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##### Subject 5. Price to Book Value
Book value per share attempts to represent the investment that common shareholders have made in the company, on a per-share basis. It can be calculated by subtracting all liabilities and preferred stock from the total assets. Since the P/B ratio contains price per share in the numerator, we restate the book value on a per share basis by dividing it by the number of fully diluted shares outstanding.

A price to book ratio is a price multiple comparing a company's current market share price to its book value per share.

P/B ratio = market price per share / book value per share

Example

Market price = \$60; book value = 200 million; shares outstanding = 5 million.

BV per share = \$200 million / 5 million = \$40.
P/B ratio = \$60/\$40 = 1.5.

• BV is usually greater than zero. Therefore the P/B is usually meaningful, as opposed to the P/E multiple.
• Because book value per share is more stable than EPS, P/B multiple maybe more useful than P/E when analyzing companies with erratic earnings pattern.
• The P/B multiple compares market value of residual assets with their book value, consequently it is most relevant when applied to companies with liquid assets (e.g., financial companies) and in case of significant doubt about the entity's ability to continue as a going concern.
• Some empirical research suggests that the P/B multiple may be a determinant of long- run returns on equity.

• The book value recognizes accounting assets only. It does not include any other valuables such as human capital and good reputation of a company.
• The book value may be distorted by certain accounting practices, such as expensing of R&D, which depress the residual asset value.
• Historical cost-based approach of GAAP leads to outdated and less relevant book values, significantly departing from the true value of shareholders investment.
• Using the P/B ratio is inappropriate when comparing companies with distinctly different business models, especially in part of the fixed asset requirements. A service company is expected to have a higher P/B multiple than a manufacturer of automotive parts when both companies are fairly valued.
• Share repurchases or issuances may distort historical comparisons.

Computation of Book Value

The computation of book value is as follows:

(Shareholders' equity) minus (the total value of equity claims that are senior to common stock) = Common shareholders' equity
(Common shareholders' equity)/(number of common stock shares outstanding) = book value per share

Possible senior claims to common stock include the value of preferred stock and dividends in arrears on preferred stock.

Some adjustments are needed to make the multiple to be more accurate to reflect the shareholders' investment, and more comparable among companies. The adjustments include excluding certain intangibles, restating inventory values using a different inventory method, adding back certain off-balance sheet liabilities, etc.

Valuation Based on Forecasted Fundamentals

P/B can be expressed in terms of the underlying fundamentals:

P0/B0 = (ROE - g) / (r-g)

It's obvious from the equation that the fundamental drivers of P/B are ROE and the required rate of return. The justified P/B based on fundamentals bears a positive relationship to the first factor (measure of profitability) and an inverse relationship to the second factor (risk). Empirical studies have also proved a strong positive relationship between the company's long-term growth and its P/B multiple.

Example

Return on equity: 20%.
Expected dividend growth rate: 6%.
Required return: 15%.

Justified P/B ratio = (0.20 - 0.06) / (0.15 - 0.06) = 1.56.

Alternatively, we can express this multiple in a different way using the residual earnings model:

P0 / B0 = 1 + Present value of expected future residual earnings / B0

This formula shows that the multiple's value is greater than 1, when the forecasted residual income stream is positive. Similarly, the justified P/B is less than 1, when the company is expected to earn less than the required rate of return.

Valuation Using Comparable P/B

Example

Which stock is more attractive? B is more attractive:

B's P/B < industry P/B, and B's ROE = industry ROE => B is undervalued.

User Comment
parry89 I don't get this equation.
P/B = ROE - g/r-g
so P/B = ROE(1-b)/r-g
as retention ratio increases, numerator gets smaller and as retention ratio decreases, numerator increases.
Can anyone explain this to me please
tsmith0440 I am having difficulties with the equation as well Parry89. I have done the algebraic decomposition as the book lays out in the notes such: Vo=[ROE*(1-b)(1+g)]/r-g.... the sustainable growth rate: g=b*ROE; b=ROE/g... giving Vo/Bo= ROE(1-ROE/g)(1+g)/r-g .. which somehow provides the equation Po/Bo=(ROE-g)/r-g... I guess I don't understand how the numerator goes from ROE*(1-ROE/g)(1+g)to just ROE-g.... It's so frustrating and I have spent way too much time on this one equation (more so that Black-Scholes) and even tried brushing up on my algebra on Khan Academy for a few hours lol. I'm sure I am over analyzing this and it's quite simple, but can anyone please shed some light on this equation?
Sanghamitra it goes like this
E = Bo*ROE
P/E = P/(Bo*ROE)
(P/E)*ROE = P/Bo
or P/Bo = [(1-b)*ROE]/ (r-g) (since P/E =(1-b)/(r-g)
1-b = 1 - (g/ROE) (since g = ROE*b)
1-b= (ROE-g)/ROE
P/Bo = (ROE-g)/ (r-g)

hope it helps
sahilb7 Thanks Sanghamitra! You rock. 