Chapter 9: Stock Valuation
Chapter 9: Stock Valuation 9.1 The Market for Stocks o o
Equity securities are certificates of ownership of a corporation. Households dominate the holdings of equity securities, owning more than 36% of outstanding corporate equities. A. Secondary Market In secondary markets, outstanding shares of stock are bought and sold among investors. An active secondary market enables firms to sell their new debt or equity issues at a lower funding cost than firms selling similar securities that have no secondary market. B. Secondary Markets and Their Efficiency In the United States, most secondary market transactions are conducted on one of the many stock exchanges. o In terms of total volume of activity and total capitalization of the firms listed, the NYSE is the largest in the world and NASDAQ is the second largest. o In terms of the number of companies listed and shares traded on a daily bases, NASDAQ is larger than the NYSE. o Firms listed on the NYSE tend to be, on average, larger in size and their shares trade more frequently than firms whose securities trade on NASDAQ. There are four types of secondary markets, and each type differs according to the amount of price information available to investors, which in turn, affects the efficiency of the market. 1. Direct Search The secondary markets farthest from our ideal of complete price information are those in which buyers and sellers must seek each other out directly. It is too costly to perform a thorough search among all possible partners done to locate the best price. Securities that sell in direct search markets are usually bought and sold so frequently that no third party, such as a broker or dealer, finds it profitable to serve the market. o The sales of common stock of small private companies and private placement transactions are good examples of direct search markets. 2. Broker Brokers bring buyers and sellers together to earn a fee, called a commission. Brokers’ extensive contracts provide them with a pool of price information that individual investors could not economically duplicate themselves.
By changing a commission see less than the cost of direct search, brokers give investors an incentive to make use of the information by hiring them as brokers. 3. Dealer Market efficiency is improved if there is someone in the marketplace to provide continuous bidding (selling or buying) for the security. Dealers provide this service by holding inventories of securities, which they own, then buying and selling from the inventory to earn profit. Dealers earn their profits from the spread on the securities they trade – the difference between their bid price (the price at which they buy) and their offer price (the price at which they sell). o The advantage of a dealer over a brokered market is that brokers cannot guarantee that an order will be executed promptly, while dealers can because they have inventory of securities. o A dealer eliminates the need for a time-consuming search for a fair deal by buying and selling immediately from the dealer’s inventory of securities. o NASDAQ is the best-known example for a dealer market. Electronic communication network (ECN) systems provide additional price information to investors and increase marketability and competition, which should improve NASDAQ efficiency. 4. Action In an action market, buyers and sellers confront each other directly and bargain over price. o The New York Stock Exchange is the best-known example of an auction market. o In the NYSE the auction for a security takes place at a specific location on the floor of the exchange, called a post. The auctioneer in this case is the specialist who is designated by the exchange to represent order placed by public customers. C. Reading the Stock Market Listings The Wall Street Journal, and New York Times, and other newspapers in large metropolitan areas provide stock listings for the major stock exchanges, such as the NYSE and the relevant regional exchanges. o Exhibit 9.1 shows a section of the listing in the Wall Street Journal for the NYSE D. Types of Equity Securities The two types of securities are common stock and preferred stock. Common stock represents the basic ownership claim in a corporation. o One of the rights of the owners is to vote on all important matters that affect the life of the company, such as electing the board of directors or voting on a proposed merger or acquisition. o Owners of common stock are not guaranteed any dividend payments and have the lowest-priority claim on the firm’s assets in the event of bankruptcy. o Legallu, common stockholders enjoy limited liability.
o Common stocks are perpetuities in the sense that they have no maturity. Preferred stock also represents ownership interest in the corporation, but preferred stock receives preferential treatment over common stock in certain matters. o If preferred dividends payment is not paid due to the firm’s financial condition, the firm is not in default technically. However, the market reacts as if the failure to make the dividend payment is default and punishes the stock accordingly. o Preferred stock owners given priority treatment over common stock with respect to dividends payments and the claims against the firm’s assets in the event of bankruptcy or liquidation. Dividends payments are paid with after-tax dollars subject to taxation. Even though preferred stock is equity, the owners have no voting privileges. E. Preferred Stock: Debt or Equity? Legally, preferred stock is equity. Like the dividends on common stock, preferred stock dividends are taxable. A strong case can be made that preferred stock is really a special type of bond. o First, regular preferred stock confers no voting powers. o Second, preferred stockholders receive a fixed dividend, regardless of the firm’s earnings, and if the firm is liquidated, they receive a stated value (usually par) and not the residual value. o Third, preferred stocks often have “credit” ratings that are similar to those issued to bonds. o Fourth, preferred stock is sometimes convertible into common stock. o Finally, most preferred stock issues today are not true perpetuities. Increasingly, preferred stock issues have the sinking fund feature, which require mandatory annual retirement schedules.
