chapter 7 equity valuation

Chapter 7 Equity ValuationWhat determines the value of stock? Old ideas are still new.

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Chapter 7 Outline7.1 Equity Securities

• The basics of valuing equity

• The required rate of return

7.2 Discounted Cash Flow Approaches to

Valuing Equity• Valuing preferred stock• Valuing common stock• The basic dividend

discount model and its limitations

• Estimating the required rate of return

• Estimating the value of growth opportunities

7.3 Using Multiples to Value Equity

• The price-earnings ratio and its limitations

• Additional multiples or relative value ratios

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A corporation will issue an equity security, which is a financial instrument that represents ownership in the corporation. We often refer to this financial instrument as the stock of the company.

A unit of ownership is represented by a share or a share of stock, and an owner of a share is a shareholder or stockholder. Because a corporation has a perpetual life, the owners of these securities own

a security that has no fixed maturity date. Companies that issue equity securities may choose to pay a cash

dividend, which is paid from after-tax earnings. Unlike interest payments on debt obligations, dividends are not a tax-

deductible expense to the paying corporation.

7.1 Equity Securities

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Equity Securities A corporation, at a minimum, has common stock, but it may

also choose to issue preferred stock. Preferred stock and common stock both represent

ownership interest, or equity, but preferred shareholders, as the name implies, have a prior claim to income and assets of the company relative to common shareholders.

Common shareholders are the residual claimants of the corporation, which means that they are entitled to income remaining only after all creditors and other, more senior claimants, including preferred shareholders, have been paid.

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Equity Securities By far, the most common type of equity security is the

common share, which represents a certificate of ownership in a corporation. A purchaser of 100 shares of common stock owns 100/n

percent of the corporation, where n is the total number of shares of common stock outstanding.

A publicly traded corporation may have millions or even billions of common shares outstanding at a point in time. For example, at the end of their June 30, 2013, fiscal year end,

Microsoft had 8.36 billion shares of stock outstanding.

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Equity Securities Preferred stock provides the owner with a claim to a fixed

amount of equity that is established when the shares are first issued. Most preferred stockholders have preference over common

stockholders with respect to income and assets (in the event of liquidation), but they rarely have any voting rights.

Traditionally, preferred stock has no maturity date, but over the past 30 years preferred stock has been increasingly issued with a fixed maturity date, similar to a bond.

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The main difference between preferred stock and a bond is that the board of directors declares the dividends and until then, and unlike an interest payment, dividends are not a legal obligation of the company.

Usually, no payments can be made to common shareholders until preferred shareholders have been paid the dividends they are due in entirety.

Dividends are not considered a cost of doing business, and therefore they are not deductible for tax purposes by the paying company. This is different than the interest paid by the company issuing

bonds; interest is a deductible expense for tax purposes.

Preferred Securities

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Valuing equity requires estimating future dividends. In the case of preferred stock, the dividends are generally

fixed in terms of the payment frequency and the amount, but these still are paid at the discretion of the company’s board of directors. We refer to preferred stock with a fixed dividend, no maturity, and no

embedded option as straight preferred stock. In the case of common stock, we possibly are dealing with

uneven cash flows, ad infinitum.

The Basics of Valuing Equity

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We generally value preferred stock using discounted cash flow methods, discounting the expected dividends at a discount rate that reflects the uncertainty associated with the payment of these dividends.

Because common stock is the last in line in terms of the pecking order of claims on a company and because some companies simply reinvest earnings instead of paying them out to shareholders, there are two common approaches to valuing common stock: The discounted cash flow approach The method of multiples

The Basics of Valuing Equity

The discounted cash flow approaches require an estimate of the required rate of return, which is the minimum return that investors expect to earn on the investment in the stock.

In the method of multiples, we approach valuation at a different angle: we estimate values based on the market’s assessment of comparable companies.

Approaches to Valuing Common Stock

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Key to the discount models used to value preferred and common stock is the required rate of return, which becomes a benchmark for valuation: If a company returns more than required, the value of the stock

rises; if a company returns less than required, the value of the stock falls. The difficulty is that we cannot observe this required rate of return directly.

We can back into this return by looking at how the market values a company’s stock, given a projection of dividends, but we cannot simply look up the required rate of return.

The Required Rate of Return

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We generally think of the discount rate for equities as the sum of the risk-free rate of return—that is, the compensation for the time value of money—plus a premium for bearing risk:

re = rf + Risk premium

where re is the required return on an equity security and rf is the risk-free rate of return.

The risk-free rate comprises the real rate of return plus expected inflation, and we often use the return on Treasury bonds to represent this rate of return.

The risk premium is based on an estimate of the risk associated with the security; the higher the risk, the higher the risk premium because investors require a higher return as compensation for bearing more risk.

The Required Rate of Return

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We estimate the expected future cash flows associated with the security and then determine the discounted present value of those future cash flows, based on an appropriate discount rate (re).

