Valuation of Stocks and Company Valuation

1
Valuation of Stocks andCompany Valuation

• Econ 181
• Corporate Finance
• Wadia Haddaji
• Department of Economics
• Duke University
• RK-CH

2
Overview

• Introduction
• Stocks and stock markets
• Transactions Orders
• Valuation
• Present Value
• Dividend growth models
• Financial ratios
• Dividend yields
• P/E multiples

3
Common Stock

• What does it mean to own common stock?
• ownership
• residual claimants.
• What rights do common shareholders have?
• vote at company meetings
• dividends
• sell their shares
• What are the benefits of stock ownership?
• dividends
• capital gains
• Why do firms issue stock?
• to finance investments
• to acquire other companies
• to repurchase debt

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Preferred Stock Debt or Equity?

• What does it mean to own preferred stock?
• ownership
• senior to equity, junior to debt securities in
  case of default
• What rights do preferred shareholders have?
• usually no voting rights, except in case of
  default on dividend
• dividends and other distributions
• What are the benefits of preferred stock
  ownership?
• periodic dividend rate, typically cumulative
• capital gains
• Why do firms issue preferred stock?
• often because of the favorable tax treatment when
  held by other firms

5
Transactions Involving Stocks

• Buy (Long Position)
• Savings motive
• Speculative
• Sell
• Liquidity needs
• Expect stock to decline in value
• Short Sell
• Sell stock without first owning it.
• Borrow stock from your broker with the promise to
  return it at some later date.
• Sell the borrowed stock.
• Repurchase it at a later date to return it to
  your broker.
• Responsible for all dividends and other
  distributions while short the stock.

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Short selling (in detail)

• 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).

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Short selling (in detail)

• 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.

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Short selling (in detail)

• 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

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Short selling (in detail)

• 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 doesnt 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).

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Types of Orders

• Market Orders
• Buy or sell at the current market price
• Limit Order
• Buy or sell at a specified price
• Limit by time period
• Stop Orders
• Stop-loss Sell if price falls below certain
  level
• Stop-buy Buy if price rises above certain level
• Used in conjunction with short selling

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ValuationThe Role of Financial Markets

• Primary Market
• New securities and investment opportunities.
• Companies need to acquire funds at a correct
  price

• Secondary Market
• Provide price information
• Transform (short term) savings into (long term)
  investments
• Liquidity
• Investors need to buy and sell at correct prices

What is a correct price? Do markets generate
correct prices?
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Stock Market Indices

• Return to holding a security
• Stock market indices average return
• of stocks in particular market (NYSE Composite,
  NASDAQ)
• market segments (e. g., small companies (Russell
  2000), value stocks, technology stocks)
• General expression
• Equally weighted wi 1/N (Value Line Index)
• Equal to portfolio strategy placing equal dollar
  amount in each stock
• Value weighted wi proportion of market
  capitalization (SP500,NASDAQ)
• Return on portfolio where investment is
  proportional to market capitalization.
• Price weighted (DJIA)
• Equal to portfolio strategy holding an equal
  number of shares of each stock

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U. S. Stock Markets

• Major U. S. Stock Exchanges
• New York Stock Exchange (NYSE)
• American Stock Exchange (AMEX)
• Over-The-Counter (OTC)
• National Association of Securities Dealers
  (NASDAQ)
• U. S. Stock Market

The NYSE Composite index was recalculated to
reflect a base value of 5,000 as of Dec/31, 2002
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Number of Listed Companies on Nasdaq, Yearly
Comparison with NYSE and AMEX
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Market Capitalization of Domestically Listed
Companies - NYSE and NASDAQ, 1985 2003
( billions)
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Why short-termists are long-termists

• Shareholders require a rate of return re for
  buying a share. They buy for
• P0 and sell after one year for P1 and receive
  dividends D1
• The next buyer also sells after one year
• The same holds for P2. Continuing gives
• Share price PV of dividends

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Stock Valuation

• Stock Price PV of future dividends
• The price an investor is willing to pay for a
  share of stock depends upon
• Magnitude and timing of expected future
  dividends.
• Risk of the stock.
• The stocks discount rate, re, is the rate of
  return investors can expect to earn on securities
  with similar risk.
• Where are capital gains?

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Another ApplicationEstimating the required
return on equity

• Holders of stock receive returns in two forms
• Dividend payouts
• Capital gains (stock price appreciation P1-P0)
• typically larger fraction of returns
• Capital gain reflects growth in future dividend
  payments
• Note
• The expected rate of return is not equal to the
  dividend yield
• The expression is in terms of the prospective
  yield, not the historic yield

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The Constant Growth Formula

• Assumption Dividends grow at a constant rate g
  forever
• Then
• Issues
• constant growth

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Simplifying the Dividend Discount Model

• Constant Dividends
• Then the pricing relation simplifies to
• Stock similar to perpetual bond
• If dividends are constant, then we have that
• Capital gains are zero
• Expected return on equity Dividend yield

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Constant DividendsTwo Examples

• Example 1 RJR Nabisco has preferred stock
  outstanding with a fixed dividend per share of
  2.50. Similar securities command a return of
  9.6. What is the per share price of the stock?
• Example 2 Consider a company that pays every
  period a dividend of
• 3 per share in bad years (Probability 50)
• 15 per share in good years (Probability 50)
• If the required rate of return is 18, what is
  the share price?