9.2 Common Stock Valuation o o
Valuation of common and preferred stock is done by using the same basic methodology that was discussed for bond valuation. Applying the valuation procedure to common stocks is more difficult than applying it to bonds for various reasons. o First, in contrast to coupon payments on bonds, the size and timing of the dividend cash flow are less certain. o Second, common stocks are true perpetuities in that they have no final maturity date. o Finally, unlike the rate of return, or yield, on bonds, the rate of return on common stock is not directly observable. A. A One-Period Model A one-period provides an estimate of the market price. The value of an asset is the present value of its future cash flows – the future dividend and the end-of-period price. B. A Two-Period Model This model can be viewed as two one-period models strung together.
C. A Perpetuity Model A series of one-period stock pricing models is strung together to arrive at a stock perpetuity model Though theoretically sound, this model is not practical to apply because the number of dividends could be infinite. D. The General Dividend Valuation Model Equation 9.1 is a general expression for the value of a share of stock. It says that the price of a share of stock is the present value of all expected future dividends. o The formula does not assume any specific pattern for future cash dividends, such as a constant-growth rate. o It does not make any assumption about when the share of stock is going to be sold in the future. o Finally, the model says that to compute a stock’s current value, we need to forecast an infinite number of dividends. Equation 9.1 implies that the underlying value of a share of stock is determined by the market’s expectations of future cash flows that the firm can generate. o In efficient markets, stock prices change constantly as new information becomes available and is discounted into the firm’s market price. o For publicly traded companies, there is a constant stream of information about the firm that reaches the market, with some having an impact on the stock price while other information has no effect. E. The Growth Stock Pricing Paradox Growth stocks are typically defined as the stocks of companies whose earnings are growing at above-average rates and are expected to continue to do for some time. Fast growing companies typically pay no dividend on their stock during their growth phase because management believes that the company has a number of high-return investment opportunities and that both the company and its investors will be better off is earnings are reinvested. o Equation 9.1 predicts and common sense says if you own stock in a company that will never pay you any cash, the market value of those shares of stock are worth absolutely nothing. o In reality, these firms will eventually pay out dividends in the distant future. o If the internal investments succeed, the stock’s price should go up significantly, and investors can sell their stock at a prick much higher than what they paid.
9.3 Stock Valuation: Some Simplifying Assumptions o o
To make Equation 9.1 more applicable, some simplifying assumptions about the pattern of dividends are necessary. Three different assumptions can cover most growth patterns: 1) Dividend payments remain constant over time; that is, they have a growth rate of zero. 2) Dividends have a constant-growth rate. 3) Dividends have a mixed growth rate pattern; that is, dividends have one payment pattern then switch to another.
A. Zero-Growth Dividend Model The dividend payment pattern remains constant over time. The dividend-discount model (Equation 9.1) becomes: P0 = D + D + D (1+R)1 (1+R)2 (1+R)3 This cash flow pattern essentially describes a perpetuity with a constant cash flow. In Chapter 6, we developed the present value of a perpetuity with a constant cash flow of CF/i, where CF is the constant cash flow and i is the interest rate. Similarly, Equation 9.2 gives the valuation model for a zero-growth stock. P0 = D / R B. Constant-Growth Dividend Model Cash dividends do not remain constant but instead grow at some average rate g from one period to the next forever. o Constant dividend growth is an appropriate assumption for mature companies with a history of stable growth. While an infinite horizon is still hard to comprehend, far-distant dividends have a small present value and contribute very little to the price of the stock. Deriving the constant-growth dividend model is fairly straightforward. First, we need to build a model to compute the value of dividend payments for any time period. o The constant-growth dividend model is easy to do because it is just an application from Chapter 6. o Recall the equation for a growing perpetuity is given by: PVA∞ = CF1 / (i - g) o In other words, the constant-growth dividend model tells us that the current price of a share of stock is the next period of dividend divided by the difference between the discount rate and the dividend growth rate. Equation 9.4 shows how the value a constant-growth stock: P0 = D1 (R – g) C. Computing Future Stock Prices The constant-growth dividend model (Equation 9.4) can be modified to determine the value, or price, of a share of stock at any point in time. This result in Equation 9.5, which shows that the price of a share of stock at time t is: P0 = Dt + 1 (R – g) D. The Relationship between R and g Te constant-growth dividend model yields solutions that are invalid anytime the dividend growth rate equals or exceeds the discount rate (g ≥ R). o If g = R, then the value of the denominator is zero and the value of the stock is infinite, which makes no sense. o If g > R, the present value of the dividend gets bigger and bigger rather than smaller and smaller, as it should. This implies that a firm that is growing at a very fast rate does so forever.