7.2 Discounted Cash Flow Approaches to Valuing Equity

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Traditional preferred stock has no maturity date and pays dividends of a fixed amount at regular intervals indefinitely (that is, to infinity, ∞), as we depict in the figure below, where we represent the periodic dividend payment as Dp.

Valuing Preferred Stock

The Cash Flow Pattern for a Straight Preferred Stock

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Because the payments are essentially fixed when the preferred shares are issued, they are often referred to as fixed-income investments.

We can estimate the value of preferred shares using the equation that determines the present value of a perpetuity, where Pp is the present value of the preferred stock, Dp is the periodic dividend amounts (or payments), and rp is the required rate of return on the preferred shares (or discount rate):

Valuing Preferred Stock

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Problem: Suppose a preferred stock has a par value of $50 per share and a dividend rate of 8%. If the required rate of return for this preferred stock is 6%, what is the value of a share of this stock?Solution: The dividend is $50 × 0.08 = $4 per share, which we discount at the rate of 6%:

The stock trades at a premium to its face value.

Valuing Preferred Stock Example

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What if the required rate of return on the given stock is 10%, instead of 6%?

In this case, the stock trades at a discount to its face value.

What if the required rate of return is 8% instead of 6%?

In this case, the stock is valued at its par value.

Valuing Preferred Stock Example

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Valuing common shares involves several complications that arise with respect to the appropriate future cash flows that should be discounted.

One of the most popular discounted cash flow valuation models, uses dividends. However, unlike bonds or even preferred shares, there is

no requirement that common shares pay dividends at all. In addition, the level of dividend payments is

discretionary, which implies we must make estimates regarding the amount and timing of any dividend payments.

Valuing Common Stock

We assume that common shares are valued according to the present value of their expected future cash flows—specifically, dividends. Based on this premise, we estimate today’s value, based on an n-year holding period:

P0 = the value of a share of common stock today, Dt = the expected dividend at the end of year t, Pn = the expected share value after n years, and re = the required return on the common shares.

The Basic Dividend Discount Model (DDM)

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Problem: Consider a stock that is expected to pay $2 at the end of the first year and $3 at the end of the second year. If the stock is expected to have a value of $20 at the end of 2 years, what is the value of the stock today if the required rate of return is 8%?Solution:

= $21.5707

Example: The Basic Dividend Discount Model

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It is impractical to estimate and discount all future dividends one by one. Fortunately, we can simplify the equation into a usable formula by making the assumption that dividends grow at a constant rate (g) indefinitely. This growth rate represents the annual growth in dividends, ad infinitum.

Valuation with Constant Growth

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If growth is expected to be constant, the value of a share of stock is:

where D1 = D0 x (1 + g)

Constant growth

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Problem:If a company’s current dividend is $2 per share, its required rate of return is 10%, and its expected growth in dividends is 4%, what is the value of a share of this company’s stock?Solution:

P =

Example: constant growth

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Problem:If a company’s current dividend is $2 per share, its required rate of return is 10%, and dividends are expected to decline 2% per year, what is the value of a share of this company’s stock?Solution:

P =

Example: constant growth

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We can estimate the rate of return required by investors on a particular share as follows:

The first term (D1 ÷ P0) is the expected dividend yield on the share and the second term, g, as the expected capital gains yield (or, simply, capital yield).

Estimating the Required Rate of Return

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Example: Consider a common stock that has an annual dividend of $2 per share. If the value of a share of this stock is $20 and the expected growth rate is 4%, what is the required rate of return?Solution: The dividend yield is $2 ÷ $20 = 10%, and the required rate of return is 10% + 4% = 14%.

Estimating the Required Rate of Return

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Let’s assume that a company that has no profitable growth opportunities should not reinvest residual profits in the company, but rather should pay out all its earnings as dividends.

Under these conditions, we have no growth (that is, g = 0), EPS1 represents the expected earnings per common share in the upcoming year, and earnings per share are equal to dividends, D1 = EPS1.

These assumptions give us the following expression:

Estimating the Value of Growth Opportunities

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It is unlikely to find a company that has exactly “zero” growth opportunities, but the point is that we can view the share value of any common stock (that satisfies the assumptions of the constant growth dividend discount model) as comprising two components: without growth and with growthWe denote this as the present value of growth opportunities (PVGO) and get the following equation:


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Example: If a company’s common stock has a market value of $25, the expected earnings per share for next year is $1 and the required rate of return is 10%, what is the stock’s present value of growth opportunities?Solution:

Rearranging:


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What if the dividends are expected to experience two different growth rates in the future? We can use time value of money and the dividend valuation model to value the stock.

Two-stage growth

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Problem:Suppose a stock currently pays a dividend of $3 per share and investors require a 10% return on this stock. And suppose the dividends are expected to grow at a rate of 15% for three years and then 5% thereafter. What is the value of the stock?

Example: Two-stage growth

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Example, cont.

