Introduction to Equity Valuation

Introduction to Equity Valuation FINANCE 352 INVESTMENTS Professor Alon Brav Fuqua School of Business Duke University Alon Brav 2004 Finance 352, Equity Valuation 1 1

Overview Stocks and stock markets Stock valuation Short-term traders have long-term views! Constant dividend growth model Valuation and financial ratios Valuation ratios and stock market outlook Alon Brav 2004 Finance 352, Equity Valuation 2 2

Capital Markets - Equity Common stock Residual claim, Limited liability Preferred stock Fixed dividends Priority over common: Failure to pay dividend does not trigger bankruptcy. Dividends will cumulate. May get some voting rights. Tax treatment: Dividends not tax deductible although if one corporation holds preferred in another it pays taxes on only 30% of dividends received. Bankruptcy: Priority over common but junior to bondholders. Alon Brav 2004 Finance 352, Equity Valuation 3 3

Short selling Why Short Sell? Short Selling is one way of benefiting from a stock that is expected to decline in price. Instead of buying today and selling later, the short seller sells today and buys later. How to Short Sell? The short-seller (A) finds an existing owner of the shares (B) who is willing and able to lend the shares to A. Once A has negotiated a loan, A can then sell the borrowed shares to any willing buyer (C). A posts collateral with B. In the US, the standard collateral is cash amounting to 102 per cent of the value of the shares, to be adjusted daily as their value fluctuates. Note though that under Federal Reserve Regulation T, in case where B is a U.S. broker/dealer A has to post an additional 50% margin (any long securities can be pledged to satisfy this requirement). Further, broker-dealers may institute higher short sale margin requirements than those imposed by self-regulatory organization rules. e.g., the NASD Rule 2520(d) and NYSE Rule 431(d). Alon Brav 2004 Finance 352, Equity Valuation 4 The following is a link to a work paper by Gene D Avolio titled The Market for Borrowing Stock in which many short selling issues are detailed: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=312979 4

Short selling How to Short Sell? (continued) A pays B a fee. The fee can be determined by the rebate rate, which is the interest that B pays A for use of the cash collateral. For example, if the market rate for cash funds were 5% and the stock loan fee were 1.5% then B would rebate A only 3.5%. (Note that is it possible to have fees that exceed the cash rate, which would result in negative rebate rates). A pays B any dividends/distributions made to the owners of the shares during the loan. B has the right to recall the shares from A at any time. Loans are open and effectively rolled over each night until either B wants the shares returned or A voluntarily returns them. Given notice of recall, A has three days to return the shares. After this, A can try borrowing the shares from another lender or can cover the short position by purchasing the shares. Alon Brav 2004 Finance 352, Equity Valuation 5 5

Short selling Who are the Participants? The role of B (the lenders) is largely assumed by the big custody banks in the U.S. who act as intermediaries for large institutional owners like pension funds, mutual funds etc. Loans of shares can also be made by a broker from his own inventory, from the margin account of another customer, or shares borrowed from another broker. These shares are used to make settlement with the buying broker within three days of the short sale transaction, and the proceeds are used to secure the loan. Another group that assume the role of B (lenders) consists of the broker-dealers (e.g. Goldman Sachs, Morgan Stanley). These broker-dealers lend from their internal supply of securities held by their market makers and proprietary trading desks, the accounts of institutional customers, and the margin accounts of individual investors. Note that Section 8 of the Exchange Act of 1934 prohibits brokers from lending shares held in retail cash or non-margin accounts. The role of A (the short-sellers) is assumed by a broader group. More obvious examples include: Specialists and market makers (for balancing buy orders with sell orders) Traders of equity options, index futures, equity return swaps and convertible bonds (for hedging their positions) Hedge Funds (to execute arbitrage strategies) Speculators Alon Brav 2004 Finance 352, Equity Valuation 6 6

Short selling The NYSE, NASD and AMEX reported short interest (the number of shares that have already been sold short) with a market value in excess of $260 billion (just over 1.7% of total market capitalization) at June 2001. Shorting is subject to many restrictions on the size, price, and types of stocks able to be shorted. For example, you cannot short sell penny stocks (they are non-marginable due to Regulation T) and most short sales need to be done in round lots. Additionally, the SEC, NYSE and NASD have rules preventing short selling unless the last trade is at the same or higher price (known as an uptick or zero plus tick), the purpose of which is to prevent short selling in a declining market (since continuous short selling will exacerbate the fall of a falling stock). Equity loans can occur for reasons other than short selling. For instance in cases where A borrows from B but then doesn t short to C, A is treated as the legal owner of the shares and is therefore entitled to the dividends distributed during the course of the loan (which, as previously mentioned, are required to be reimbursed by A to B). This might happen in cases where A values the distribution received more than the reimbursements given (for taxation reasons, for example) In lending, B forfeits voting rights to A (to C in the case of the short sale). Alon Brav 2004 Finance 352, Equity Valuation 7 7

