Essays of warren buffet (before Common stock)

LOS 46.a: Evaluate whether a security, given its current market price and a value estimate, is overvalued, fairly valued, or undervalued by the market. Recall from the reading on Market Efficiency that intrinsic value or fundamental value is defined as the rational value investors would place on the asset if they had full knowledge of the asset’s characteristics. Analysts use valuation models to estimate the intrinsic values of stocks and compare them to the stocks’ market prices to determine whether individual stocks are overvalued, undervalued, or fairly valued. In doing valuation analysis for stocks, analysts are assuming that some stocks’ prices deviate significantly from their intrinsic values. To the extent that market prices deviate from intrinsic values, analysts who can estimate a stock’s intrinsic value better than the market can earn abnormal profits if the stock’s market price moves toward its intrinsic value over time. There are several things to consider, however, in deciding whether to invest based on differences between market prices and estimated intrinsic values. 1. The larger the percentage difference between market prices and estimated values, the more likely the investor is to take a position based on the estimate of intrinsic value. Small differences between market prices and estimates of intrinsic values are to be expected. 2. The more confident the investor is about the appropriateness of the valuation model used, the more likely the investor is to take an investment position in a stock that is identified as overvalued or undervalued. 3. The more confident the investor is about the estimated inputs used in the valuation model, the more likely the investor is to take an investment position in a stock that is identified as overvalued or undervalued. Analysts must also consider the sensitivity of a model value to each of its inputs in deciding whether to act on a difference between model values and market prices. If a decrease of one-half percent in the long-term growth rate used in the valuation model would produce an estimated value equal to the market price, an analyst would have to be quite sure of the model’s growth estimate to take a position in the stock based on its estimated value. 4. Even if we assume that market prices sometimes deviate from intrinsic values, market prices must be treated as fairly reliable indications of intrinsic value. Investors must consider why a stock is mispriced in the market. Investors may be more confident about estimates of value that differ from market prices when few analysts follow a particular security. 5. Finally, to take a position in a stock identified as mispriced in the market, an investor must believe that the market price will actually move toward (and certainly not away from) its estimated intrinsic value and that it will do so to a significant extent within the investment time horizon. LOS 46.b: Describe major categories of equity valuation models. Analysts use a variety of models to estimate the value of equities. Usually, an analyst will use more than one model with several different sets of inputs to determine a range of possible stock values. In discounted cash flow models (or present value models), a stock’s value is estimated as the present value of cash distributed to shareholders (dividend discount models) or the present value of cash available to shareholders after the firm meets its necessary capital expenditures and working capital expenses (free cash flow to equity models). There are two basic types of multiplier models (or market multiple models) that can be used to estimate intrinsic values. In the first type, the ratio of stock price to such fundamentals as earnings, sales, book value, or cash flow per share is used to determine if a stock is fairly valued. For example, the price to earnings (P/E) ratio is frequently used by analysts. The second type of multiplier model is based on the ratio of enterprise value to either earnings before interest, taxes, depreciation, and amortization (EBITDA) or revenue. Enterprise value is the market value of all a firm’s outstanding securities minus cash and short-term investments. Common stock value can be estimated by subtracting the value of liabilities and preferred stock from an estimate of enterprise value. In asset-based models, the intrinsic value of common stock is estimated as total asset value minus liabilities and preferred stock. Analysts typically adjust the book values of the firm’s assets and liabilities to their fair values when estimating the market value of its equity with an asset-based model. LOS 46.c: Describe regular cash dividends, extra dividends, stock dividends, stock splits, reverse stock splits, and share repurchases. Cash dividends, as the name implies, are payments made to shareholders in cash. They may be regularly scheduled dividends or one-time special dividends. Regular dividends occur when a company pays out a portion of profits on a consistent schedule (e.g., quarterly). A long-term record of stable