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Valuation with Growing DividendsAn Example
Valuation of XYZ

• Consider data for XYZ
• Number of shares 856,695
• Market capitalization 46.31m
• Historic dividend 1.60 per share
• Forecasted Dividend 1.75 per share
• What valuation do you obtain for XYZ, depending
  on g and r?

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Valuation of XYZ

• Alternative valuations
• Example
• 856,6951.751.499m

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Valuing a BusinessA Hybrid Approach

• Sometimes equity analysts have knowledge about
  the immediate, but not the distant future
• Dividend forecasts for immediate future (2-5
  years)
• Assume constant growth for distant future (gt5
  years)
• How do you change the model?

Dividends
Time
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Modifying the Constant Growth Model

• The formula for a T-year horizon can be written
  as
• Apply the constant growth model to get the price
  in period T
• Then the current value of the share is

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Valuing a Business

• Consider a company with cash flows from
  operations of 1 million for the most recent
  year.
• The companys cash flows are expected to grow at
  a rate of 10 for the next 5 years and at a
  constant rate of 5 thereafter.
• To generate this increase in cash flows, the
  company is required to reinvest 50 of its cash
  flows for the first 5 years and 25 of its cash
  flows thereafter.
• Given the risk of the business, the required rate
  of return is 15.
• What is the value of the business?

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Valuing a Business (cont.)
Step 1 Find the present value of the first 5
dividends.
Present value CF(1)...CF(5)0.480.450.430.42
0.402.18
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Valuing a Business (Cont.)

• Step 2 Find the present value of the dividends
  after year 5.
• Value of business at the end of the 5th year.
• Find present value (as of time 0) of this figure.
• Step 3 Add result from steps 1 and 2 to get the
  total present value of the company

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Expected Returns and the Dividend Growth Model

• Use the growth model formula to solve for the
  required rate of return
• Note that you can synthesize with the previous
  result,
• to show
• Therefore, if dividends grow at a constant rate,
  then
• share prices grow at the same rate
• yield stays constant

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P/E-ratios

• Start with basic pricing formula
• Algebra yields
• Which assumption does one make when arguing that
  stocks with a low P/E are undervalued?
• Some more algebra gives us
• Implications for re?

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Growth Stocks and Value Stocks

• Value of stock depends on two components
• Profits generated by assets in place, past
  capital budgeting decisions
• Profits generated by growth opportunities in the
  future
• Decompose value of stock
• P/E Ratio

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Historical and Prospective Ratios

• Expected values have to be estimated
• Use model to forecast future yields or multiples
• Historic
• Prospective
• Exampled 0.5, g 10, r 12
• Prospective DY2.0, PE25
• Historic DY1.81, PE27.5

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Historical Yields and Growth

• You can use the expression for the historic yield
  to infer the growth rate
• Consider the Alphabet industry

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Growth rates in the Industry

• Infer growth rate in the Alphabet industry
• Example

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Valuing a Company Using P/E-Multiples

• The three steps of using P/E multiples company
  valuation
• Find sample of comparable companies
• Compute average of their P/E ratios
• Multiply earnings by average P/E from step 2.
• Example Value XYZ
• Use ABC and DEF as comparables
• Average P/E(8.759.22)/28.99
• Estimated value of XYZ share8.996.0654.45
• Market price per share is 54.06 (
  46.31m/856,695)

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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).

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Valuation Ratios and Stock Market Outlook
(continued)

• The dividend-price ratio is measured as previous
  years 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 years total
  earnings
• P/E ratios have normally moved in the range 820.
• Graham and Dodd (1934) said that one should use
  an average of earnings of no less than five
  years, preferably seven or ten years.

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P/E ratio 1880-2003

• Source Robert Shiller

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D/P ratio 1880-2002
Source Robert Shiller
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Summary

• Stocks and equity securities 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
• Investors are compensated through cash dividends
  and through capital gains
• Required returns on equity are generally not
  equal to the dividend yield, but to the dividend
  yield plus the growth rate
• P/E-ratios should be used with caution
• Depends on simplifying assumptions

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International Stock Market Indices
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Estimating the Cost of Equity Capital (re)

• The current stock price of MyCo is 50 per share
  and the predicted dividend payment for next year
  is 2 per share. How might you estimate the
  return on equity?
• Method 1 Obtain an estimate of the growth rate
  from analysts and then use
• Method 2 Use the payout ratio in conjunction
  with the return on equity.

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Example

• Consider a firm with one-period future earnings
  per share of 4. The plowback rate is 60 and the
  required rate of return is 16. The firm is
  expected to maintain future earnings growth of
  12.
• What is the stock price?
• What is the P/E ratio?
• What is the PVGO?

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Example

• Dot-bomb is expecting two years of 20 growth in
  its earnings before reverting to its long-run
  growth rate of -4. Its most recent earnings are
  100. Assume that the cost of equity capital is
  12 and Dot-bomb pays out 50 of its earnings in
  dividends, reinvesting the other half. What is
  the value of its stock?

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Questions

• Can I use this valuation technique to buy (sell)
  undervalued (overvalued) stocks?
• Yes
• Should I use this technique to buy (sell)
  undervalued (overvalued) stocks?
• Probably not

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Concluding Remarks

• Method for equity valuation
• Pros
• Intuitively appealing
• Simple to use
• Often used in industry for firm valuation (in
  conjunction with other techniques)
• Cons
• Based on a lot of strong assumptions
• Requires even more assumptions to implement