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## Friday, September 26, 2008

### Stock pricing book value

To clearly distinguish the market price of shares from the core ownership equity or shareholders' equity, the term 'book value' is often used since it focuses on the values that have been added and subtracted in the accounting books of a business (assets - liabilities). The term is also used to distinguish between the market price of any asset and its accounting value which depends more on historical cost and depreciation. It may be used interchangeably with carrying value. While it can be used to refer to the business' total equity, it is most often used:

• as a 'per share' value': The balance sheet Equity value is divided by the number of shares outstanding at the date of the balance sheet (not the average o/s in the period).
• as a 'diluted per share value': The Equity is bumped up by the exercise price of the options, warrants or preferred shares. Then it is divided by the number of shares that has been increased by those added.

### Uses

1. Book value is used in the financial ratio price/book. It is a valuation metric that sets the floor for stock prices under a worst-case scenario. When a business is liquidated, the book value is what may be left over for the owners after all the debts are paid. Paying only a price/book = 1 means the investor will get all his investment back. Shares of capital intensive industries trade at lower price/book ratios because they generate lower earnings per dollar of assets. Business depending on human capital will generate higher earnings per dollar of assets, so will trade at higher price/book ratios.
2. Book value per share can be used to generate a measure of comprehensive earnings, when the opening and closing values are reconciled. BookValuePerShare, beginning of year - Dividends + ShareIssuePremium + Comprehensive EPS = BookValuePerShare, end of year.

### Changes are caused by

1. The sale of shares/units by the business increases the total book value. Book/sh will increase if the additional shares are issued at a price higher than the pre-existing book/sh.
2. The purchase of its own shares by the business will decrease total book value. Book/sh will decrease if more is paid for them than was received when originally issued (pre-existing book/sh).
3. Dividends paid out will decrease book value and book/sh.
4. Comprehensive earnings/losses will increase/decrease book value and book/sh. Comprehensive earnings, in this case, includes net income from the Income Statement, foreign exchange translation changes to Balance Sheet items, accounting changes applied retroactively, and the opportunity cost of options exercised.

### New share issues and dilution

The issue of more shares does not necessarily decrease the value of the current owner. While it is correct that when the number of shares is doubled the EPS will be cut in half, it is too simple to be the full story. It all depends on how much was paid for the new shares and what return the new capital earns once invested. See the discussion at stock dilution.

### Net book value of long term assets

Book value is often used interchangeably with "net book value" or "carrying value", which is the original acquisition cost less accumulated depreciation, depletion or amortization.

### Corporate book value

A company or corporation's book value, as an asset held by a separate economic entity, is the company or corporation's shareholders' equity, the acquisition cost of the shares, or the market value of the shares owned by the separate economic entity.

A corporation's book value is used in fundamental financial analysis to help determine whether the market value of corporate shares is above or below the book value of corporate shares. Neither market value nor book value is an unbiased estimate of a corporation's value. The corporation's bookkeeping or accounting records do not generally reflect the market value of assets and liabilities, and the market or trade value of the corporation's stock is subject to variations.

### Net asset value

In the United Kingdom, the term net asset value may refer book value.

A mutual fund is an entity which primarily owns "financial assets" or capital assets such as bonds, stocks and commercial paper. The net asset value of a mutual fund is the market value of assets owned by the fund minus the fund's liabilities.This is similar to shareholders' equity, except the asset valuation is market-based rather than based on acquisition cost. In financial news reporting, the reported net asset value of a mutual fund is the net asset value of a single share in the fund. In the mutual fund's accounting records, the financial assets are recorded at acquisition cost. When assets are sold, the fund records a capital gain or capital loss.

Financial assets include stock shares and bonds owned by an individual or company. These may be reported on the individual or company balance sheet at cost or at market value.

### Liability book value

"Discount on notes payable" is a contra-liability account which decreases the balance sheet valuation of the liability.

When a company sells (issues) bonds, this debt is a long-term liability on the company's balance sheet, recorded in the account Bonds Payable based on the contract amount. After the bonds are sold, the book value of Bonds Payable is increased or decreased to reflect the actual amount received in payment for the bonds. If the bonds sell for less than face value, the contra account Discount on Bonds Payable is debited for the difference between the amount of cash received and the face value of the bonds.

### Depreciable, amortizable and depletable assets

Monthly or annual depreciation, amortization and depletion are used to reduce the book value of assets over time as they are "consumed" or used up in the process of obtaining revenue.These non-cash expenses are recorded in the accounting books after a trial balance is calculated to ensure that cash transactions have been recorded accurately. Depreciation is used to record the declining value of buildings and equipment over time. Land is not depreciated. Amortization is used to record the declining value of intangible assets such as patents. Depletion is used to record the consumption of natural resources.

