FIN 303 CH8 & 9
zero growth stock
A common stock whose future dividends are not expected to grow at all; that is, g=0
proxy
A document giving one person the authority to act for another, typically the power to vote shares of common stock.
probability distribution
A listing of possible outcomes or events with a probability (chance of occurrence) assigned to each outcome. The tighter (or more peaked) the probability distributions, the more likely the actual outcome will be close to the expected value and, consequently, the less likely the actual return will end up far below the expected return. Thus, the tighter the probability distribution, the lower the risk.
beta coefficient, b
A metric that shows the extent to which a given stock's returns move up and down with the stock market. Beta measures market risk. we often use historical data and assume that the stock's historical beta will give us a reasonable estimate of how the stock will move relative to the market in the future.
preemptive right
A provision in the corporate charter or bylaws that gives common stockholders the right to purchase on a pro rata basis new issues of common stock (or convertible securities). In some states, the preemptive right is automatically included in every corporate charter; in other states, it must be specifically inserted into the charter. First, it prevents the management of a corporation from issuing a large number of additional shares and purchasing those shares itself. Management could use this tactic to seize control of the corporation and frustrate the will of the current stockholders. The second, and far more important, reason for the preemptive right is to protect stockholders from a dilution of value. Thus, selling common stock at a price below the market value would dilute a firm's price and transfer wealth from its present stockholders to those who were allowed to purchase the new shares. The preemptive right prevents this.
marginal investor
A representative investor whose actions reflect the beliefs of those people who are currently trading a stock. It is the marginal investor who determines a stock's price. whose actions actually determine the equilibrium stock price, is critical; but every investor, marginal or not, implicitly goes through the same type of analysis.
standard deviation, σ
A statistical measure of the variability of a set of observations that is a .measure of how far the actual return is likely to deviate from the expected return. Because past results are often repeated in the future, the historical σ is often used as an estimate of future risk. All financial calculators (and Excel) have easy-to-use functions for finding σ based on historical data.Footnote Simply enter the rates of return and press the key marked S (or ) to obtain the standard deviation. However, neither calculators nor Excel have a built-in formula for finding σ where probabilistic data are involved
Slope of risk-return line
A steeper line suggests that an investor is very averse to taking on risk, whereas a flatter line would suggest that the investor is more comfortable bearing risk Investors who are less comfortable bearing risk tend to gravitate toward lower-risk investments, while investors with a greater-risk appetite tend to put more of their money into higher-risk, higher-return investments From a company's perspective, the risk-return line represents its cost of obtaining capital, and the slope of the risk-return line reflects the average investor's current willingness to take on risk
Corporate Valuation Model
A valuation model used as an alternative to the discounted dividend model to determine a firm's value, especially one with no history of dividends, or the value of a division of a larger firm. The corporate model first calculates the firm's free cash flows, then finds their present values to determine the firm's value. if a company has significant non-operating assets that are not captured in the estimated free cash flows, then they should be included as part of the company's total corporate value. Examples may include large holdings of excess cash, real estate holdings outside of its main operations, or a company's minority stake in another business. Alternatively, an analyst may also need to account for significant non-operating liabilities such as an underfunded pension liability or contingencies related to future litigation. Finally, another example is executive stock options—to the extent these options are valuable, it means that the company's executive will receive some portion of the company's future gains. For some companies, these other factors can be quite important, and often quite complicated. Consequently, we will leave a more detailed discussion of these issues to more advanced finance courses that focus more specifically on valuation.