Year

Growth rate (from prior

year’s dividend) Dividend

0 $3.001 15% $3.452 15% $3.973 15% $4.564 5% $4.79

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0 1 2 3 4| | | |

$3.45 $3.97 $4.56$4. 79

$3.45 $3.97 $100.38$81.83

Example, cont.5% growth

after period 3

Next period’s

dividend

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The dividend discount model is based on several assumptions that are not met by a large number of companies. In particular, it is best suited for companies that:

Pay dividends based on a stable dividend payout history that

they want to maintain in the future Are growing at a steady and sustainable rate

As such, the model works reasonably well for large corporations in mature industries with stable profits and an established dividend policy.

Limitations of the Dividend Discount Model

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We can use relative valuation to estimate the value of common shares by comparing the market values of similar companies, relative to a common variable, such as earnings, cash flow, book value, or sales.

7.3 Using Multiples to Value Equity

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Because relative valuation relies on multiples, we refer to this methodology as the method of multiples. Conceptually, relative valuation appears simple to apply: All we need to do is find a group of comparable companies and then use their financial data and market values to infer the value of the company in question.

However, finding comparable companies is difficult: what company is similar to Microsoft, for example? Disney? GE?

Using Multiples to Value Equity

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The most commonly used relative valuation multiple is the price-earnings (P/E) ratio. Represents the number of times investors are willing to pay for a

company’s earnings, as expressed in the share price, or the share price divided by the earnings per share.

Implemented by estimating the company’s earnings per share (EPS) and multiplying it by a justifiable P/E multiple.

The justified P/E is the multiple that is considered sustainable over the long term. The typical P/E formulation for valuation purposes uses

estimated earnings per share (EPS1) for the next 12 months.

Using the Price-Earnings Ratio

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Aside from the difficulties in estimating an appropriate P/E ratio and in estimating future EPS, there are several other practical concerns regarding the use of P/E ratios:

The P/E ratio is uninformative when companies have negative or very small earnings.

The P/E ratio may be highly variable across an industry. The volatile nature of earnings implies a great deal of volatility in

P/E multiples. For example, the earnings of cyclical companies fluctuate quite dramatically throughout a typical business cycle.

Net income, and hence earnings per share, are susceptible to the influence of accounting choices and earnings management.

Price-Earnings Ratio Limitations

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For these reasons, P/E ratios are often based on smoothed or normalized estimates of earnings for the forecast year. This is also why analysts use other, similar relative value approaches along with a P/E analysis.

Practical approach to P/E

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The market-to-book (M/B) ratio is the market value per share divided by the book value per share.

Equivalently, we can calculate the market-to-book ratio as the ratio of the market capitalization of the common stock divided by the book value of common equity.

Additional Multiples or Relative Value Ratios

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Book value provides a relatively stable, intuitive measure of value relative to market values that can be easily compared with those of other companies, provided accounting standards do not vary greatly across the comparison group.

Using book value eliminates several of the problems arising from the use of P/E multiples because book values are rarely negative and do not exhibit the volatility associated with earnings levels.


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The use of the M/B ratio fell out of favor in the 1980s and 1990s because of high rates of inflation that distorted the M/B ratio. This is because using historical cost accounting in an

inflationary period results in understated carrying or book values.

However, the low rate of inflation of the last 10 to 15 years has removed most of these problems, whereas changes in accounting standards have made the book value of equity more useful.


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Another commonly used relative valuation ratio is the price-to-cash-flow (P/CF) ratio, where cash flow (CF) is often estimated as cash flow from operations.

By focusing on cash flow rather than on accounting income, this ratio alleviates some of the accounting concerns regarding measures of earnings.


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A value of a share of stock is the future value of future cash flows to that share. In terms of preferred and common stock, the value of a share is

the present value of expected future dividends. The valuation of preferred stock is rather straightforward;

we typically use the present value of a perpetuity formula to estimate the value of a share of preferred stock.

Summary

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Because the dividend rate on common stock is not set, but rather the amount and timing of dividends is left to the discretion of the board of directors, the valuation of a share of common stock is more complicated than the value of preferred stock. A useful model is the dividend discount model, assuming

a constant growth in dividends. This model can be modified to consider multiple stages of

growth, and other patterns of future dividends.

Summary

Problems

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Suppose a company had dividends of $2.50 per share in 2013 and is expected to pay dividends of $4 per share in 2018. What is the average annual rate of growth of dividends from 2013 to 2018?

Problem 1

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Suppose a stock has a current dividend of $4.50 per share and dividends are expected to increase at a rate of 5% a year, forever. If investors require a 12% return on this stock, what is the value of a share of this stock?

Problem 2

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Suppose a stock has a current dividend of $4.50 per share and dividends are expected to increase at a rate of 5% a year, forever. Investors required a 12% return on this stock, but have now revised it to 15% because of the company’s misfortunes. how much is the value of this share expected to change with this revision?

Problem 3

chapter 7 equity valuation

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