1. Lecture 14 Dividend Discount Models (cont’d …) & Market Based Valuation Investment Analysis

2. Calculating Terminal Value No matter which dividend discount model we use, we have to estimate a terminal value at some point in the future. There are two ways to do this: (i) using GGM and, (ii) the market multiple approach. The most common method is to estimate the terminal value with GGM. In other words, at some point in the future, we assume dividends will begin tot grow at a constant long-term rate. Then the terminal value at that point is just the value derived from GGM. Many analysts also use market multiples to estimate the terminal value rather than use GGM of discounting dividends. For example, we could forecast earnings and a P/E ratio at the forecast horizon and then estimate the terminal value as the P/E times the earnings estimate. Investment Analysis

3. Estimating Terminal Value – Example Level Partners is expected to have earnings in ten years of $12.00 per share, a dividend payout ratio of 50% and an expected return of 11%. At that time, the dividend growth rate is expected to fall to 4% in perpetuity and the trailing P/E ratio is forecasted to be eight time earnings. Estimate the terminal value at the end of ten years using GGM and the P/E multiple. Solution: The dividend at the end of 10 years is expected to be $6 ($12 times 50%). The dividend in year 11 is then $6 x 1.04 = $6.24. The terminal value using GGM is: Terminal Value in year 10 using GGM = $6.24 / (0.11 – 0.04) = $89.14 The terminal value given forecasted earnings of $12 and a P/E ratio of 8 is: Terminal Value in year 10 using trailing P/E ratio = $12.00 x 8 = $96.00 Investment Analysis

4. Valuation using the two stage model The two stage fixed growth rate model is based on the assumption that the firm will enjoy an initial period of high growth, followed by a mature or sable period in which growth will be lower but sustainable. nD 0 (1 + g s ) t D 0 (1 + g s )n x (1 + g L ) V 0 = ∑ + t=1 (1 + r) t (1 + r) n x (r – g L ) Where: gs=short term growth rate gL=long term growth rate r=required return n=length of high growth period Investment Analysis

5. Example Sea Island Recreation currently pays a dividend of $1.00. An analyst forecasts growth of 10% for the next three years followed by 4% growth in perpetuity thereafter. The required return is 12%. Calculate the current value per share. Solution: We could solve the problem by plugging the appropriate the numbers in to the formula as follows: 3 $1.00x(1.10) 3 $1.00x(1.10) 3 x(1.04) V 0 = ∑ + t=1 (1.12) 3 (1.12) 3 x (0.12-0.04) $1.00x(1.10) 1 $1.00x(1.10) 2 $1.00x(1.10) 3 $1.00x(1.10) 3 x(1.04) V 0 = + + + (1.12) 1 (1.12) 2 (1.12) 3 (1.12) 3 x(0.12-0.04) V 0 = $15.21 Investment Analysis

6. Using the H-Model The earning growth of most firms does not abruptly change from a high rate to a low rate as in the two stage model but tends to decline over time as competitive forces come into play. The H-model approximates the value of a firm assuming initially a high rate of growth that declines linearly over a specified period. The formula for this approximation is: D 0 x (1 +g L )D 0 x H x (g s – g L ) V 0 = + r – g L r – g L Where: H=(t/2)=half life (in years) of high growth period t=length of high growth period g s =short term growth rate g L =long term growth rate r=required return Investment Analysis

7. Calculating Value with H-Model (Example) Omega Foods currently pays a dividend of €2.00. The growth rate which is currently 20% is expected to decline linearly over the next 10 years to a stable rate of 5% thereafter. The required rate of return is 12%. Calculate the current value of Omega. Solution: €2.00 x 1.05€2.00 x (10/2) x (0.20-0.05) V 0 = + = €51.43 0.12 – 0.05 0.12 - 0.05 The H-model provides only an approximation of the value of Omega’s shares. To find the exact answer, we’d have to forecast each of the first ten dividends, applying a different growth rate to each and then discount them back to the present at 12%. In general, the H-value approximation is more accurate the shorter the high growth period, t, and/or the smaller the spread between the short-term and long-term growth rates, i.e., (g s – g L ) Investment Analysis

