Introduction to Valuation Stock Valuation

1
Introduction to ValuationStock Valuation

• Financial Management
• P.V. Viswanath
• For a First course in Finance

2
Absolute and Relative Pricing

• In economics, we tend to price goods and assets
  by considering the factors affecting the supply
  and demand for them.
• The number of goods and assets are very many.
  Each of them is different in some way or another
  from the other.
• Computing the price of one good does not allow us
  to price another good, except to the extent that
  other goods are substitutes or complements for
  the first good.
• In finance, the number of assets can be
  reasonably characterized in terms of a smaller
  number of basic characteristics.
• Hence most assets can, to a first approximation
  be priced by considering them as combinations of
  more fundamental assets.

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Relative pricing of financial assets

• Consider first riskless financial assets, i.e,
  assets that are claims on riskless cashflows over
  time.
• Consider a fundamental asset, i, defined by a
  claim to 1 at time t i.
• There can be T such fundamental assets,
  corresponding to the t 1,..,T time units.
• Then, any arbitrary riskless financial asset that
  is a claim to ci at time i, i 1,..,T can be
  considered a portfolio of these T fundamental
  assets.
• Hence, the price, P of any such asset is related
  to the prices of these first T fundamental
  assets, Pi, i 1,,T.
• In fact, the price of this asset would simply be

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Relative pricing of risky financial assets

• What about risky financial assets?
• We can equivalently imagine, for every level of
  risk, a set of T fundamental risky assets. Then,
  for any arbitrary risky asset of this level of
  risk, we can equivalently write

• Of course, this is not entirely satisfactory,
  because wed have TxM fundamental assets
  corresponding to each of M levels of risk. We
  will come back to this when we talk about the
  CAPM.
• In any case, we need to examine how this pricing
  is established in the market-place.

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Arbitrage and the Law of One Price

• Law of One Price In a competitive market, if two
  assets generate the same cash (utility) flows,
  they will be priced the same.
• How is this enforced?
• If the law is violated if asset 1 sells for
  more than asset 2, then investors can make a
  riskless profit by buying asset 2 and selling it
  as asset 1!
• In practice we need to take transactions costs
  into account.
• Also, it may be difficult to execute the two
  transactions at the same time prices might
  change in that interval this introduces some
  risk.

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Exchange Rates and Triangular Arbitrage

• Consider the exchange rates reigning at closing
  on January 30.
• The yen/euro rate was 157.87 yen per euro
• The euro/ rate was 1.4835 per euro.
• The yen/ rate was 106.4 yen per dollar.
• If we start with a dollar, we can buy 106.4 yen
  these can then be used to buy 106.4/157.87 or
  0.674 euros, which can, in turn, be used to
  acquire 0.9998, which is very close to a dollar.

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Triangular Currency Arbitrage

• Suppose the euro/ rate had been 1.50 per euro.
• Then, it would have been possible to start with
  one dollar, acquire 0.674 euros, as above, and
  then get (0.674)(1.5) or 1.011, or a gain of
  1.1 on the initial investment of a dollar.
• This would imply that the dollar was too cheap,
  relative to the euro and the yen.
• Many traders would attempt to perform the
  arbitrage discussed above, leading to excess
  supply of dollars and excess demand for the other
  currencies.
• The net result would be a drop a rise in the
  price of the dollar vis-à-vis the other
  currencies, so that the arbitrage trades would no
  longer be profitable.

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Risk Arbitrage

• In this case, trading will continue until there
  are no more riskfree profit opportunities.
• Thus, arbitrage can ensure that the sorts of
  pricing relationships referred to above can be
  supported in the marketplace, viz

• What if there are still opportunities that will,
  on average, lead to profit, but the investors
  intending to benefit from this profit will have
  to take on some risk?
• Presumably investors will trade off the risk
  against the expected profit so that there will be
  few of these expected profit opportunities, as
  well this brings us to the notion of the
  informational efficiency of financial markets.

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Efficient Markets Hypothesis EMH

• An assets current price reflects all available
  information this is the EMH.
• If it didnt, there would be an incentive for
  investors to act on that information.
• Suppose, for example, that investors noticed that
  good news led to stock prices rising slowly over
  two consecutive days.
• This would mean that at the end of the first day,
  the good news was not all incorporated in the
  stock price.