Stock Indexes Uses Track average returns, assess performance of managers, base of derivatives contracts Factors in constructing or using an Index Representative? Broad or narrow? How is it constructed? Domestic Dow Jones Industrial Average (30 Stocks), Standard & Poor s 500 Composite, NASDAQ Composite, NYSE Composite, Wilshire 5000 International Nikkei 225 & Nikkei 300, FTSE (Financial Times of London), Dax Region and Country Indexes: EAFE, Far East, United Kingdom How are the stocks weighted? Price weighted (DJIA), Market-value weighted (S&P500, NASDAQ), Equally weighted (Value Line Index) How are returns averaged? Arithmetic (Value Line index, DJIA and S&P500), Geometric (Value Line Index) Alon Brav 2004 Finance 352, Equity Valuation 8 8

Short-Term Traders Have Long-Term Views Recall the definition of the return R t+1 on a stock: 1+R t+1 (P t+1 + D t+1 )/P t where R t+1 is the nominal return between time t and t + 1 P t is the price of the stock at time t D t+1 is the dividend of the stock at time t+1 Suppose that the return investors can expect to earn on securities with similar risks is constant and equal to r e, that is, we have that E(R t+1 ) = r e. We can (after repeated substitution) show that the price today, P 0, is: E( D1 ) E( D2 ) E( D3 ) P0 = + + +... 2 3 1+ re ( 1+ r ) ( 1+ r ) Assuming that as t increases to infinity the present value of P t tends to zero we obtain that the asset s price today is the present value of all future dividends. Hence, long-term valuation (ought to) hold even for short-term investors! e e Alon Brav 2004 Finance 352, Equity Valuation 9 9

The Constant Growth Formula Assumption: Dividends grow at a constant rate g for ever and g < r e. The asset s price is then D1 P0 = re g This Gordon Model allows us to think about various performance metrics metrics that investors employ. For example, expected return, r e, is equal to r D t E P t +1 e = + g Alon Brav 2004 Finance 352, Equity Valuation 10 10

Example: Implied Growth Rate in the U.S. Stock Market At the end of December 1999 the S&P500 was at 1469.25 and its dividend yield was approximately 1.5%. Assuming that the required rate of return is 12% per year, what is the built in growth rate? From the constant dividend growth model formula we get: r g = D P e 0 0 1 + D0 P0 Expected return Yield = 1 + Yield This gives a growth rate of 10.3% per year, which might suggest overvaluation if you believe that the implied growth rate is too high. Alternatively, someone who expects 12% return per year and is willing to invest in the market must also believe the implicit rate of nominal growth is at least 10.3%. The average growth rate 1960 2001 has been approximately 5.2%. Note also that the growth rate is a stable growth rate and, on average, cannot be higher than the growth rate of the economy in which the firm/market operates. Alon Brav 2004 Finance 352, Equity Valuation 11 11

Valuation and Financial Ratios Price-Earnings (or P/E) ratios are frequently used among practitioners to price equities. Stocks with low P/E ratios (relative to their peers) are labeled cheap or value stocks. How can we justify this? How does this relate to the dividend discount model? Some notation: P t is the stock price (per share) today E t+1 is the earnings per share next period E t+1 /P t is the (forward looking) earnings yield P t /E t+1 is the (forward looking) price-earnings ratio D t+1 is the dividends per share paid next period D t+1 /P t is the (forward looking) dividend yield π t+1 = D t+1 /E t+1 is the (forward looking) payout ratio Alon Brav 2004 Finance 352, Equity Valuation 12 12

Using Forward-Looking P/E Ratios to Price Stocks Start with the constant dividend growth model and by dividing both sides by next period s earnings we obtain Pt π = E t + 1 re g We see that companies should have the same P/E-ratio if they have the same: Payout ratio (similar technology, efficiency). Discount rate (business risk, financial risk). Growth rate (business prospects, market share development). Firms with high P/E ratios are often called growth stocks. Suppose two firms have the same payout ratio (π t+1 ) and the same required rate of return (r). The firm with a higher growth rate (g) will have a higher P/E ratio. Alon Brav 2004 Finance 352, Equity Valuation 13 13

Using Forward-Looking P/E Ratios to Price Stocks (continued) The idea is to value an asset compared to the values assessed by the market for similar or comparable assets. To conduct relative valuation we first identify a set of publicly traded comparable firms. We then scale their market values, for example, by dividing by earnings or cashflows. Then, compare the scaled value or multiple for the firm to the scaled values for comparable firms. Need to account for any differences between the firms that might affect the multiple, to judge whether the asset is under or over valued. For IPOs we infer their market value based on the comparable firms ratios. (see http://bear.cba.ufl.edu/ritter/valueipo.pdf) No guarantee against an entire industry being undervalued or overvalued. Alon Brav 2004 Finance 352, Equity Valuation 14 14