8. Sustainable growth Rate The sustainable growth rate (SGR) is the rate at which earnings (dividends) can continue to grow indefinitely, assuming that the firm’s debt-to-equity ratio is unchanged and it doesn’t issue new equity. SGR is a simple function of the earnings retention ratio and the return on equity: SGR = b x ROE Where: b = earnings retention ratio = 1 – dividend payout ratio ROE = return on equity SGR is important because it tells us how quickly a firm can grow with internally generated funds. Calculating SGR – Example Biotechnia. Inc., is growing earnings at an annual rate of 9%. It currently pays out dividends equal to 20% of earnings. Biotechnia’s ROE is 15%. Calculate its SGR. Solution: g = (1 – 0.20) x (15%) = 12% Investment Analysis

9. ROE and Growth Rate A firm’s rate of growth is a function of both its earnings retention and its return on equity. ROE can be estimated with the DuPont formula, which presents the relationship between margins, sales and leverage as determinants of ROE. net incomenet income sales total assets ROE = = x x stockholder’s sales total assets stockholder’s equity equity If the other factors remain constant, we can see that the growth of a firm’s earnings (dividends) is a function of its ROE and its retention ratio: net income – dividends net income sales total assets g = x x x net income sales total assets stockholder’s equity This has also been called the PRAT model, where SGR is a function of the profit margin (P), the retention rate (R), the asset turnover (A) and financial leverage (T). Two of these factors are functions of the firm’s financing decisions (leverage and earnings retention) and two are the functions of performance (return on assets equals profit margin times asset turnover). These factors can be used as building blocks in developing an estimate of a firm’s growth. If the actual growth rate is forecasted to be greater than SGR, the firm will have to issue equity unless the firm increases its retention ratio, profit margin, total asset turnover or leverage. Investment Analysis

10. Justified Price Multiple Price multiples are ratios of a common stocks market price to some fundamental variable. The most common example is the price-to-earnings (P/E) ratio. A justified price multiple is what the multiple should be if the stock is fairly valued. If the actual multiple is greater than the justified price multiple, the stock is overvalued; if the actual multiple is less than the justified price multiple, the stock is undervalued (all else being equal) A justified price multiple can be justified based on one of the two methods: 1.The justified price multiple for the method of comparables is an average multiple of similar stocks in the same peer group. The economic rationale for the method of comparables is the Law of One Price, which states that two similar assets should sell at comparable prices (i.e., multiples). It’s a relative valuation method, so we can only assert that a stock is relatively over or undervalued relative to some benchmark. 2.The justified price multiple for the method of forecasted fundamentals is the ratio of the value of the stock from a discounted cash flow (DCF) valuation model divided by some fundamental variable (e.g., earnings per share). The economic rationale for the method of forecasted fundamentals is that the value used in the numerator of the justified price multiple is derived from a DCF model that is based on the most basic concept in finance; value is equal to the present value of expected future cash flows discounted at the appropriate risk-adjusted rate of return. Investment Analysis

11. Example – Method of Comparables ABC’s shares are selling for $50. earnings for the last 12 months were $2.00 per share. The average trailing P/E ratio for firms in ABC’s industry is 32 times. Determine whether ABC is over or undervalued using the method of comparables. Solution ABC’s trailing P/E is: $50.00/$2.00 =25 times ABC is relatively undervalued because its observed trailing P/E ratio (25 times) is less than the industry average trailing P/E ratio (32 times) Investment Analysis

12. Example – Method of Forecasted Fundamentals Shares of XYZ Inc. are selling for $30. The mean earnings per share forecast for next year is $4.00 and the long-run growth rate is 5%. XYZ has a dividend payout ratio of 60%. The required return is 14%. Calculate the fundamental value of XYZ using GGM and use that value to calculate XYZ’s justified leading P/E ratio. Then determine whether XYZ shares are over or undervalued using the method of forecasted fundamentals. Solution The fundamental value according to GGM is: V 0 = D 1 / r-g = (0.6 x 4) / (0.14 – 0.05) = $26.67 The justified leading P/E ratio is: $26.67 / $4 = 6.67 times The observed(actual) leading P/E ratio based on the current market price is: $30 / $4 = 7.50 times XYZ is overvalued because the observed P/E multiple of 7.5 is greater than the justified P/E ratio of 6.67. Notice that we would have comet o the same conclusion by comparing market price ($30) to intrinsic value ($26.67) Investment Analysis