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Efficient Markets Hypothesis

• In this situation, it would be optimal for
  traders to buy even more of a stock that was
  noted to be rising on a given day, since the
  stock would rise more the next day, giving the
  trader an unusually good chance of making money
  on the trade.
• But if many traders pursue this strategy, the
  stock price would rise on the first day, itself,
  and the informational inefficiency would be
  eliminated.
• Empirically, financial markets seem to be
  reasonably close to being efficient.
• This allows us to price financial assets with
  respect to fundamentals without worrying about
  deviations from these fundamental prices.

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Stock Price Fundamentals

• What determines the price of a stock? Or, in
  other words, why would an investor hold stocks?
• The answer is that s/he expects to receive
  dividends and hopefully benefit from a price
  increase, as well.
• In other words, P0 PV(D1) PV(P1) , where P0
  is the price today and P1 is the price tomorrow.
• However what determines P1?
• Again, using the previous logic, we must say that
  its the expectation of a dividend in period 2
  and hopefully a further price rise. Continuing,
  in this vein, we see that the stock price must be
  the sum of the present values of all future
  dividends.

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Dividend Mechanics

• Declaration date The board of directors declares
  a paymentRecord date The declared dividends are
  distributable to shareholders of record on this
  date.Payment date The dividend checks are
  mailed to shareholders of record.
• Ex-dividend date A share of stock becomes
  ex-dividend on the date the seller is entitled to
  keep the dividend.   At this point, the stock is
  said to be trading ex-dividend. 

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Dividend Discount Model

• What is the price of a stock on its ex-dividend
  date?
• Using the previous logic, we see that its simply

• where k is the appropriate discount rate to
  discount the dividends consistent with their
  riskiness.
• We assume that the one-period ahead discount rate
  is the same for all periods. That is, we use the
  same rate to discount D1 to time 0, as we use to
  discount D2 to time 1.

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Gordon Growth Model

• If we assume that the dividend is growing at a
  rate of g per annum forever, this formula
  simplifies to

• We see that the price of a stock is higher, the
  higher the level of dividends, the higher the
  growth rate of dividends and the lower the
  required rate of return or the discount rate, k.

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Earnings and Investment Opportunities

• Dividends Earnings Net New Investment
• Hence a firms stock price cannot be the present
  value of discounted earnings!
• Unless the firm needs no new investment to
  maintain its earnings.
• What determines the price of the stock of a
  company that reinvests part of its earnings?

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Reinvestment and Stock Price

• Suppose a firm starts out with a certain stock of
  investment capital at the beginning of period 1
  (end of period 0).
• Assume that it earns a return, ROE, on this
  capital, so as to assure it of earnings of E1
  each period forever.
• Assume, furthermore, that this firm pays out all
  of these earnings as dividends, each period.
• Then, its stock price today, P0 will be equal to
  E1/k.

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Reinvestment and Stock Price

• Now assume, in addition to its existing
  investments, that the firm expects to have at
  t1, an investment opportunity with a t1 value
  of M1 (that is, this is the present value at t1
  of all the future cashflows that will be
  generated by this investment opportunity.
• Implementation of this idea requires additional
  capital of DI1, which the firm raises from the
  marketplace.
• If the capital market is efficient, the firm will
  have to pay for this additional capital with
  promises of future cashflows with a present value
  equal to the amount of additional capital raised.
  

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Reinvestment and Stock Price

• Hence the t1 value that will accrue to the
  firms shareholders is only M1- DI1.
• Denote by NPV1, the t0 value of M1- DI1. That
  is, NPV1 (M1- DI1)/(1k).
• Taking this additional investment opportunity
  into account, the firms stock price will not
  just be E1/k, but E1/k NPV1.
• Similarly, let NPVi represent the t0 value of
  investment opportunities that the firm expects to
  have a time ti, for each future time period.
• Proceeding thus, we see that P0 E1/k NPVGO,
  where NPVGO S NPVi for all i 2,

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Reinvestment and Stock Price

• Upto this point, we have assumed that the firm
  has raised this additional capital from other
  investors in the market place.
• Suppose, however, that the firm raises the
  additional capital in period 1 from its own
  shareholders, by reducing the amount of dividends
  that it pays. That is, D1 E1 DI1.
• This reduction in dividends will cause the stock
  price to drop by an amount equal to the present
  value of DI1. However, the firm will no longer
  have to pay the outside investors future
  compensation for the contribution of the
  additional capital, DI1.
• These two quantities will cancel each other out.
  We, see, therefore, that P0 E1/k NPVGO.