Depreciation, amortization and depletion are recorded as expenses against a contra account. Contra accounts are used in bookkeeping to record asset and liability valuation changes. "Accumulated depreciation" is a contra-asset account used to record asset depreciation.

Sample general journal entry for depreciation

• Depreciation expenses: building... debit = $150, under expenses in retained earnings • Accumulated depreciation: building... credit =$150, under assets

The balance sheet valuation for an asset is the asset's cost basis minus accumulated depreciation. Similar bookkeeping transactions are used to record amortization and depletion.

### Asset book value

An asset's initial book value is its actual cash value or its acquisition cost. Cash assets are recorded or "booked" at actual cash value. Assets such as buildings, land and equipment are valued based on their acquisition cost, which includes the actual cash cost of the asset plus certain costs tied to the purchase of the asset, such as broker fees. Not all purchased items are recorded as assets; incidental supplies are recorded as expenses. Some assets might be recorded as current expenses for tax purposes. An example of this is assets purchased and expensed under Section 179 of the US tax code.

### Book value

In accounting, book value or carrying value is the value of an asset or according to its balance sheet account balance. For assets, the value is based on the original cost of the asset less any depreciation, amortization or impairment costs made against the asset. A company's book value is its total assets minus intangible assets and liabilities. In the United Kingdom, the term net asset value may refer to the book value of a company.

The EPS formula does not include preferred dividends for categories outside of continued operations and net income. Earnings per share for continuing operations and net income are more complicated in that any preferred dividends are removed from net income before calculating EPS. Remember that preferred stock rights have precedence over common stock. If preferred dividends total $100,000, then that is money not available to distribute to each share of common stock. Earnings Per Share (Basic Formula) $\mbox{Earnings Per Share}=\frac{\mbox{Profit}}{\mbox{Weighted Average Common Shares}}$ Earnings Per Share (Net Income Formula) $\mbox{Earnings Per Share}=\frac{\mbox{Net Income}}{\mbox{Weighted Average Common Shares}}$ Earnings Per Share (Continuing Operations Formula) $\mbox{Earnings Per Share}=\frac{\mbox{Income from Continuing Operations}}{\mbox{Weighted Average Common Shares}}$ Note: Only preferred dividends actually declared in the current year are subtracted. The exception is when preferred shares are cumulative, in which case annual dividends are deducted regardless of whether they have been declared or not. Dividends in arrears are not relevant when calculating EPS ### Earnings per share Earnings per share (EPS) are the earnings returned on the initial investment amount. In the US, the Financial Accounting Standards Board (FASB) requires companies' income statements to report EPS for each of the major categories of the income statement: continuing operations, discontinued operations, extraordinary items, and net income. ### S&P 500 In 1982 the dividend yield on the S&P 500 Index reached 6.7%. Over the following 16 years, the dividend yield declined to just a percentage value of 1.4% during 1998, because stock prices increased faster than dividend payments from earnings, and public company earnings increased slower than stock prices. During the 20th century, the highest growth rates for earnings and dividends over any 30-year period were 6.3% annually for dividends, and 7.8% for earnings. As of 2008, the average dividend yield is around 2% ### Dow Industrials The dividend yield of the Dow Jones Industrial Average, which is obtained from the annual dividends of all 30 companies in the average divided by their cumulative stock price, has also been considered to be an important indicator of the strength of the U.S. stock market. Historically, the Dow Jones dividend yield has fluctuated between 3.2% (during market highs, for example in 1929) and around 8.0% (during typical market lows). The highest ever Dow Jones dividend yield occurred during the stock market collapse of 1932, when it exceeded 15%. With the decreased emphasis on dividends since the mid-1990s, the Dow Jones dividend yield has fallen well below its historical low-water mark of 3.2% and reached as low as 1.4% during the stock market peak of 2000 ### History Historically, a higher dividend yield has been considered to be desirable among investors. A high dividend yield can be considered to be evidence that a stock is under priced or that the company has fallen on hard times and future dividends will not be as high as previous ones. Similarly a low dividend yield can be considered evidence that the stock is overpriced or that future dividends might be higher. Dividend yield fell out of favor somewhat during the 1990s because of an increasing emphasis on price appreciation over dividends as the main form of return on investments. The importance of the dividend yield in determining investment strength is still a debated topic. The persistent historic low in the Dow Jones dividend yield during the early 21st century is considered by some bearish investors as indicative that the market is still overvalued. ### Common share dividend yield Unlike preferred stock, there is no stipulated dividend for common stock. Instead, dividends paid to holders of common stock are set by management, usually in relation to the company's earnings. There is no guarantee that future dividends will match past dividends or even be paid at all. Due to the difficulty in accurately forecasting future dividends, the most commonly-cited figure for dividend yield is the current yield which is calculated using the following formula: $\mbox{Current Dividend Yield}=\frac{\mbox{Most Recent Full-Year Dividend}}{\mbox{Current Share Price}}$ For example, take a company which paid dividends totaling$1 last year and whose shares currently sell for $20. Its dividend yield would be calculated as follows: $\begin{array}{lcl} \mbox{Current Dividend Yield} & = & \frac{\mbox{Most Recent Full-Year Dividend}}{\mbox{Current Share Price}} \\ & = & \frac{1}{20} \\ & = & 0.05 \\ & = & 5% \\ \end{array}$ Rather than use last year's dividend, some try to estimate what the next year's dividend will be and use this as the basis of a future dividend yield. Such a scheme is used for the calculation of the FTSE UK Dividend+ Index. It should be noted that estimates of future dividend yields are by definition uncertain. ### Dividend yield The dividend yield on a company stock is the company's annual dividend payments divided by its market cap, or the dividend per share divided by the price per share. It is often expressed as a percentage. ## Preferred share dividend yield Dividend payments on preferred shares are stipulated by the prospectus. The company will typically refer to a preferred share by its initial name which is the yield on its original price — for example, a 6% preferred share. However, the price of preferred shares varies according to the market so the yield based on the current price fluctuates. Owners of preferred shares calculate multiple yields to reflect the different possible outcomes over the life of the security. • current yield is the$Dividend / Pfd share current price.
• Since the share may be purchased at a lower (higher) cost than its final redemption value, holding it to maturity will result in a capital gain (loss). The annualized rate of gain is calculated using the Present value of a dollar calculation. ('PV' is the current stock price. 'FV' is the redemption value. 'n' is the number of years to redemption. Solve for the interest rate 'r'.) The yield to maturity is the sum of this annualized gain (loss) and the current yield.
• There are other possible yields discussed at Yield to maturity.