Portfolio Risk, SDp
Although the expected return on a portfolio is simply the weighted average of the expected returns on its individual stocks, the portfolio's risk is not the weighted average of the individual stocks' standard deviations. The portfolio's risk is generally smaller than the average of the stocks' σs because diversification lowers the portfolio's risk.
takeovers
An action whereby a person or group succeeds in ousting a firm's management and taking control of the company. The frequency of proxy fights has increased, as have attempts by one corporation to take over another by purchasing a majority of the outstanding stock Managers without more than 50% of their firms' stock are very concerned about proxy fights and takeovers, and many of them have attempted to obtain stockholder approval for changes in their corporate charters that would make takeovers more difficult. a number of companies have persuaded their stockholders to agree (1) to elect only one-third of the directors each year (rather than electing all directors each year), (2) to require 75% of the stockholders (rather than 50%) to approve a merger, and (3) to vote in a "poison pill" provision that would allow the stockholders of a firm that is taken over by another firm to buy shares in the second firm at a reduced price. The poison pill makes the acquisition unattractive and thus helps ward off hostile takeover attempts. Managers' moves to make takeovers more difficult have been countered by stockholders, especially large institutional stockholders, who do not like barriers erected to protect incompetent managers.
proxy fight
An attempt by a person or group to gain control of a firm by getting its stockholders to grant that person or group the authority to vote its shares to replace the current management.
average stock's beta, bA
By definition, bA = 1 because an average-risk stock is one that tends to move up and down in step with the general market. A plot of the data shows that the three stocks moved up or down with the market but that H was twice as volatile as the market, A was exactly as volatile as the market, and L had only half the market's volatility. It is apparent that the steeper the line, the greater the stock's volatility and thus the larger its loss in a down market. The slopes of the lines are the stocks' beta coefficients.
classified stock
Common stock that is given a special designation such as Class A or Class B to meet special needs of the company. Class A: public Class B: insiders (founders' shares)
Discounted Dividend Model
Dividends are paid out of earnings. Therefore, growth in dividends requires growth in earnings. Earnings growth in the long run occurs primarily because firms retain earnings and reinvest them in the business. Therefore, the higher the percentage of earnings retained, the higher the growth rate.
If a firm currently pays no dividends but is expected to pay future dividends, the value of its stock can be found as follows:
Estimate at what point dividends will be paid, the amount of the first dividend, the growth rate during the supernormal growth period, the length of the supernormal period, the long-run (constant) growth rate, and the rate of return required by investors. Use the constant growth model to determine the stock price after the firm reaches a stable growth situation. Set out on a time line the cash flows (dividends during the supernormal growth period and the stock price once the constant growth state is reached); then find the present value of these cash flows. That present value represents the value of the stock today. we see that the discounted dividend model can be applied to firms that currently pay no dividends, provided we can estimate future dividends with a fair degree of confidence. However, in many cases, we can have more confidence in the forecasts of free cash flows, and in these situations, it is better to use the corporate valuation mode
Company perspective of a company raising money to invest in risky projects
Good investment: project's return exceeds the cost of capital Bad investment: does not exceed slope of cost of capital depends on the willingness of the average investor in the market to take on risk. A steeper line indicates that average investor is more risk-aware
Investor's perspective on returns and risk
Good investment: return is sufficient to compensate for the perceived risk Bad investment: return is insufficient to compensate for the perceived risk slope depends on investor's willingness to take on risk. A steeper line indicates that the investor is more risk-averse
stock's beta
If a stock whose beta is greater than 1.0 (say 1.5) is added to a bp = 1.0 portfolio, the portfolio's beta and consequently its risk will increase. Conversely, if a stock whose beta is less than 1.0 is added to a bp= 1.0 portfolio, the portfolio's beta and risk will decline. Thus, because a stock's beta reflects its contribution to the riskiness of a portfolio, beta is the theoretically correct measure of the stock's riskiness.
Portfolio P consists of two stocks: 50% is invested in Stock A and 50% is invested in Stock B. Stock A has a standard deviation of 25% and a beta of 1.2, and Stock B has a standard deviation of 35% and a beta of 0.80. The correlation between these stocks is 0.4. What is the standard deviation of Portfolio P? Less than 30% 30% More than 30%
No calculation is needed to answer this question. Remember that the standard deviation of a portfolio of two stocks is less than the weighted average of the individual stocks' standard deviations, as long as the correlation between the stocks is less than 1.0. So, in this case because the correlation is 0.4, we know that the standard deviation of Portfolio P is less than 30%.
