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The Characteristics and Valuation of Preferred Stock

Many consider preferred stock to be a hybrid security with characteristics of both common stock and bonds. Preferred stock is similar to common stock in that it has no fixed repayment date, and the firm is not obligated to pay dividends. Preferred stock is similar to bonds in that the periodic payment amount is fixed. Preferred stock is normally issued by established, publicly traded firms to raise capital without diluting the current investors' common stock ownership. Because of the flexibility of terms, preferred stock is also frequently used in the initial private financing of startup companies.

Preferred Stock Characteristics

The following is a list of the significant characteristics of preferred stock as compared to the other two securities, common stock and bonds.

· Preferred stock does not provide the preferred stockholder a claim to ownership or voting rights in the firm.

· Preferred stock does entitle the stockholder to priority over the common stockholders in claims on the firm's assets in the event of bankruptcy.

· Preferred stockholders receive periodic dividends instead of interest, however, unlike with bond interest, failure to pay the dividends is not a cause for bankruptcy.

· Multiple classes of preferred stock can be issued with each class having different characteristics.

· Preferred stock normally carries a cumulative feature that requires that all past unpaid preferred stock dividends must be paid in full before any common stock dividends can be issued.

· Preferred stock may contain other varied protective and incentive provisions that are designed to protect the investor's investment.

· Preferred stock may contain a provision that allows it to be converted to a predetermined number of shares of common stock (convertible preferred).

· Most preferred stocks are perpetuities (nonmaturing), however, retirement features are frequently included. Two common retirement features are:

· callable provision, which allows preferred stock to be called at the issuer's request and retired, like a bond

· sinking fund provision, which requires the firm periodically to repurchase and retire a set amount of the preferred stock

· Preferred Stock Valuation

· According to the general valuation theory, the value of preferred stock is equal to the sum of all the cash flows generated from the investment, discounted by the investor's required rate of return. Because the only cash flow generated from preferred stock is the dividend payment, the value of a preferred stock equals the present value of all the future preferred stock dividends. Because a preferred stock is normally nonmaturing, and the dividends are expected to be paid in equal amounts each year in perpetuity, the value of the preferred stock can be determined simply by dividing the annual dividend by the required rate of return:

· Vps = annual dividend/required rate of return 

· Vps = D/kps

· where:

· Vps = value of the preferred stock D    = annual dividend kps  = required rate of return

A Method of Calculating the Required Rate of Return

Every investor has his or her own unique risk-return utility function. Therefore, for any given investment, different investors will perceive different estimates of the risks involved and have different requirements for what constitutes an acceptable or required rate of return. The required rate of return is the minimum rate of return necessary to compensate an investor for accepting the degree of risk that he or she personally associates with the purchase and ownership of an asset or security.

It is generally accepted that two factors determine the required rate of return for the investor:

1. the risk-free rate of interest, which recognizes only the time value of money

2. the risk premium, which considers the perceived riskiness (variability of returns) of the asset, based on the specific investor's attitude toward risk associated with that investment

The first factor, the risk-free rate of interest is relatively easy to estimate. For example, U.S. Treasury T-bills are often used as the risk-free standard. The financial community has had some difficulty, however, in determining a reliable method of measuring the risk premium. One approach that has had reasonable success is called the capital asset pricing model (CAPM). This method combines the concepts of risk-free rate, systematic risk, and market risk into the following formula:

The required rate of return = risk-free rate + (beta) https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/common/images/math/multiply.gif (market-risk rate – risk-free rate)

or:

https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/rate5.gif 

where:

k j

= required rate of return for security j

krf

= risk-free rate of return

km

= expected rate of return for the market

ßj

= systematic risk

Here is a linear construct designating the risk-return tradeoff existing in the market where risk is defined in terms of Beta.

Although the CAPM is a useful analytical tool, it has two significant limitations.

1. It relies totally on a security's sensitivity to the market (Beta) for measuring risk.

2. It is difficult to test empirically.

Expected Rate of Return

The expected financial returns, to be received from an investment in a capital project or financial security come directly from the cash flows the investment generates. So far, we have treated these cash flows as a certainty. In reality, they are subject to different outcomes, are generally quite uncertain, and require a quantitative method if they are to be properly analyzed. Fortunately, we can use some very basic probability and statistics theory to quantify this uncertainty and develop the concept of an expected return, which is useful for most financial decision making.