or increasing dividends is widely viewed by investors as a sign of a company’s financial stability. Special dividends are used when favorable circumstances allow the firm to make a one-time cash payment to shareholders, in addition to any regular dividends the firm pays. Many cyclical firms (e.g., automakers) will use a special dividend to share profits with shareholders when times are good but maintain the flexibility to conserve cash when profits are poor. Other names for special dividends include extra dividends and irregular dividends. Stock dividends are dividends paid out in new shares of stock rather than cash. In this case, there will be more shares outstanding, but each one will be worth less. Total shareholders’ equity remains unchanged. Stock dividends are commonly expressed as a percentage. A 20% stock dividend means every shareholder gets 20% more stock. Stock splits divide each existing share into multiple shares, creating more shares. There are now more shares, but the price of each share will drop correspondingly to the number of shares created, so there is no change in the owner’s wealth. Splits are expressed as a ratio. In a 3-for-1 stock split, each old share is split into three new shares. Stock splits are currently more common than stock dividends. Reverse stock splits are the opposite of stock splits. After a reverse split, there are fewer shares outstanding but there is a higher stock price. Because these factors offset one another, shareholder wealth is unchanged. A share repurchase is a transaction in which a company buys outstanding shares of its own common stock. Share repurchases are an alternative to cash dividends as a way of distributing cash to shareholders, and they have the same effect on shareholders’ wealth as cash dividends of the same size. A company might repurchase shares to support their price or to signal that management believes the shares are undervalued. Share repurchases may also be used to offset an increase in outstanding shares from the exercise of employee stock options. In countries that tax capital gains at lower rates than dividends, shareholders may prefer share repurchases to dividend payments as a way to distribute cash to shareholders. LOS 46.d: Describe dividend payment chronology. The dates relevant to dividend payments are shown in Figure 46.1. Figure 46.1: Dividend Payment Chronology Declaration date. The date the board of directors approves payment of a dividend, specifying the per-share dividend amount, the date shareholders must own the stock to receive the dividend (record date), and the date the dividend payment will be made (payment date). Ex-dividend date. The first day on which a share purchaser will not receive the next dividend. The ex-dividend date is one or two business days before the holder-of-record date, depending on the settlement period for stock purchases. If you buy the share on or after the ex-dividend date, you will not receive the dividend. Holder-of-record date (record date). The date on which all owners of shares become entitled to receive the dividend payment on their shares. Payment date. The date dividend checks are mailed to, or payment is made electronically to, holders of record. On the ex-dividend date, the share price will decrease from the previous day’s closing price by approximately the amount of the dividend, in the absence of other factors affecting the stock price. Consider shares that are trading at $25 on the day prior to the ex-dividend date and will pay a $1 dividend. Purchasing a share on the day prior to the ex-dividend date will give the owner a share of stock and the $1 dividend on the payment date. Purchasing a share on the ex-dividend date will entitle the owner only to the share; the dividend payment will go to the seller.

LOS 46.e: Explain the rationale for using present value models to value equity and describe the dividend discount and free-cash-flowto-equity models. The dividend discount model (DDM) is based on the rationale that the intrinsic value of stock is the present value of its future dividends. The most general form of the model is as follows: One-year holding period DDM. For a holding period of one year, the value of the stock today is the present value of any dividends during the year plus the present value of the expected price of the stock at the end of the year (referred to as its terminal value). The one-year holding period DDM is simply:

The most general form of the DDM uses an infinite holding period because a corporation has an indefinite life. In an infinite-period DDM model, the present value of all expected future dividends is calculated and there is no explicit terminal value for the stock. In practice, as we will see, a terminal value can be calculated at a time in the future after which the growth rate of dividends is expected to be constant. Free cash flow to equity (FCFE) is often used in discounted cash flow models instead of dividends because it represents the potential amount of cash that could be paid out to common shareholders. That is, FCFE reflects the firm’s capacity to pay dividends. FCFE is also useful for firms that do not currently pay dividends. FCFE is defined as the cash remaining after a firm meets all of its debt obligations and provides for the capital expenditures necessary to maintain existing assets and to purchase the new assets needed to support the assumed growth of the firm. In other words, it is the cash available to the firm’s equity holders after a firm meets all of its other obligations. FCFE for a period is often calculated as: FCFE can also be calculated as: In the second formula, net borrowing is the increase in debt during the period (i.e., amount borrowed minus amount repaid) and is assumed to be available to shareholders. Fixed capital investment must be subtracted because the firm must invest in assets to sustain itself. FCFE is projected for future periods using the firm’s financial statements. Restating the general form of the DDM in terms of FCFE, we have: Estimating the Required Return for Equity The capital asset pricing model (CAPM) provides an estimate of the required rate of return (ki ) for security i as a function of its systematic risk (βi ), the risk-free rate (Rf ), and the expected return on the market [E(Rmkt )] as: There is some controversy over whether the CAPM is the best model to calculate the required return on equity. Also, different analysts will likely use different inputs, so there is no single number that is correct. PROFESSOR’S NOTE The CAPM is discussed in detail in Portfolio Management. For firms with publicly traded debt, analysts often estimate the required return on the firm’s common equity by adding a risk premium to the firm’s current bond yield. If the firm does not have publicly traded debt, an analyst can add a larger risk premium to a government bond yield

The Gordon growth model (or constant growth model) assumes the annual growth rate of dividends, gc , is constant. Hence, next period’s dividend, D1 , is D0 (1 + gc ), the second year’s dividend, D2 , is D0 (1 + gc ) 2 , and so on. The extended equation using this assumption gives the present value of the expected future dividends (V0 ) as: When the growth rate of dividends is constant, this equation simplifies to the Gordon (constant) growth model: PROFESSOR’S NOTE In much of the finance literature, you will see this model referred to as the constant growth DDM, infinite period DDM, or the Gordon growth model. Whatever you call it, memorize D1 over (k minus g). Note that our valuation model for preferred stock is the same as the constant growth model with no growth (g = 0). The assumptions of the Gordon growth model are: Dividends are the appropriate measure of shareholder wealth. The constant dividend growth rate, gc , and required return on stock, ke , are never expected to change. ke must be greater than gc . If not, the math will not work. If any one of these assumptions is not met, the model is not appropriate. EXAMPLE: Gordon growth model valuation Calculate the value of a stock that paid a $1.50 dividend last year, if dividends are expected to grow at 8% forever and the required return on equity is 12%. Answer: PROFESSOR’S NOTE When doing stock valuation problems on the exam, watch for words like “forever,” “infinitely,” “indefinitely,” “for the foreseeable future,” and so on. This will tell you that the Gordon growth model should be used. Also watch for words like “just paid” or “recently paid.” These will refer to the last dividend, D0 . Words like “will pay” or “is expected to pay” refer to D1 . This example demonstrates that the stock’s value is determined by the relationship between the investor’s required rate of return on equity, ke , and the projected growth rate of dividends, gc : As the difference between ke and gc widens, the value of the stock falls. As the difference narrows, the value of the stock rises. Small changes in the difference between ke and gc can cause large changes in the stock’s value. Because the estimated stock value is very sensitive to the denominator, an analyst should calculate several different value estimates using a range of required returns and growth rates. An analyst can also use the Gordon growth model to determine how much of the estimated stock value is due to dividend growth. To do this, assume the growth rate is zero and calculate a value. Then, subtract this value from the stock value estimated using a positive growth rate.

Estimating the Growth Rate in Dividends To estimate the growth rate in dividends, the analyst can use three methods: 1. Use the historical growth in dividends for the firm. 2. Use the median industry dividend growth rate. 3. Estimate the sustainable growth rate. The sustainable growth rate is the rate at which equity, earnings, and dividends can continue to grow indefinitely assuming that ROE is constant, the dividend payout ratio is constant, and no new equity is sold. The quantity (1 − dividend payout ratio) is also referred to as the retention rate, the proportion of net income that is not paid out as dividends and goes to retained earnings, thus increasing equity.