E. Supernormal Growth Dividend Model During the early part of their lives, very successful firms experience a supernormal rate of growth in earnings. To value a share of stock for a firm with supernormal dividend growth patterns, we can apply Equation 9.1, out general dividend model, and Equation 9.5, which gives us the price of a share of stock with constant dividend growth at any point in time. o Thus, out valuation is (Equation 9.6): P0 = PV (Mixed dividend growth) + PV (Constant dividend growth)
9.4 Valuing Preferred Stock o o o
In computing the value of preferred stock, one needs to know whether the preferred stock has an effective “maturity” because of a sinking fund option or call option. The most significant difference between preferred stock with a fixed maturity and a bond is the risk of default. The failure to pay a preferred stock dividend as promised is a serious financial breach and signals to the market that the firm is in serious financial difficulty. A. Preferred Stock with a Fixed Maturity We can use the bond valuation model to determine its price, or value. Preferred stock price = PV (Dividend payments) + PV (Par value) Since most preferred stock make quarterly dividend payments, m equals 4. B. Perpetual Preferred Stock Some preferred stock issues have no maturity. o Dividends are constant over time (g = 0) o Fixed dividend payments go on forever. We can use Equation 9.2 to value such preferred stock issues. P0 = D R
Equity securities are certificates of ownership of a corporation. Households dominate the holdings of equity securities, owning more than 36% of outstanding corporate equities. A. Secondary Market In secondary markets, outstanding shares of stock are bought and sold among investors. An active secondary market enables firms to sell their new debt or equity issues at a lower funding cost than firms selling similar securities that have no secondary market. B. Secondary Markets and Their Efficiency In the United States, most secondary market transactions are conducted on one of the many stock exchanges. o In terms of total volume of activity and total capitalization of the firms listed, the NYSE is the largest in the world and NASDAQ is the second largest. o In terms of the number of companies listed and shares traded on a daily bases, NASDAQ is larger than the NYSE. o Firms listed on the NYSE tend to be, on average, larger in size and their shares trade more frequently than firms whose securities trade on NASDAQ. There are four types of secondary markets, and each type differs according to the amount of price information available to investors, which in turn, affects the efficiency of the market. 1. Direct Search The secondary markets farthest from our ideal of complete price information are those in which buyers and sellers must seek each other out directly. It is too costly to perform a thorough search among all possible partners done to locate the best price. Securities that sell in direct search markets are usually bought and sold so frequently that no third party, such as a broker or dealer, finds it profitable to serve the market. o The sales of common stock of small private companies and private placement transactions are good examples of direct search markets. 2. Broker Brokers bring buyers and sellers together to earn a fee, called a commission. Brokers’ extensive contracts provide them with a pool of price information that individual investors could not economically duplicate themselves.