Pitfalls in P/E Analysis Use of accounting earnings Historical costs May not reflect economic earnings Clearly hinges on the discounted dividend setup. Other Valuation Ratios Price-to-Book Price-to-Cashflow Price-to-Sales Impossible to interpret with zero or negative earnings. Alon Brav 2004 Finance 352, Equity Valuation 15 15

Valuation Ratios and Stock Market Outlook Stock market valuation ratios have been at extreme levels a few years ago by historical standards. When stock prices are very high relative to indicators of fundamental values (such as dividends and earnings), prices tend to fall in the future... Consider two measures of fundamental values: (i) dividend-price ratio (D/P ratio), or dividend yield. (ii) price-earnings ratio (P/E ratio). Alon Brav 2004 Finance 352, Equity Valuation 16 16

Valuation Ratios and Stock Market Outlook (continued) The dividend-price ratio is measured as previous year s total dividends divided by current stock price D/P ratios have normally moved in the range from 3% to 7% (with an extreme of much less than 2% a few years ago). The price-earnings ratio is measured as current stock price divided by previous year s total earnings P/E ratios have normally moved in the range 8 20. Graham and Dodd (1934) said that one should use an average of earnings of no less than five years, preferably seven or ten years. Alon Brav 2004 Finance 352, Equity Valuation 17 17

P/E ratio 1880-2003 Price-Earnings Ratio 50 45 40 35 30 25 20 15 10 5 0 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year Source: Robert Shiller Alon Brav 2004 Finance 352, Equity Valuation 18 18

D/P ratio 1880-2002 16% 14% Dividend yield 12% 10% 8% 6% 4% 2% 0% 1881.01 1884.04 1887.07 Source: Robert Shiller 1890.1 1894.01 1897.04 1900.07 1903.1 1907.01 1910.04 1913.07 1916.1 1920.01 1923.04 1926.07 1929.1 1933.01 1936.04 1939.07 1942.1 1946.01 Year 1949.04 1952.07 1955.1 1959.01 1962.04 1965.07 1968.1 1972.01 1975.04 1978.07 1981.1 1985.01 1988.04 1991.07 1994.1 1998.01 2001.04 Alon Brav 2004 Finance 352, Equity Valuation 19 19

Forecasts from the Dividend-Price Ratio One-year horizon Empirical evidence suggests a negative relation to real dividend growth Very little forecasting power for real stock price changes Ten-year horizon Only a weak relation to real dividend growth Substantial positive relation to real price growth Example: The low D/P ratio in 1997 (about 1.8%) implies a real loss in stock prices of almost 50% over the next ten years! Recall that a few years ago there was uncertainty whether valuation ratios would remain at their historical ranges. Over the past century economies have been transformed in many fundamental ways (rational stories) Agriculture gave way to industry Industry has given way to services as the leading sector So it was reasonable to entertain the possibility that financial markets entered a new era. These questions are important for the limits of arbitrage topic that we will discuss later! Alon Brav 2004 Finance 352, Equity Valuation 20 20

Some Remarks on Structural Changes in D/P Ratios and Statistical Pitfalls Corporate financial policy May need to adjust D/P ratios for repurchases (upwards) and employee stock option plans (downward) The figure presents a break out of aggregate dividends, aggregate repurchases and the ratio of repurchases to total payouts (dividends + repurchases). Source: Boudoukh, Michaely, Richardson, Roberts (2003) Alon Brav 2004 Finance 352, Equity Valuation 21 Dark bars are aggregate dividends, light bars are aggregate repurchases (of common equity, not preferred, which are relatively small). Note that the light bars (on top) grow in magnitude from the early 80's on ways, even surpassing dividends at the end of the 90's. 21

Dividend Yield, Repurchase Yield and Total Yield Yield 10% 8% 6% 4% 2% 0% Source: Boudoukh, Michaely, Richardson, Roberts (2003) Dividend Yield Repurchase yield Total Yield 1926 1931 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 Alon Brav 2004 Finance 352, Equity Valuation 22 22

Some Remarks on Structural Changes in D/P Ratios and Statistical Pitfalls The baby boom and the demand for stocks It has been argued that baby boomers are more risk tolerant and tend to favor stocks over bonds This may push prices up, and D/P ratios down We need fairly sophisticated statistical techniques The observations in long-term horizons are overlapping, which means that observations are not statistically independent Regressions with highly persistent regressors The regression extrapolates linearly from a relation between valuation ratios and long-horizon returns that holds in historically normal times to get a prediction for the current, historically abnormal situation Alon Brav 2004 Finance 352, Equity Valuation 23 23

Concluding Comments Stocks can be valued by using present value techniques The discounting horizon does not depend on the investment horizon of individual investors in the stock market (short-term traders have long-term views!) Investors are compensated through cash dividends and through capital gains P/E ratios should be used with caution in valuation (through comparables): Depends on simplifying assumptions Alon Brav 2004 Finance 352, Equity Valuation 24 24