13. Price Multiples (P/E) Ratio There are a number of rationales for using P/E ratios in valuation: Earnings power, as measured by earnings per share (EPS), is the primary determinant of investment value. The P/E ratio is popular in the investment community. Empirical research shows that P/E differences are significantly related to long-run average stock returns. On the other hand, P/E ratios have a number of shortcomings: Earnings can be negative, which produces a meaningless P/E ratio. The volatile, transitory portion of earnings makes the interpretation of P/E’s difficult for analyst. Management discretion within allowed accounting practices can distort reported earnings, and thereby lessen the comparability of P/E’s across firms. Investment Analysis

14. P/E Ratio (cont’d …) We can define tow versions of the P/E ratio: trailing and leading P/E. the difference between the two is how earnings are calculated. Trailing P/E uses earnings over the most recent 12 months in the denominator. Leading P/E (also know as forward or prospective P/E) uses next year’s expected earnings, which is defined as either expected earnings per share (EPS) for the next four quarters, or expected EPS for the next fiscal year. Trailing P/E = market price per share / EPS over previous 12 months Leading P/E = market price per share / forecasted EPS over next 12 months Trailing P/E is not useful for forecasting and valuation if the firm’s business has changed (e.g., as a result of an acquisition) Leading P/E may not be relevant if earnings are sufficiently volatile so that next year’s earnings can not forecasted with any degree of accuracy. Investment Analysis

15. P/B Ratio In P/E ratio, the measure of value EPS in the denominator is a flow variable relating to the income statement. In contrast, the measure of value in P/B’s denominator (book value per share) is a stock or level variable coming from the balance sheet. Intuitively, book value per share attempts to represent the investment that common shareholders have made in the company, on a per share basis. (Book refers to the fact that the measurement of value comes from accounting records or books, in contrast to market value.) To define book value per share more precisely, we first find shareholders’ equity (total assets minus total liabilities). Because our purpose is to value common stock, we subtract from shareholder’s equity any value attributable to preferred stock; we thus obtain common shareholders’ equity or the book value of equity (often simply called book value.) Dividing book value by the number of common stock shares outstanding, we obtain book value per share, the denominator in P/B. Investment Analysis

16. P/B Ratio (cont’d …) Advantages of using P/B include: Book value is a cumulative amount that is usually positive, even when the firm reports a loss and EPS is negative. Thus, a P/B can typically be used when P/E cannot. Book value is more stable than EPS, so it may be more useful than P/E when EPS is particularly high, low or volatile. Book value is an appropriate measure of net asset value (or firms that primarily hold liquid assets. Example include, finance, investment, insurance and banking firms.) P/B can be useful in valuing companies that are expected to go out of business. Empirical research shows that P/Bs help explain differences in long-run average stock return. Investment Analysis

17. P/B Ratio Disadvantages of P/B include: P/Bs do not reflect the value of intangible economic assets, such as human capital. P/Bs can be misleading when there are significant differences in the asset size of the firms under consideration because in some cases the firm’s business model dictates the size of its asset base. A firm that outsources its production will have fewer assets, lower book value, and a higher P/B ratio than an otherwise similar firm in the same industry that doesn’t outsource. Different accounting conventions can obscure the true investment in the firm made by shareholders, which reduces the comparability of P/B across firms and countries. For examples, research and development costs are expensed in the US which can understate investment. Investment Analysis

18. P/B Ratio (cont’d …) The P/B is defined as: P/B = market value of equity / book value of equity P/B = market price per share / book value per share Where: Book value of equity = common stockholder’s equity = (Total assets – Total liabilities) – preferred stock We often make adjustments to book value to create more useful comparisons of P/B ratios across different stocks. A common adjustment is to use tangible book value, which is equal to book value of equity less tangible assets. Examples of tangible assets include goodwill from acquisitions (which makes sense because it is not really an asset) and patents (which is more questionable since the asset and patent are separate.) Furthermore, balance sheets should be adjusted for significant off-balance-sheet assets and liabilities and for difference between the fair and recorded value of assets and liabilities. Finally, book values often need to be adjusted to ensure comparability. For example, companies using FIFO for inventory valuation cannot be accurately compared with peers using LIFO. Thus, book values should be restated on a consistent basis.