Price-to-Book Ratios and Return on Equity

What Price-to-Book Measures

The price-to-book ratio compares the market’s valuation of common equity with the accounting value of that equity. It is a compact measure, but it does not explain by itself why investors value the equity above or below its recorded book amount. Expected profitability, growth, and the return investors require help provide that explanation.

A meaningful comparison requires consistent units and claims. Per-share price must be compared with common book value per share; total market capitalization must be compared with total common shareholders’ equity. Book value is an accounting measure, not an estimate of what the company could necessarily sell its assets for.

Definition: The price-to-book ratio (P/B) is the market price of common equity divided by its accounting book value. On a per-share basis, $P/B=P_0/B_0$, where $P_0$ is the current share price and $B_0$ is current common book equity per share. On a total-equity basis, it is market capitalization divided by common book equity. Use matching share counts and equity definitions.

For the stable-growth analysis below, $ROE_1$ means expected next-year earnings attributable to common shareholders divided by current common book equity per share. This beginning-book denominator makes the model’s growth relationship explicit. Reported historical return on equity may instead use average book equity, so it may not match this forward-looking model measure exactly.

The Stable-Growth Relationship

The price-to-book connection follows from the constant-growth dividend discount model. The model assumes the company pays a constant fraction of earnings as dividends, retains the rest, earns a constant return on beginning book equity, and grows at a constant rate forever. It also requires a required return $r$ greater than the growth rate $g$. These are strong assumptions: the formula is a benchmark for a stable business, not a universal identity for every company.

Let $b$ be the fraction of earnings retained. The payout fraction is $1-b$. If next-year earnings per share are $E_1$, then expected dividends per share are $D_1=(1-b)E_1$. Under the stable assumptions, growth in book equity and earnings is $g=bROE_1$. Substituting these quantities into the Gordon growth model gives the price-to-book relationship.

P_0=\frac{D_1}{r-g} =\frac{(1-b)E_1}{r-g}

Since $ROE_1=E_1/B_0$, divide the price equation by $B_0$. Then replace $b$ using $g=bROE_1$. The resulting derivation explains why profitability relative to the required return matters.

\frac{P_0}{B_0} =\frac{(1-b)(E_1/B_0)}{r-g} =\frac{(1-b)ROE_1}{r-g} =\frac{ROE_1-g}{r-g}

The last equality uses $bROE_1=g$, so $(1-b)ROE_1=ROE_1-bROE_1=ROE_1-g$. Thus, when the model assumptions hold and $r>g$, the stable price-to-book ratio is above one when expected ROE exceeds the required return, equals one when they are equal, and is below one when expected ROE is lower.

Model result: Under constant ROE, constant retention, sustainable growth $g=bROE_1$, and $r>g$, $P/B=(ROE_1-g)/(r-g)$. The comparison with one follows from $P/B-1=(ROE_1-r)/(r-g)$. Do not apply this result mechanically when growth, profitability, or payout is unstable, or when book equity is zero or negative.

Worked Valuations

Worked Example: A Stable Business With ROE Above Its Required Return

A hypothetical firm has current common book equity of $40 per share. Its expected next-year ROE on current book equity is 15%, it retains 40% of earnings, and investors require a 10% return. Under the stable-growth assumptions, find its sustainable growth rate, price-to-book ratio, and implied share price.

Method. First find growth from retention and ROE: $g=bROE_1=0.40(0.15)=0.06$, or 6%. The model condition is satisfied because $r=10\%$ exceeds $g=6\%$.

The stable formula gives $P/B=(ROE_1-g)/(r-g)=(0.15-0.06)/(0.10-0.06)=0.09/0.04=2.25$. The implied share price is $P_0=2.25($40)=$90.00$.

Check. Expected earnings are $0.15($40)=$6.00$ per share. The payout fraction is 60%, so $D_1=0.60($6.00)=$3.60$. The dividend model gives $P_0=$3.60/(0.10-0.06)=$90.00$, matching the ratio calculation. The common mistake avoided here is using current earnings in place of next-year dividends without applying the payout fraction.

Worked Example: ROE Below the Required Return

A hypothetical company has book equity of $32 per share, expected next-year ROE of 8%, a retention fraction of 25%, and a required return of 10%. Calculate the sustainable-growth P/B and implied price.

Method. Sustainable growth is $g=0.25(0.08)=0.02$, or 2%. Since 10% is greater than 2%, the constant-growth valuation denominator is positive. The ratio is $P/B=(0.08-0.02)/(0.10-0.02)=0.06/0.08=0.75$. Therefore $P_0=0.75($32)=$24.00$.

Check. Expected earnings per share are $0.08($32)=$2.56$. With 75% paid out, $D_1=0.75($2.56)=$1.92$. The dividend model gives $P_0=$1.92/(0.10-0.02)=$24.00$. The result is below book value because the model’s expected ROE is below the required return; it does not establish that every real company with P/B below one is undervalued or distressed.

Worked Example: A High Ratio With Very Small Book Equity

A hypothetical firm reports current book equity of $0.40 per share. Expected next-year earnings are $0.12 per share, the retention fraction is 40%, and the required return is 16%. Under the stable assumptions, calculate the model P/B and price. Then explain why the ratio needs careful interpretation.

Method. Forward ROE on current book equity is $ROE_1=$0.12/$0.40=0.30$, or 30%. Sustainable growth is $g=0.40(0.30)=0.12$, or 12%. Since 16% exceeds 12%, the model applies. Thus $P/B=(0.30-0.12)/(0.16-0.12)=0.18/0.04=4.50$, and $P_0=4.50($0.40)=$1.80$.