Let's examine how we can incorporate the reality of uncertainty into financial cash-flow analysis. Conventionally, we measure the expected cash flow, https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/X-bar.gif, of an investment as follows. We begin by factoring every individual cash flow, Xi, by the probability of its occurrence, P (Xi): 

https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/X-bar.gif= X1P(X1) + X2P(X2) + X3P(X3) + X4P(X4) + --- + XnP(Xn)

Combining terms and using the summation concept, we can create the following generic formula:

The expected cash flow = https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/rate2.gif

where:

n

= the number of possible cash-flow outcomes

Xi 

= the ith possible cash flow

P(Xi)

= the probability that the ith cash flow will occur

https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/X-bar.gif

= the expected rate of return

In finance, we are normally interested in one of two values, (1) the expected cash flow, https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/X-bar.gif, or (2) the expected rate of return, https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/k-bar1.gif. Having calculated the formula for expected cash flow above, it is now one small step to compute a formula for the expected rate of return, https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/k-bar1.gif. By definition, https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/k-bar1.gif is the weighted average of all the possible returns (ki,), each return weighted by the probability that each individual return will occur P(ki).

https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/k-bar1.gif = k1P(k1) + k2P(k2) + k3P(k3) + k4P(k4) + --- + knP(kn)

or: The expected rate of return https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/rate3.gif

where:

n

= the number of possible cash-flow outcomes

ki

= the ith possible rate of return

P(ki)

= the probability that the ith cash flow will occur

https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/k-bar1.gif

= the expected rate of return

Having defined and computed the expected cash flows and the expected rate of return, let's now examine the risk involved in obtaining the expected outcomes.

The Riskiness of Cash Flow

Financial risk is the possible variation in actual cash flows about the expected cash flow. This variability of outcomes, or financial risk, is measured by the standard deviation (https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/sigma.gif),

where:

https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/Cashflow-1.gif

where:

https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/sigma.gif

= the standard deviation

n

= the number of possible cash-flow outcomes

ki

= the ith possible cash flow

P(ki)

= the probability that the ith cash flow will occur

https://content.umuc.edu/file/36015307-74b1-48bb-bb7c-f0b8aba72c10/1/FINC330-1109.zip/Modules/M2-Module_2/images/k-bar1.gif

= the expected rate of return

Statistically, financial risk is measured by the standard deviation about the expected cash flow (how much each possible cash-flow outcome varies from the expected cash-flow outcome).

Total financial variability, or risk, can be divided into two types, unsystematic risk and systematic risk.

1. Unsystematic (diversifiable or company-unique) risk is the variability of cash flows that are unique to an individual security (e.g. the individual company's inherent risks because of its business actions, its competitors' actions, and so on).

2. Systematic risk (nondiversifiable or market) risk is the risk related to overall market movements, which is independent of the risk of an individual company.

Generally speaking, the market rewards diversification, which is the purchase of a set, or portfolio, of unrelated securities. With this diversification, the investor can lower the overall risk without sacrificing expected return or can increase overall expected return without having to assume more risk. Therefore, the financial market does not usually offer a higher return for unsystematic risk because by properly diversifying his or her investments, the investor can essentially eliminate any unsystematic security risk.

Systematic risk, however, cannot be diversified away and thereby becomes the determining factor in quantifying financial risk. Therefore, we will concentrate on developing a quantitative method for measuring systematic, or market, risk. This method, called the characteristic line, is a two-dimensional plot of the returns of an individual stock versus the average returns of some aggregate market standard such as the S&P 500 index over a given period of time. The holding period return for each period, kt, is calculated for both the stock and the S&P 500 using the following formula:

kt = (pt/pt-1) – 1

where P equals the stock price for the respective periods t and t–1.

The individual stock values are traditionally plotted on the X-axis, and the S&P 500 equivalent values are plotted on the Y-axis. For example at time t, a specific stock with a kt of 10% and an S&P 500 with a Pt of 5% would result in a Pt plot of (10, 5). A statistically calculated line of best fit drawn through these points at various times is called the characteristic line. The slope of this line, which has come to be called beta (ß), is a measure of a stock's systematic or market risk. Remember that beta (ß) is calculated as the ratio of the rise, or change in y value, of the line relative to the run, or change, in x value.

This presentation demonstrates the graphical construction of a typical characteristic line.

Now let's interpret exactly what the beta represents in measuring financial risk. If a security's beta equals one (ß = 1), a 10% increase (or decrease) in the S&P 500 market returns will produce a corresponding 10% increase (or decrease) in that individual security's returns. In this case, the stock is perfectly correlated with the market and therefore possesses no incremental risk benefit or penalty relative to the S&P 500 market.

If a security's beta is greater than one, then a 10% increase (or decrease) in the S&P 500 market returns will produce a greater than 10% increase (or decrease) in that individual security's returns. In this case, the individual stock is considered riskier than the average S&P 500 stock. The converse is also true, and a security having a lower beta is considered less risky than the S&P 500 market. In general, the lower the beta value, the less risky the stock.

Chapter 7 Section 1, 2,3,4,5,6,

Chapter 8

Chapter 9

http://www.teachmefinance.com/stockvaluation.html

http://www.teachmefinance.com/capm.html

http://www.teachmefinance.com/standarddeviation.html

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