By changing a commission see less than the cost of direct search, brokers give investors an incentive to make use of the information by hiring them as brokers. 3. Dealer Market efficiency is improved if there is someone in the marketplace to provide continuous bidding (selling or buying) for the security. Dealers provide this service by holding inventories of securities, which they own, then buying and selling from the inventory to earn profit. Dealers earn their profits from the spread on the securities they trade – the difference between their bid price (the price at which they buy) and their offer price (the price at which they sell). o The advantage of a dealer over a brokered market is that brokers cannot guarantee that an order will be executed promptly, while dealers can because they have inventory of securities. o A dealer eliminates the need for a time-consuming search for a fair deal by buying and selling immediately from the dealer’s inventory of securities. o NASDAQ is the best-known example for a dealer market. Electronic communication network (ECN) systems provide additional price information to investors and increase marketability and competition, which should improve NASDAQ efficiency. 4. Action In an action market, buyers and sellers confront each other directly and bargain over price. o The New York Stock Exchange is the best-known example of an auction market. o In the NYSE the auction for a security takes place at a specific location on the floor of the exchange, called a post. The auctioneer in this case is the specialist who is designated by the exchange to represent order placed by public customers. C. Reading the Stock Market Listings The Wall Street Journal, and New York Times, and other newspapers in large metropolitan areas provide stock listings for the major stock exchanges, such as the NYSE and the relevant regional exchanges. o Exhibit 9.1 shows a section of the listing in the Wall Street Journal for the NYSE D. Types of Equity Securities The two types of securities are common stock and preferred stock. Common stock represents the basic ownership claim in a corporation. o One of the rights of the owners is to vote on all important matters that affect the life of the company, such as electing the board of directors or voting on a proposed merger or acquisition. o Owners of common stock are not guaranteed any dividend payments and have the lowest-priority claim on the firm’s assets in the event of bankruptcy. o Legallu, common stockholders enjoy limited liability.
o Common stocks are perpetuities in the sense that they have no maturity. Preferred stock also represents ownership interest in the corporation, but preferred stock receives preferential treatment over common stock in certain matters. o If preferred dividends payment is not paid due to the firm’s financial condition, the firm is not in default technically. However, the market reacts as if the failure to make the dividend payment is default and punishes the stock accordingly. o Preferred stock owners given priority treatment over common stock with respect to dividends payments and the claims against the firm’s assets in the event of bankruptcy or liquidation. Dividends payments are paid with after-tax dollars subject to taxation. Even though preferred stock is equity, the owners have no voting privileges. E. Preferred Stock: Debt or Equity? Legally, preferred stock is equity. Like the dividends on common stock, preferred stock dividends are taxable. A strong case can be made that preferred stock is really a special type of bond. o First, regular preferred stock confers no voting powers. o Second, preferred stockholders receive a fixed dividend, regardless of the firm’s earnings, and if the firm is liquidated, they receive a stated value (usually par) and not the residual value. o Third, preferred stocks often have “credit” ratings that are similar to those issued to bonds. o Fourth, preferred stock is sometimes convertible into common stock. o Finally, most preferred stock issues today are not true perpetuities. Increasingly, preferred stock issues have the sinking fund feature, which require mandatory annual retirement schedules.
9.2 Common Stock Valuation o o
Valuation of common and preferred stock is done by using the same basic methodology that was discussed for bond valuation. Applying the valuation procedure to common stocks is more difficult than applying it to bonds for various reasons. o First, in contrast to coupon payments on bonds, the size and timing of the dividend cash flow are less certain. o Second, common stocks are true perpetuities in that they have no final maturity date. o Finally, unlike the rate of return, or yield, on bonds, the rate of return on common stock is not directly observable. A. A One-Period Model A one-period provides an estimate of the market price. The value of an asset is the present value of its future cash flows – the future dividend and the end-of-period price. B. A Two-Period Model This model can be viewed as two one-period models strung together.
C. A Perpetuity Model A series of one-period stock pricing models is strung together to arrive at a stock perpetuity model Though theoretically sound, this model is not practical to apply because the number of dividends could be infinite. D. The General Dividend Valuation Model Equation 9.1 is a general expression for the value of a share of stock. It says that the price of a share of stock is the present value of all expected future dividends. o The formula does not assume any specific pattern for future cash dividends, such as a constant-growth rate. o It does not make any assumption about when the share of stock is going to be sold in the future. o Finally, the model says that to compute a stock’s current value, we need to forecast an infinite number of dividends. Equation 9.1 implies that the underlying value of a share of stock is determined by the market’s expectations of future cash flows that the firm can generate. o In efficient markets, stock prices change constantly as new information becomes available and is discounted into the firm’s market price. o For publicly traded companies, there is a constant stream of information about the firm that reaches the market, with some having an impact on the stock price while other information has no effect. E. The Growth Stock Pricing Paradox Growth stocks are typically defined as the stocks of companies whose earnings are growing at above-average rates and are expected to continue to do for some time. Fast growing companies typically pay no dividend on their stock during their growth phase because management believes that the company has a number of high-return investment opportunities and that both the company and its investors will be better off is earnings are reinvested. o Equation 9.1 predicts and common sense says if you own stock in a company that will never pay you any cash, the market value of those shares of stock are worth absolutely nothing. o In reality, these firms will eventually pay out dividends in the distant future. o If the internal investments succeed, the stock’s price should go up significantly, and investors can sell their stock at a prick much higher than what they paid.