Some firms do not currently pay dividends but are expected to begin paying dividends at some point in the future. A firm may not currently pay a dividend because it is in financial distress and cannot afford to pay out cash or because the return the firm can earn by reinvesting cash is greater than what stockholders could expect to earn by investing dividends elsewhere. For these firms, an analyst must estimate the amount and timing of the first dividend in order to use the Gordon growth model. Because these parameters are highly uncertain, the analyst should check the estimate from the Gordon growth model against estimates made using other models. EXAMPLE: A firm with no current dividend A firm currently pays no dividend but is expected to pay a dividend at the end of Year 4. Year 4 earnings are expected to be $1.64, and the firm will maintain a dividend payout ratio of 50%. Assuming a constant growth rate of 5% and a required rate of return of 10%, estimate the current value of this stock. Answer: The first step is to find the value of the stock at the end of Year 3. Remember, P3 is the present value of dividends in Years 4 through infinity, calculated at the end of Year 3, one period before the first dividend is paid. Calculate D4 , the estimate of the dividend that will be paid at the end of Year 4: Apply the constant growth model to estimate V3 : The second step is to calculate the current value, V0 : Multistage Dividend Growth Models A firm may temporarily experience a growth rate that exceeds the required rate of return on the firm’s equity, but no firm can maintain this relationship indefinitely. A firm with an extremely high growth rate will attract competition, and its growth rate will eventually fall. We must assume the firm will return to a more sustainable rate of growth at some point in the future in order to calculate the present value of expected future dividends. One way to value a dividend-paying firm that is experiencing temporarily high growth is to add the present values of dividends expected during the high-growth period to the present value of the constant growth value of the firm at the end of the high-growth period. This is referred to as the multistage dividend discount model. Steps in using the multistage model: Determine the discount rate, ke . Project the size and duration of the high initial dividend growth rate, g*. Estimate dividends during the high-growth period. Estimate the constant growth rate at the end of the high-growth period, gc . Estimate the first dividend of the constant growth period. Use this dividend to calculate the stock value at the end of the high-growth period. Add the PVs of all dividends during the high-growth period to the PV of the value of the stock at the end of the high-growth period. EXAMPLE: Multistage growth Consider a stock with dividends that are expected to grow at 15% per year for two years, after which they are expected to grow at 5% per year, indefinitely. The last dividend paid was $1.00, and ke = 11%. Calculate the value of this stock using the multistage growth model. Answer: Calculate the dividends over the high-growth period: Calculate the first dividend of the constant-growth period: Use the constant growth model to get P2, a value for all the (infinite) dividends expected from time = 3 onward: Finally, we can sum the present values of dividends 1 and 2 and of P2 to get the present value of all the expected future dividends during both the high-growth and constant-growth periods:

LOS 46.i: Identify characteristics of companies for which the constant growth or a multistage dividend discount model is appropriate. The Gordon growth model uses a single constant growth rate of dividends and is most appropriate for valuing stable and mature, non-cyclical, dividend-paying firms. For dividend-paying firms with dividends that are expected to grow rapidly, slowly, or erratically over some period, followed by constant dividend growth, some form of the multistage growth model should be employed. The important points are that dividends must be estimable and must grow at a constant rate after some initial period so that the constant growth model can be used to determine the terminal value of the stock. Thus, we can apply multistage dividend growth models to a firm with high current growth that will drop to a stable rate in the future or to a firm that is temporarily losing market share and growing slowly or getting smaller, as long as its growth is expected to stabilize to a constant rate at some point in the future. One variant of a multistage growth model assumes that the firm has three stages of dividend growth, not just two. These three stages can be categorized as growth, transition, and maturity. A 3-stage model would be suitable for firms with an initial high growth rate, followed by a lower growth rate during a second, transitional period, followed by the constant growth rate in the long run, such as a young firm still in the high growth phase. When a firm does not pay dividends, estimates of dividend payments some years in the future are highly speculative. In this case, and in any case where future dividends cannot be estimated with much confidence, valuation based on FCFE is appropriate as long as growth rates of earnings can be estimated. In other cases, valuation based on price multiples may be more appropriate.