P/E multiple approach
P/E ratio shows how much investors are willing to pay for each dollar of reported earnings. As a starting point, you might conclude that stocks with low P/E ratios are undervalued because their price is "low" given current earnings, whereas stocks with high P/E ratios are overvalued. Unfortunately, however, valuing stocks is not that simple. We should not expect all companies to have the same P/E ratio. P/E ratios are affected by risk—investors discount the earnings of riskier stocks at a higher rate. Thus, all else equal, riskier stocks should have lower P/E ratios. In addition, when you buy a stock, you have a claim not only on current earnings but also on all future earnings. All else equal, companies with stronger growth opportunities will generate larger future earnings and thus should trade at higher P/E ratios. Therefore, Chipotle Mexican Grill is not necessarily overvalued just because its P/E ratio is 46.7 at a time when the median firm in its industry has a P/E of 31.3. Investors believe that Chipotle's growth potential is well above average. Whether the stock's future prospects justify its P/E ratio remains to be seen; but in and of itself, a high P/E ratio does not mean that a stock is overvalued. Nevertheless, P/E ratios can provide a useful starting point in stock valuation. If a stock's P/E ratio is well above its industry average and if the stock's growth potential and risk are similar to other firms in the industry, the stock's price may be too high. Likewise, if a company's P/E ratio falls well below its historical average, the stock may be undervalued—particularly if the company's growth prospects and risk are unchanged and if the overall P/E for the market has remained constant or increased. One obvious drawback of the P/E approach is that it depends on reported accounting earnings. For this reason, some analysts choose to rely on other multiples to value stocks. For example, some analysts look at a company's price-to-cash-flow ratio, whereas others look at the price-to-sales ratio.
Realized Rate of Return, r bar
Returns that were actually earned during some past period. Actual returns usually turn out to be different from expected returns except for riskless assets.
risk aversion
Risk-averse investors dislike risk and require higher rates of return as an inducement to buy riskier securities. If you choose the less risky investment, you are risk-averse. Most investors are risk-averse, and certainly the average investor is with regard to his or her "serious money." The implications of risk aversion for security prices and rates of return is that, other things held constant, the higher a security's risk, the higher its required return; and if this situation does not hold, prices will change to bring about the required condition.
diversifiable risk
That part of a security's risk associated with random events; it can be eliminated by proper diversification. This risk is also known as company-specific, or unsystematic, risk. Diversifiable risk is caused by such random, unsystematic events as lawsuits, strikes, successful and unsuccessful marketing and R&D programs, the winning or losing of a major contract, and other events that are unique to the particular firm. Because these events are random, their effects on a portfolio can be eliminated by diversification—bad events for one firm will be offset by good events for another
Horizon (Terminal) Date
The date when the growth rate becomes constant. At this date, it is no longer necessary to forecast the individual dividends. First, we assume that the dividend will grow at a nonconstant rate (generally a relatively high rate) for N periods, after which it will grow at a constant rate, g
WACC (weighted average cost of capital)
The firm finances with debt, preferred stock, and common equity. The WACC is the weighted average of these three types of capital Free cash flow is the cash generated before any payments are made to any investors; so it must be used to compensate common stockholders, preferred stockholders, and bondholders. Moreover, each type of investor has a required rate of return; and the weighted average of those returns is the WACC, which is used to discount the free cash flows.
expected rate of return, ^r (r-hat)
The rate of return expected to be realized from an investment; the weighted average of the probability distribution of possible results rate of return x probability = ERR ERR = expected ending value - cost/ cost
Which stock is riskier to a diversified investor?
The relevant measure of risk to a diversified investor is beta. It follows that a diversified investor would view the higher beta stock (Stock A) as being more risky.