9.3 Stock Valuation: Some Simplifying Assumptions o o
To make Equation 9.1 more applicable, some simplifying assumptions about the pattern of dividends are necessary. Three different assumptions can cover most growth patterns: 1) Dividend payments remain constant over time; that is, they have a growth rate of zero. 2) Dividends have a constant-growth rate. 3) Dividends have a mixed growth rate pattern; that is, dividends have one payment pattern then switch to another.
A. Zero-Growth Dividend Model The dividend payment pattern remains constant over time. The dividend-discount model (Equation 9.1) becomes: P0 = D + D + D (1+R)1 (1+R)2 (1+R)3 This cash flow pattern essentially describes a perpetuity with a constant cash flow. In Chapter 6, we developed the present value of a perpetuity with a constant cash flow of CF/i, where CF is the constant cash flow and i is the interest rate. Similarly, Equation 9.2 gives the valuation model for a zero-growth stock. P0 = D / R B. Constant-Growth Dividend Model Cash dividends do not remain constant but instead grow at some average rate g from one period to the next forever. o Constant dividend growth is an appropriate assumption for mature companies with a history of stable growth. While an infinite horizon is still hard to comprehend, far-distant dividends have a small present value and contribute very little to the price of the stock. Deriving the constant-growth dividend model is fairly straightforward. First, we need to build a model to compute the value of dividend payments for any time period. o The constant-growth dividend model is easy to do because it is just an application from Chapter 6. o Recall the equation for a growing perpetuity is given by: PVA∞ = CF1 / (i - g) o In other words, the constant-growth dividend model tells us that the current price of a share of stock is the next period of dividend divided by the difference between the discount rate and the dividend growth rate. Equation 9.4 shows how the value a constant-growth stock: P0 = D1 (R – g) C. Computing Future Stock Prices The constant-growth dividend model (Equation 9.4) can be modified to determine the value, or price, of a share of stock at any point in time. This result in Equation 9.5, which shows that the price of a share of stock at time t is: P0 = Dt + 1 (R – g) D. The Relationship between R and g Te constant-growth dividend model yields solutions that are invalid anytime the dividend growth rate equals or exceeds the discount rate (g ≥ R). o If g = R, then the value of the denominator is zero and the value of the stock is infinite, which makes no sense. o If g > R, the present value of the dividend gets bigger and bigger rather than smaller and smaller, as it should. This implies that a firm that is growing at a very fast rate does so forever.
E. Supernormal Growth Dividend Model During the early part of their lives, very successful firms experience a supernormal rate of growth in earnings. To value a share of stock for a firm with supernormal dividend growth patterns, we can apply Equation 9.1, out general dividend model, and Equation 9.5, which gives us the price of a share of stock with constant dividend growth at any point in time. o Thus, out valuation is (Equation 9.6): P0 = PV (Mixed dividend growth) + PV (Constant dividend growth)
9.4 Valuing Preferred Stock o o o
In computing the value of preferred stock, one needs to know whether the preferred stock has an effective “maturity” because of a sinking fund option or call option. The most significant difference between preferred stock with a fixed maturity and a bond is the risk of default. The failure to pay a preferred stock dividend as promised is a serious financial breach and signals to the market that the firm is in serious financial difficulty. A. Preferred Stock with a Fixed Maturity We can use the bond valuation model to determine its price, or value. Preferred stock price = PV (Dividend payments) + PV (Par value) Since most preferred stock make quarterly dividend payments, m equals 4. B. Perpetual Preferred Stock Some preferred stock issues have no maturity. o Dividends are constant over time (g = 0) o Fixed dividend payments go on forever. We can use Equation 9.2 to value such preferred stock issues. P0 = D R