RELATIVE VALUATION MEASURES LOS 46.j: Explain the rationale for using price multiples to value equity, how the price to earnings multiple relates to fundamentals, and the use of multiples based on comparables. Because the dividend discount model is very sensitive to its inputs, many investors rely on other methods. In a price multiple approach, an analyst compares a stock’s price multiple to a benchmark value based on an index, industry group of firms, or a peer group of firms within an industry. Common price multiples used for valuation include price-to-earnings, price-to-cash flow, price-to-sales, and price-to-book value ratios. Price multiples are widely used by analysts and readily available in numerous media outlets. Price multiples are easily calculated and can be used in time series and crosssectional comparisons. Many of these ratios have been shown to be useful for predicting stock returns, with low multiples associated with higher future returns. A critique of price multiples is that they reflect only the past because historical (trailing) data are often used in the denominator. For this reason, many practitioners use forward (leading or prospective) values in the denominator. The use of projected values can result in much different ratios. An analyst should be sure to use price multiple calculations consistently across firms. When we compare a price multiple, such as P/E, for a firm to those of other firms based on market prices, we are using price multiples based on comparables. By contrast, price multiples based on fundamentals tell us what a multiple should be based on some valuation model and therefore are not dependent on the current market prices of other companies to establish value. LOS 46.k: Calculate and interpret the following multiples: price to earnings, price to an estimate of operating cash flow, price to sales, and price to book value. Price multiples used for valuation include: Price-earnings (P/E) ratio: The P/E ratio is a firm’s stock price divided by earnings per share and is widely used by analysts and cited in the press. Price-sales (P/S) ratio: The P/S ratio is a firm’s stock price divided by sales per share. Price-book value (P/B) ratio: The P/B ratio is a firm’s stock price divided by book value of equity per share. Price-cash flow (P/CF) ratio: The P/CF ratio is a firm’s stock price divided by cash flow per share, where cash flow may be defined as operating cash flow or free cash flow. Other multiples can be used that are industry specific. For example, in the cable television industry, stock market capitalization is compared to the number of subscribers. Multiples Based on Fundamentals To understand fundamental price multiples, consider the Gordon growth valuation model: If we divide both sides of the equation by next year’s projected earnings, E1 , we get which is the leading P/E for this stock if it is valued in the market according to the constant growth DDM. This P/E based on fundamentals is also referred to as a justified P/E. It is “justified” because, assuming we have the correct inputs for D1 , E1 , ke , and g, the previous equation will provide a P/E ratio that is based on the present value of the future cash flows. We refer to this as a leading P/E ratio because it is based on expected earnings next period, not on actual earnings for the previous period, which would produce a lagging or trailing P/E ratio. One advantage of this approach is that it makes clear how the firm’s P/E ratio should be related to its fundamentals. It illustrates that the P/E ratio is a function of: D1 / E1 = expected dividend payout ratio. k = required rate of return on the stock. g = expected constant growth rate of dividends. EXAMPLE: P/E based on fundamentals A firm has an expected dividend payout ratio of 30%, a required rate of return of 13%, and an expected dividend growth rate of 6%. Calculate the firm’s fundamental (justified) leading P/E ratio. Answer: The justified P/E ratio serves as a benchmark for the price at which the stock should trade. In the previous example, if the firm’s actual P/E ratio (based on the market price and expected earnings) was 8, the stock would be considered overvalued. If the firm’s market P/E ratio was 2, the stock would be considered undervalued. P/E ratios based on fundamentals are very sensitive to the inputs (especially the denominator, k − g), so the analyst should use several different sets of inputs to indicate a range for the justified P/E. Because we started with the equation for the constant growth DDM, the P/E ratio calculated in this way is the P/E ratio consistent with the constant growth DDM. We can see from the formula that, other things equal, the P/E ratio we have defined here will increase with (1) a higher dividend payout rate, (2) a higher growth rate, or (3) a lower required rate of return. So, if the subject firm has a higher dividend payout ratio, higher growth rate, and lower required return than its peers, a higher P/E ratio may be justified. In practice, other things are not equal. An increase in the dividend payout ratio, for example, will reduce the firm’s sustainable growth rate. While higher dividends will increase firm value, a lower growth rate will decrease firm value. This relationship is referred to as the dividend displacement of earnings. The net effect on firm value of increasing the