Risk of a portfolio
The risk of a stock held in a portfolio is typically lower than the stock's risk when it is held alone. Because investors dislike risk and because risk can be reduced by holding portfolios, most stocks are held in portfolios. Banks, pension funds, insurance companies, mutual funds, and other financial institutions are required by law to hold diversified portfolios. Most individual investors—at least those whose security holdings constitute a significant part of their total wealth—also hold portfolios. Therefore, the fact that one particular stock's price increases or decreases is not important—what is important is the return on the portfolio and the portfolio's risk Logically, then, the risk and return of an individual stock should be analyzed in terms of how the security affects the risk and return of the portfolio in which it is held.
market risk
The risk that remains in a portfolio after diversification has eliminated all company-specific risk. This risk is also known as nondiversifiable or systematic or beta risk. Market risk, on the other hand, stems from factors that systematically affect most firms: war, inflation, recessions, high interest rates, and other macro factors. Because most stocks are affected by macro factors, market risk cannot be eliminated by diversification. First, high administrative costs and commissions would more than offset the benefits for individual investors. Second, index funds can be used by investors for diversification, and many individuals can and do get broad diversification through these funds. Third, some people think they can pick stocks that will "beat the market," so they buy them rather than the broad market. And fourth, some people can, through superior analysis, beat the market; so they find and buy undervalued stocks and sell overvalued ones and, in the process, cause most stocks to be properly valued, with their expected returns consistent with their risks.
relevant risk
The risk that remains once a stock is in a diversified portfolio is its contribution to the portfolio's market risk. It is measured by the extent to which the stock moves up or down with the market.
coefficient of variation
The standardized measure of the risk per unit of return; calculated as the standard deviation divided by the expected return. CV shows the risk per unit of return, and it provides a more meaningful risk measure when the expected returns on two alternatives are not the same.
Horizon (Continuing) Value
The value at the horizon date of all dividends expected thereafter.
preferred stock
This hybrid nature becomes apparent when we try to classify preferred stock in relation to bonds and common stock. Like bonds, preferred stock has a par value and a fixed dividend that must be paid before dividends can be paid on the common stock. However, the directors can omit (or "pass") the preferred dividend without throwing the company into bankruptcy. So although preferred stock calls for a fixed payment like bonds, skipping the payment will not lead to bankruptcy. As noted earlier, a preferred stock entitles its owners to regular, fixed dividend payments. If the payments last forever, the issue is a perpetuity.
correlation coefficient, p (rho)
a measure of the degree of relationship between two variables In statistical terms, we say that the returns on Stocks W and M are perfectly negatively correlated, with p = -1.0. The opposite of perfect negative correlation is perfect positive correlation, with p = +1.0. If returns are not related to one another at all, they are said to be independent and p=0 . The returns on two perfectly positively correlated stocks with the same expected return would move up and down together, and a portfolio consisting of these stocks would be exactly as risky as the individual stocks. In a graph, we would see just one line because the two stocks and the portfolio would have the same return at each point in time. Thus, diversification is completely useless for reducing risk if the stocks in the portfolio are perfectly positively correlated. We see then that when stocks are perfectly negatively correlated, all risk can be diversified away; but when stocks are perfectly positively correlated, diversification does no good. In reality, most stocks are positively correlated, but not perfectly so. Past studies have estimated that on average, the correlation coefficient between the returns of two randomly selected stocks is about 0.30.Footnote Under this condition, combining stocks into portfolios reduces risk but does not completely eliminate it.
Capital Asset Pricing Model (CAPM)
a model based on the proposition that any stock's required rate of return is equal to the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification we simply use its intuition to explain how risk should be considered in a world where stocks and other assets are held in portfolios
market portfolio
a portfolio consisting of all stocks.
benchmark betas
b=0.5 : Stock is only half as volatile, or risky, as an average stock. b=1.0 : Stock is of average risk. b=2.0 : Stock is twice as risky as an average stock
What is the beta of Portfolio P?
bp = 0.5(1.2) + 0.5(0.8) bp = 1.0 The beta of a portfolio is equal to the weighted average of the individual stocks' betas.
