROE can be hard to compare across companies. A DuPont breakdown in Financial Statement Analysis shows where a change comes from.

How do ROE, the cost of equity and the required return compare?

Returns tied to equityeasy to confuse, each answers a different question

• Accounting ROE Memorize net income ÷ book equity; the past
• Cost of equity Use it what the company must offer to attract and keep investors; estimated with a dividend discount model (DDM) or the capital asset pricing model (CAPM)
• Investors' required return Use it each investor's minimum; varies by investor

The three measures answer different questions.

Measure	Whose view	How measured
Accounting ROE	the company’s past performance	net income ÷ book equity
Cost of equity	what the company must offer to attract and keep equity investors	estimated (for example with a dividend discount model or the capital asset pricing model, CAPM)
Investors’ required rate of return	each investor’s minimum acceptable return	estimated, varies by investor

Unlike debt, equity carries no contractual payment, so the cost of equity is harder to estimate than the cost of debt. Because companies want capital at the lowest cost, the cost of equity is often used as a stand-in for investors’ required return.

If investors require more than a share is expected to deliver, they sell, the price falls, and the expected return rises until it meets the requirement.

The test for value creation follows: ROE above the cost of equity creates value; ROE below it destroys value, even when profits are positive. Net income ignores the cost of using equity capital, so a company can report a profit and still earn less than its owners could elsewhere.

Exam tip When a question gives ROE and the cost of equity, compare them first. Ignore whether net income is positive.

Go deeper Why book value understates some companies

Accounting records many assets at their historical cost and leaves out others. A brand built over decades, software written in-house or a trained workforce may add little or nothing to book equity. Companies rich in these assets have high price-to-book ratios without being overvalued. In contrast, a company with old factories that earn poorly can have a book value well above its intrinsic value.

Go deeper A rule of thumb that links ROE, the cost of equity and P/B (beyond Level I)

For a company with no growth that pays out all its earnings, P/B works out to ROE ÷ cost of equity. With ROE of 13.125% and a cost of equity of 10%, P/B is about 1.31. With ROE of 9% against 11%, it is about 0.82. This is a simple illustration of why ROE above the cost of equity pushes price above book. Level II develops it properly, and estimates of the cost of equity are covered in Corporate Issuers and Portfolio Management.