dividend payout ratio is ambiguous. As intuition would suggest, firms cannot continually increase their P/Es or market values by increasing the dividend payout ratio. Otherwise, all firms would have 100% payout ratios. PROFESSOR’S NOTE Watch for the wording “other things equal” or “other variables unchanged” in any exam questions about the effect of changing one variable. EXAMPLE: Fundamental P/E ratio comparison Holt Industries makes decorative items. The following figures are for Holt and its industry. Which of these factors suggest a higher fundamental P/E ratio for Holt? Answer: The higher dividend payout ratio supports Holt having a higher P/E ratio than the industry. Higher growth in sales suggests that Holt will be able to increase dividends at a faster rate, which supports Holt having a higher P/E ratio than the industry. The higher level of debt, however, indicates that Holt has higher risk and a higher required return on equity, which supports Holt having a lower P/E ratio than the industry. Multiples Based on Comparables Valuation based on price multiple comparables (or comps) involves using a price multiple to evaluate whether an asset is valued properly relative to a benchmark. Common benchmarks include the stock’s historical average (a time series comparison) or similar stocks and industry averages (a cross-sectional comparison). Comparing firms within an industry is useful for analysts who are familiar with a particular industry. Price multiples are readily calculated and provided by many media outlets. The economic principle guiding this method is the law of one price, which asserts that two identical assets should sell at the same price, or in this case, two comparable assets should have approximately the same multiple. The analyst should be sure that any comparables used really are comparable. Price multiples may not be comparable across firms if the firms are different sizes, are in different industries, or will grow at different rates. Furthermore, using P/E ratios for cyclical firms is complicated due to their sensitivity to economic conditions. In this case, the P/S ratio may be favored over the P/E ratio because the sales are less volatile than earnings due to both operating and financial leverage. The disadvantages of using price multiples based on comparables are (1) a stock may appear overvalued by the comparable method but undervalued by the fundamental method, or vice versa; (2) different accounting methods can result in price multiples that are not comparable across firms, especially internationally; and (3) price multiples for cyclical firms may be greatly affected by economic conditions at a given point in time.

RELATIVE VALUATION MEASURES LOS 46.j: Explain the rationale for using price multiples to value equity, how the price to earnings multiple relates to fundamentals, and the use of multiples based on comparables. Because the dividend discount model is very sensitive to its inputs, many investors rely on other methods. In a price multiple approach, an analyst compares a stock’s price multiple to a benchmark value based on an index, industry group of firms, or a peer group of firms within an industry. Common price multiples used for valuation include price-to-earnings, price-to-cash flow, price-to-sales, and price-to-book value ratios. Price multiples are widely used by analysts and readily available in numerous media outlets. Price multiples are easily calculated and can be used in time series and crosssectional comparisons. Many of these ratios have been shown to be useful for predicting stock returns, with low multiples associated with higher future returns. A critique of price multiples is that they reflect only the past because historical (trailing) data are often used in the denominator. For this reason, many practitioners use forward (leading or prospective) values in the denominator. The use of projected values can result in much different ratios. An analyst should be sure to use price multiple calculations consistently across firms. When we compare a price multiple, such as P/E, for a firm to those of other firms based on market prices, we are using price multiples based on comparables. By contrast, price multiples based on fundamentals tell us what a multiple should be based on some valuation model and therefore are not dependent on the current market prices of other companies to establish value. LOS 46.k: Calculate and interpret the following multiples: price to earnings, price to an estimate of operating cash flow, price to sales, and price to book value. Price multiples used for valuation include: Price-earnings (P/E) ratio: The P/E ratio is a firm’s stock price divided by earnings per share and is widely used by analysts and cited in the press. Price-sales (P/S) ratio: The P/S ratio is a firm’s stock price divided by sales per share. Price-book value (P/B) ratio: The P/B ratio is a firm’s stock price divided by book value of equity per share. Price-cash flow (P/CF) ratio: The P/CF ratio is a firm’s stock price divided by cash flow per share, where cash flow may be defined as operating cash flow or free cash flow. Other multiples can be used that are industry specific. For example, in the cable television industry, stock market capitalization is compared to the number of subscribers. Multiples Based on Fundamentals To understand