Stock A
defined as an average-risk stock because it has a beta of b = 1.0 and thus moves up and down in step with the general market. Thus, an average stock will, in general, move up by 10% when the market moves up by 10% and fall by 10% when the market falls by 10%. A large portfolio of such b = 1.0 stocks would (1) have all of its diversifiable risk removed but (2) still move up and down with the broad market averages and thus have a degree of risk
value of a share of common stock
depends on the cash flows it is expected to provide, and those flows consist of two elements: (1) the dividends the investor receives each year while he or she holds the stock and (2) the price received when the stock is sold. The final price includes the original price paid plus an expected capital gain
models to estimate intrinsic values
discounted dividend model and corporate valuation model
EVA approach
equation suggests that companies can increase their EVA by investing in projects that provide shareholders with returns that are above their cost of equity capital, which is the return they could expect to earn on alternative investments with the same level of risk. When you purchase stock in a company, you receive more than just the book value of equity—you also receive a claim on all future value that is created by the firm's managers (the present value of all future EVAs) We can find the "fundamental" value of the stock, , by simply dividing the preceding expression by the number of shares outstanding. As is the case with the discounted dividend model, we can simplify the expression by assuming that at some point in time, annual EVA becomes a perpetuity, or grows at some constant rate over time. Presented here is a simplified version of what is often referred to as the Edwards-Bell-Ohlson (EBO) model. However, if we were studying just one company or a few companies, especially companies still in the high-growth stage of their life cycles, we would want to project future financial statements before estimating future dividends. Because we would already have projected future financial statements, we would go ahead and apply the corporate model
Stock L
on the other hand, with b=0.5 , is only half as volatile as the average stock, and a portfolio of such stocks would rise and fall only half as rapidly as the market. Thus, its risk would be half that of an average-risk portfolio with b=1.0
common stock goal
purchase stock that are undervalued and avoid stocks that are overvalued Wall Street analysts, institutional investors who control mutual funds and pension funds, and many individual investors are interested in finding reliable models that help predict a stock's intrinsic value. First, managers need to know how alternative actions are likely to affect stock prices; the models of intrinsic value that we cover help demonstrate the connection between managerial decisions and firm value. Second, managers should consider whether their stock is significantly undervalued or overvalued before making certain decisions
risk
the chance that some unfavorable event will occur Bonds offer relatively low returns, but with relatively little risk—at least if you stick to Treasury and high-grade corporate bonds. Stocks offer the chance of higher returns, but stocks are generally riskier than bonds. If you invest in speculative stocks (or, really, any stock), you are taking a significant risk in the hope of making an appreciable return. An asset's risk can be analyzed in two ways: (1) on a stand-alone basis, where the asset is considered by itself, and (2) on a portfolio basis, where the asset is held as one of a number of assets in a portfolio.
risk premium
the difference between the expected rate of return on a given risky asset and that on a less risky asset In a market dominated by risk-averse investors, riskier securities compared to less risky securities must have higher expected returns as estimated by the marginal investor. If this situation does not exist, buying and selling will occur until it does exist
supernormal, or nonconstant, growth
the part of the firm's life cycle in which it grows much faster than the economy as a whole For many companies, it is not appropriate to assume that dividends will grow at a constant rate. Indeed, most firms go through life cycles where they experience different growth rates during different parts of the cycle. In their early years, most firms grow much faster than the economy as a whole; then they match the economy's growth; and finally they grow at a slower rate than the economy
stand-alone risk
the risk an investor would face if he or she held only one asset No investment should be undertaken unless the expected rate of return is high enough to compensate for the perceived risk
Correlation
the tendency of two variables to move together
expected return on a portfolio, ^rp
the weighted average of the expected returns on the assets held in the portfolio ^ri is the expected return on the ith stock; the wi are the stocks' weights, or the percentage of the total value of the portfolio invested in each stock; and N is the number of stocks in the portfolio The key point to remember is that the expected return on a portfolio is a weighted average of expected returns on the stocks in the portfolio. Adding relatively risky companies: their expected returns as estimated by the marginal investor would be relatively high; otherwise, investors would sell them, drive down their prices, and force the expected returns above the returns on safer stocks.
constant growth, Gordon model
used to find value of a constant growth stock
Stock H
which has b = 2.0, is twice as volatile as an average stock, which means that it is twice as risky. The value of a portfolio consisting of b = 2.0 stocks could double—or halve—in a short time; and if you held such a portfolio, you could quickly go from being a millionaire to being a pauper. .