Check. The payout fraction is 60%, so next-year dividends are $0.60($0.12)=$0.072$. The dividend model gives $P_0=$0.072/(0.16-0.12)=$1.80$. The arithmetic is consistent, but the small book-value denominator makes the ratio sensitive: a small accounting change in book equity can materially alter P/B even if the market price changes little. The common mistake avoided is treating a high multiple as conclusive evidence of strong economics without inspecting the denominator and model assumptions.

Worked Example: Negative Book Equity

A hypothetical company’s common book equity is negative $4 per share, while its market price is $12 per share. During the year it reports positive common earnings of $0.80 per share. Calculate the arithmetic P/B and ROE using the stated book amount, then assess what those numbers can tell an analyst.

Method. The arithmetic ratio is $P/B=$12/(-$4)=-3.00$. Dividing earnings by the negative book amount gives $ROE=$0.80/(-$4)=-20\%$.

Interpretation and check. The calculations are correct, but neither figure has the usual positive-book interpretation. A negative P/B is not evidence that the shares are exceptionally cheap, and the negative ROE here does not mean the company had a loss: earnings were positive. The conventional stable-growth formula is not useful with negative book equity. An analyst should explain the unusual book position and use measures appropriate to the valuation question rather than rank the company by this P/B. The trap avoided is interpreting the negative signs as if both measures had their ordinary meaning.

Reading the Ratio and Its Limits

The model isolates an economic comparison: the return earned on equity versus the return required by investors. The relationship can also be seen by subtracting one from the formula. Because $r-g$ is positive, the sign of the difference between P/B and one is determined by $ROE_1-r$. This conclusion is conditional on the stable model; it does not prove that the accounting book value equals intrinsic value or that the company will actually sustain its forecast.

A high P/B can be consistent with expected ROE well above the required return, but it can also reflect unusually low recorded book equity or optimistic assumptions. A low positive P/B can reflect expected returns below the required return, but accounting measurement, risk, or changing business conditions may also matter. The multiple alone does not identify which explanation is correct.

Growth must be treated carefully. In the model, higher retention increases sustainable growth only because retained earnings are assumed to earn the same constant ROE. If additional investment earns a return below the required return, retaining more earnings need not create value. Further, as $g$ approaches $r$ from below, the denominator $r-g$ becomes small and the valuation becomes highly sensitive to modest changes in inputs. If $g$ is equal to or above $r$, the constant-growth perpetuity formula does not produce a finite valid value.

Match the quantities.
Use price per share with book equity per share, or market capitalization with total common book equity.

Check the book denominator.
Confirm book equity is positive and not so small that rounding or accounting changes dominate the ratio.

Test the stable-model conditions.
Confirm the assumptions of constant ROE and retention are plausible and that the implied growth rate is below the required return.

Interpret, do not just label.
Compare expected ROE with required return under the model, then state why that model-based conclusion may not describe an actual firm.

Common Mistakes

Mixing per-share and total amounts. Dividing share price by total equity, or market capitalization by book equity per share, produces a meaningless ratio.
Using growth without checking its source. The relation $g=bROE_1$ requires stable retention and reinvestment at the assumed ROE; it is not a general growth identity for every forecast.
Ignoring the required-return condition. The constant-growth formula needs $r>g$. A small positive spread also makes the result sensitive to input estimates.
Calling every P/B above one expensive. Under the stable model, a ratio above one can be justified when expected ROE exceeds the required return. The ratio is not a complete valuation conclusion.
Interpreting negative-book P/B conventionally. When book equity is negative, a negative ratio does not mean “cheap,” and ROE’s sign can be counterintuitive.

Key takeaway: Under a stable dividend-growth model, $P/B=(ROE_1-g)/(r-g)$ when $g=bROE_1$ and $r>g$. This makes the relationship between expected profitability and required return explicit, but small or negative book equity and unstable assumptions can make the ratio uninformative.

Check Your Understanding

For each question, use the stated assumptions and keep per-share quantities consistent.

A hypothetical firm has book equity of $25 per share, expected ROE of 12%, retention of 50%, and a required return of 9%. Find sustainable growth, P/B, and the model share price. (Answer: $g=6\%$, $P/B=2.00$, price = $50.00.)
A hypothetical company has expected ROE of 7%, retains 40% of earnings, and has a required return of 11%. Under the stable model, find P/B. (Answer: $g=2.8\%$, $P/B=(0.07-0.028)/(0.11-0.028)=0.5122$, to four decimal places.)
A firm has market capitalization of $12 million, common book equity of $6 million, and 2 million shares outstanding. Find book equity per share and P/B. (Answer: book equity per share = $3.00; P/B = 2.00.)
A hypothetical firm has book equity of $0.20 per share, expected earnings of $0.04 per share, retention of 50%, and required return of 14%. Under the stable model, find P/B and price, and state one interpretive caution. (Answer: $ROE_1=20\%$, $g=10\%$, $P/B=2.50$, price = $0.50; the small book denominator makes the ratio sensitive to accounting changes.)
A company has a share price of $8 and book equity of negative $2 per share. What is the arithmetic P/B, and can it be interpreted as an ordinary cheapness signal? (Answer: $P/B=-4.00$; no, negative book equity makes the conventional interpretation inappropriate.)

What You'll Learn