## Derivation

We want to find out the value of Pn as $n \rightarrow \infty$, where

$P_n = \sum_{t=1}^{n} D\times \frac{(1+g)^t}{(1+k)^t} = D\times \sum_{t=1}^{n} \frac{(1+g)^t}{(1+k)^t} = D\times \sum_{t=1}^{n} \left(\frac{1+g}{1+k}\right)^t$

Let

$a = \frac{1+g}{1+k}$.

Then

$P_n = D\times \sum_{t=1}^{n} a^t$.

Since

$1-a^{(n+1)} = (1-a) \times (1 + a + a^2 + ... + a^n) = (1-a) \times (1 + \sum_{t=1}^{n} a^t)$,

we get

$\frac{1-a^{(n+1)}}{1-a} - 1 = \sum_{t=1}^{n} a^t$.

Therefore,

$P_n = D \times \left[ \frac{1-a^{(n+1)}}{1-a} - 1 \right]$.

If g < k, then a <> and

$a^{(n+1)} \rightarrow 0$ as $n \rightarrow \infty$.

Thus, we get

$P_\infty = D \times \left( \frac{1}{1-a} - 1 \right) = D \times \left( \frac{a}{1-a} \right) = D \times \left(\frac{1+g}{1+k}\right) / \left[ 1 - \left(\frac{1+g}{1+k}\right) \right] = D \times \left( \frac{1+g}{k-g} \right)$.

## Problems with the model

a) The model requires one perpetual growth rate

But for many growth stocks, the current growth rate can vary with the cost of capital significantly year by year. In this case this model should not be used.

b) If the stock does not currently pay a dividend, like many growth stocks, more general versions of the discounted dividend model must be used to value the stock. One common technique is to assume that the Miller-Modigliani hypothesis of dividend irrelevance is true, and therefore replace the stocks's dividend D with E earnings per share.

But this has the effect of double counting the earnings. The model's equation recognizes the trade off between paying dividends and the growth realized by reinvested earnings. It incorporates both factors. By replacing the (lack of) dividend with earnings, and multiplying by the growth from those earnings, you double count.

c) Gordon's model is sensitive if k is close to g. For example, if

• dividend = $1.00 • cost of capital = 8% Say the • growth rate = 1% - 2% So the price of the stock • assuming 1% growth=$14.43 = 1.00(1.01/.07)
• assuming 2% growth= $17.00 = 1.00(1.02/.06) The difference determined in valuation is relatively small. Now say the • growth rate = 6% - 7% So the price of the stock • assuming 6% growth=$53 = 1.00(1.06/.02)

### Incentives

One other reason for a company to buy back its own stock is to reward holders of stock options. Option holders are hurt by dividend payments, since, typically, they are not eligible to receive them. A share buyback program may increase the value of remaining shares (if the buyback is executed when shares are underpriced); if so, option holders benefit. A dividend payment short term always decreases the value of shares after the payment, so, on the day shares go ex-dividend, option holders always lose. Finally, if the sellers into a corporate buyback are actually the option holders themselves, they may directly benefit from temporarily unrealistically favorable pricing.