fundamental price multiples, consider the Gordon growth valuation model: If we divide both sides of the equation by next year’s projected earnings, E1 , we get which is the leading P/E for this stock if it is valued in the market according to the constant growth DDM. This P/E based on fundamentals is also referred to as a justified P/E. It is “justified” because, assuming we have the correct inputs for D1 , E1 , ke , and g, the previous equation will provide a P/E ratio that is based on the present value of the future cash flows. We refer to this as a leading P/E ratio because it is based on expected earnings next period, not on actual earnings for the previous period, which would produce a lagging or trailing P/E ratio. One advantage of this approach is that it makes clear how the firm’s P/E ratio should be related to its fundamentals. It illustrates that the P/E ratio is a function of: D1 / E1 = expected dividend payout ratio. k = required rate of return on the stock. g = expected constant growth rate of dividends. EXAMPLE: P/E based on fundamentals A firm has an expected dividend payout ratio of 30%, a required rate of return of 13%, and an expected dividend growth rate of 6%. Calculate the firm’s fundamental (justified) leading P/E ratio. Answer: The justified P/E ratio serves as a benchmark for the price at which the stock should trade. In the previous example, if the firm’s actual P/E ratio (based on the market price and expected earnings) was 8, the stock would be considered overvalued. If the firm’s market P/E ratio was 2, the stock would be considered undervalued. P/E ratios based on fundamentals are very sensitive to the inputs (especially the denominator, k − g), so the analyst should use several different sets of inputs to indicate a range for the justified P/E. Because we started with the equation for the constant growth DDM, the P/E ratio calculated in this way is the P/E ratio consistent with the constant growth DDM. We can see from the formula that, other things equal, the P/E ratio we have defined here will increase with (1) a higher dividend payout rate, (2) a higher growth rate, or (3) a lower required rate of return. So, if the subject firm has a higher dividend payout ratio, higher growth rate, and lower required return than its peers, a higher P/E ratio may be justified. In practice, other things are not equal. An increase in the dividend payout ratio, for example, will reduce the firm’s sustainable growth rate. While higher dividends will increase firm value, a lower growth rate will decrease firm value. This relationship is referred to as the dividend displacement of earnings. The net effect on firm value of increasing the dividend payout ratio is ambiguous. As intuition would suggest, firms cannot continually increase their P/Es or market values by increasing the dividend payout ratio. Otherwise, all firms would have 100% payout ratios. PROFESSOR’S NOTE Watch for the wording “other things equal” or “other variables unchanged” in any exam questions about the effect of changing one variable. EXAMPLE: Fundamental P/E ratio comparison Holt Industries makes decorative items. The following figures are for Holt and its industry. Which of these factors suggest a higher fundamental P/E ratio for Holt? Answer: The higher dividend payout ratio supports Holt having a higher P/E ratio than the industry. Higher growth in sales suggests that Holt will be able to increase dividends at a faster rate, which supports Holt having a higher P/E ratio than the industry. The higher level of debt, however, indicates that Holt has higher risk and a higher required return on equity, which supports Holt having a lower P/E ratio than the industry. Multiples Based on Comparables Valuation based on price multiple comparables (or comps) involves using a price multiple to evaluate whether an asset is valued properly relative to a benchmark. Common benchmarks include the stock’s historical average (a time series comparison) or similar stocks and industry averages (a cross-sectional comparison). Comparing firms within an industry is useful for analysts who are familiar with a particular industry. Price multiples are readily calculated and provided by many media outlets. The economic principle guiding this method is the law of one price, which asserts that two identical assets should sell at the same price, or in this case, two comparable assets should have approximately the same multiple. The analyst should be sure that any comparables used really are comparable. Price multiples may not be comparable across firms if the firms are different sizes, are in different industries, or will grow at different rates. Furthermore, using P/E ratios for cyclical firms is complicated due to their sensitivity to economic conditions. In this case, the P/S ratio may be favored over the P/E ratio because the sales are less volatile than earnings due to both operating and financial leverage. The disadvantages of using price multiples based on comparables are (1) a stock may appear overvalued by the comparable method but undervalued by the fundamental method, or vice versa; (2) different accounting methods can result in price multiples that are not comparable across firms, especially internationally; and (3) price multiples for cyclical firms may be greatly affected by economic conditions at a given point in time.