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Fundamental Determinant of Growth Rate

• What are the determinants of growth in a firms
  earnings?
• Earnings in any period depends on the investment
  base, as well as the rate of return that the firm
  earns on that investment base
• Et1 (It)ROE
• (It-1 DIt)(ROE), where DIt is the
  increment in investment in period t over and
  above that in period t-1.
• (It-1)ROE (DIt)(ROE)
• Et (DIt)(ROE)
• Hence Et1 - Et (DIt)(ROE)
• Dividing both sides by Et , we get gt
  (Retention Ratio)(ROE), assuming that the
  additional investment is made possible by
  retaining part of the firms earnings.

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Reinvestment and Stock Price

• We see from the previous demonstration that
  retention of earnings by a firm for reinvestment
  will not increase in a higher stock price if that
  additional investment has a zero NPV
• That is, if it earns a return no greater than the
  rate of return required by the market on
  financial investments of similar risk, already
  available to investors in the marketplace.
• We see, furthermore, that it is not the firms
  dividend policy that causes the firms stock
  price to be higher, but rather the availability
  of positive NPV investment opportunities.
• This can be seen clearly in the following example.

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Example of Dividend Irrelevance

• Stellar, Inc. has decided to invest 10 m. in a
  new project with a NPV of 20 m., but it has not
  made an announcement.
• The company has 10 m. in cash to finance the
  new project.
• Stellar has 10 m. shares of stock outstanding,
  selling for 24 each, and no debt.
• Hence, its aggregate value is 240 m. prior to
  the announcement (24 per share).

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Example of Dividend Irrelevance

• Two alternatives
• One, pay no dividend and finance the project with
  cash.The value of each share rises to 26
  following the announcement. Each shareholder can
  sell 0.0385 ( 1/26) shares to obtain a 1
  dividend, leaving him with .9615 shares value at
  25 (26 x 0.9615). Hence the shareholder has one
  share worth 26, or one share worth 25 plus 1
  in cash.

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Example of Dividend Irrelevance

• Two, pay a dividend of 1 per share, sell 10m.
  worth of new shares to finance the project.
• After the company announces the new project and
  pays the 1 dividend, each share will be worth
  25.
• To raise the 10 m. needed for the project, the
  company must sell 400,000 (10,000,000/25)
  shares. Immediately following the share issue,
  Stellar will have 10,400,000 shares trading for
  25 each, giving the company an aggregate value
  of 25 x 10,400,000 260m.
• If a shareholder does not want the 1 dividend,
  he can buy 0.04 shares (1/25).
• Hence, the shareholder has one share worth 25
  and 1 in dividends, or 1.04 shares worth 26 in
  total.

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Assumptions for Dividend Irrelevance

1. The issue of new stock (to replace excess
   dividends) is costless and can, therefore, cover
   the shortfall caused by paying excess dividends.
2. Firms that face a cash shortfall do not respond
   by cutting back on projects and thereby affect
   future operating cash flows.
3. Stockholders are indifferent between receiving
   dividends and price appreciation.
4. Any cash remaining in the firm is invested in
   projects that have zero net present value. (such
   as financial investments) rather than used to
   take on poor projects.

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Implications of Dividend Irrelevance

• A firm cannot resurrect its image with
  stockholders by offering higher dividends when
  its true prospects are bad.
• The price of a company's stock will not be
  affected by its dividend policy, all other things
  being the same. (Of course, the price will fall
  on the ex-dividend date.)

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Dividends in the Real World

• In practice, dividends are taxed higher than
  capital gains. Hence investors may prefer that
  the firm retain funds for new investment rather
  than raise it from the financial marketplace.
• On the other hand, managers have to justify the
  need for additional funds in order to get them
  from investors. This ensures a greater check on
  managers. Hence, the marketplace might prefer
  that managers raise funds externally.
• In practice, firms have to take both factors into
  account and craft the best dividend policy.