## Sunday, 27 December 2009

### The Market Price-to-Book and Intrinsic Price-to-Book Ratio

The balance sheet equation corresponds to the value equation.

The value equation can be written as:

Value of the firm = Value of equity + Value of debt
or
Value of equity = Value of firm - Value of debt

• The value of the firm is the value of the firm's assets and its investments.
•  The value of the debt is the value of the liability claims.

The value equation and the balance sheet equation are of the same form but differ in how the assets, liabilities, and equity are measured.

The measure of stockholders' equity on the balance sheet,l the book value of equity, typically does not give the intrinsic value of what the equity is worth.
• Correspondingly, the net assets are not measured at their values.
• If they were, there would be no analysis to do!  It is because the accountant does not, or cannot, calculate the intrinsic value that fundamental analysis is required.
The diffeence between the intrinsic value of equity and its book value is called the intrinsic premium:

Intrinsic premium = Intrinsic value of equity - Book value of equity

The difference between the market price of equity and its book value is called the market premium:

Market premium = Market price of equity - Book value of equity

If these premiums are negative, they are called discounts (from book value).  Premiums sometimes are referred to as unrecorded goodwill because someone purchasing the firm at a price greater than book value could record the premium paid as an asset, purchased goodwill, on the balance sheet; without a purchase of the firm, the premium is unrecorded.

Premiums can be calculated for the total equity or on a per-share basis.

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Example:
Company A
2,060 outstanding shares
Market Price \$20 per share.
Market value of these shares: \$41,200 million.
Book value \$3,735 million
Therefore the market premium was \$37,465 million.

The market saw \$37,465 million of shareholder value that was not on the balance sheet.
And it saw \$37,465 million of net assets that were not on the balance sheet.
With 2060 million shares outstanding,
• the book value per share (BPS) was \$1.81 and
• the market premium was \$18.19 per share.
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The ratio of market price to book value is the price-to-book ratio or the market-to-book ratio.

The ratio of intrinsic value to book value is the intrinsic price-to-book ratio.

• Investors talk of buying a firm for a number of times book value, referring to the P/B ratio.
• The market P/B ratio is the multiple of book value at the current market price.
• The intrinsic P/B ratio is the multiple of book value that the equation is worth.
• An investor will spend considerable time estimating intrinsic price-to-book ratios and asking if those intrinsic ratios indicate the the market P/B is mispriced.
Historical Perspective of P/B ratios

In asking such questions, it is important to have a sense of history so that any calculation can be judged against what was normal in the past.  The history provides a benchmark for our analysis.
• P/B ratios in the 1990s were high relative to historical averages, indicating that the stock market was overvalued.
• The medican P/B ratios (the 50th percentile) for the U.S. listed firms were indeed high in the 1990s - over 2.0 - relative to the 1970s.
• But they were around 2.0 in the 1960s.
• The 1970s experienced exceptionally low P/B ratios, with medians below 1.0 in some years.

What causes the variation in ratios?
• Is it due to mispricing in the stock market?
• Is it due to the way accountants calculate book values?

The low P/B ratios in the 1970s certainly preceded a long bull market.
• Could this bull market have been forecast in 1974 by an analysis of intrinsic P/B ratios?
• Were market P/B ratios in 1974 too low
• Would an analysis of intrinsic P/B ratios in the 1990s find that they were too high?

Company A's P/B of 11.0 in 2008 looks high relative to historical averages.
• Was it too high?

The fundamental investor sees himself as providing answers to these questions.  He estimates the intrinsic value of equity that is not recorded on the balance sheet.

You can screen for firms with particular levels of P/B ratios using stock screener from links on the Web.