Describe enterprise value multiples and their use in estimating equity value. Enterprise value (EV) measures total company value. EV can be viewed as what it would cost to acquire the firm: Cash and short-term investments are subtracted because an acquirer’s cost for a firm would be decreased by the amount of the target’s liquid assets. Although an acquirer assumes the firm’s debt, it also receives the firm’s cash and short-term investments. Enterprise value is appropriate when an analyst wants to compare the values of firms that have significant differences in capital structure. EBITDA (earnings before interest, taxes, depreciation, and amortization are subtracted) is probably the most frequently used denominator for EV multiples; operating income can also be used. Because the numerator represents total company value, it should be compared to earnings of both debt and equity owners. An advantage of using EBITDA instead of net income is that EBITDA is usually positive even when earnings are not. When net income is negative, value multiples based on earnings are meaningless. A disadvantage of using EBITDA is that it often includes non-cash revenues and expenses. A potential problem with using enterprise value is that the market value of a firm’s debt is often not available. In this case, the analyst can use the market values of similar bonds or can use their book values. Book value, however, may not be a good estimate of market value if firm and market conditions have changed significantly since the bonds were issued.

: Describe asset-based valuation models and their use in estimating equity value. Our third category of valuation model is asset-based models, which are based on the idea that equity value is the market or fair value of assets minus the market or fair value of liabilities. Because market values of firm assets are usually difficult to obtain, the analyst typically starts with the balance sheet to determine the values of assets and liabilities. In most cases, market values are not equal to book values. Possible approaches to valuing assets are to value them at their depreciated values, inflationadjusted depreciated values, or estimated replacement values. Applying asset-based models is especially problematic for a firm that has a large amount of intangible assets, on or off the balance sheet. The effect of the loss of the current owners’ talents and customer relationships on forward earnings may be quite difficult to measure. Analysts often consider asset-based model values as floor or minimum values when significant intangibles, such as business reputation, are involved. An analyst should consider supplementing an asset-based valuation with a more forward-looking valuation, such as one from a discounted cash flow model. Asset-based model valuations are most reliable when the firm has primarily tangible short-term assets, assets with ready market values (e.g., financial or natural resource firms), or when the firm will cease to operate and is being liquidated. Asset-based models are often used to value private companies but may be increasingly useful for public firms as they move toward fair value reporting on the balance sheet

Explain advantages and disadvantages of each category of valuation model. Advantages of discounted cash flow models: They are based on the fundamental concept of discounted present value and are well grounded in finance theory. They are widely accepted in the analyst community. Disadvantages of discounted cash flow models: Their inputs must be estimated. Value estimates are very sensitive to input values. Advantages of comparable valuation using price multiples: Evidence that some price multiples are useful for predicting stock returns. Price multiples are widely used by analysts. Price multiples are readily available. They can be used in time series and cross-sectional comparisons. EV/EBITDA multiples are useful when comparing firm values independent of capital structure or when earnings are negative and the P/E ratio cannot be used. Disadvantages of comparable valuation using price multiples: Lagging price multiples reflect the past. Price multiples may not be comparable across firms if the firms have different size, products, and growth. Price multiples for cyclical firms may be greatly affected by economic conditions at a given point in time. A stock may appear overvalued by the comparable method but undervalued by a fundamental method or vice versa. Different accounting methods can result in price multiples that are not comparable across firms, especially internationally. A negative denominator in a price multiple results in a meaningless ratio. The P/E ratio is especially susceptible to this problem. Advantages of price multiple valuations based on fundamentals: They are based on theoretically sound valuation models. They correspond to widely accepted value metrics. Disadvantage of price multiple valuations based on fundamentals: Price multiples based on fundamentals will be very sensitive to the inputs (especially the k − g denominator). Advantages of asset-based models: They can provide floor values. They are most reliable when the firm has primarily tangible short-term assets, assets with ready market values, or when the firm is being liquidated. They are increasingly useful for valuing public firms that report fair values. Disadvantages of asset-based models: Market values are often difficult to obtain. Market values are usually different than book values. They are inaccurate when a firm has a high proportion of intangible assets or future cash flows not reflected in asset values. Assets can be difficult to value during periods of hyperinflation