Corporate Finance: Securities

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Corporate FinanceSecurities

• Professor Scott Hoover
• Business Administration 221

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• Bonds
• definition A bond is a security with
  pre-specified cash flows to be paid on
  pre-specified dates.
• Terms
• face value or maturity value
• coupon rate / coupon payment
• maturity
• yield-to-maturity
• is the interest rate that makes the PV of the
  promised future cash flows equal to the current
  price.
• Important note the yield-to-maturity is always
  quoted as an APR.

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• Bond Valuation
• example
• face value 1000
• annual coupon 100 (coupon rate 10)
• maturity 10 years
• yield-to-maturity 8
• V0 1000/1.0810 100 PVIFA8,10 1134.20
• this is called a premium bond because it sells
  for more than the face value.

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• We can continue this example using different
  yields.
• ytm 11 ? V0 941.41
• called a discount bond because it sells for
  less than face value
• 9 coupons, 8 ytm ? V0 1,067.10
• ytm 10 ? V0 1,000
• called a par bond because it sells at par
  (sells for the face value)
• What do we learn here?
• Higher interest rates (yields) ? lower bond
  prices
• Higher coupon rates ? higher bond prices
• yield gt coupon rate ? discount bond
• yield coupon rate ? par bond
• yield lt coupon rate ? premium bond

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• example Suppose you purchased a bond one year
  ago at par.
• coupon rate 8 (paid annually)
• maturity 5 years
• What was the ytm one year ago?
• yield-to-maturity 8.
• Why?because the bond sold at par.
• Today, you receive the first coupon. Also, the
  YTM has now changed to 7.5. What was the return
  on your investment?
• value today 1000/1.0754 80?PVIFA7.5,4
  1016.75
• Total return (801016.75-1000)/1000
  9.675
• Two components
• current yield coupon/initial price 80/1000
  8
• capital gain increase in price/initial price
  1.675

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• Two sources of returns
• interest (coupon) payments
• changes in interest rates
• changes in risk
• changes in macroeconomic rates

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• example Suppose you observe the following bond
  information
• I 50 (annual coupons, coupon rate 5)
• n 6 years
• price 975
• What is the yield-to-maturity on the bond?
• bond selling at a discount ? Rd gt 5.
• guess 6 ? V0 1000/1.066 50 PVIFA6,6
  950.83
• too low.need to decrease the interest rate
• guess 5.6 ? V0 1000/1.0566 50 PVIFA5.6,6
  970.12
• a bit too low again
• guess 5.5 ? V0 1000/1.0556 50 PVIFA5.5,6
  975.02
• close enough.the actual yield is 5.50045

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• Non-Annual Coupons
• Background EAR vs. APR
• Annual Percentage Rate (APR) ? per period rate ?
  of periods per year.
• ignores compounding of interest
• Effective Annual Rate (EAR) ? actual annual
  interest rate.
• assumes interest is compounded
• Example Suppose the semi-annual rate is 6.
• The APR is 62 12
• The EAR is 1.062-1 12.36.
• Why?
• If we invest a dollar, we will have 1.06 in six
  months. If we reinvest that money for another
  six months, we will have 1.061.06 1.1236,
  for a 12.36 return.

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• The APR is often a misleading indictor of the
  true interest rate.
• Why?
• ...then why is it used?
• Converting from APR to EAR (and vice versa) is
  easy if we remember the definitions.
• We might even have an infinite number of
  compounding periods per year (continuous
  compounding).
• In that case, we find that EAR eAPR 1, where
  e is the constant e 2.7182818

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• example
• coupon rate 12, paid semi-annually
• 5 years to maturity.
• appropriate discount rate 10 EAR
• What is the price of the bond?
• Coupons and coupon rates are calculated on an
  annual basis, so a 12 coupon rate is 6 every
  six months.
• V0 60/1.10.5 60/1.1 60/1.14.5
  1000/1.15 1086.92
• Alternatively, we can use the semi-annual rate.
• Rsa 1.10.5 1 4.88
• V0 60?PVIFA4.88,10 1000/1.048810
  1086.92

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• Suppose, instead, that the price is 985. What
  is the yield-to-maturity
• 985 60 x PVIFAr,10 1000/(1r)10
• discount bond, so the interest rate must be
  higher than 6 semi-annually.
• Try 6.5 V0 60 ? PVIFA6.5,10 1000/1.06510
  964.05
• 964 lt 985, so rate must be less than 6.5.
• Try 6.2 V0 60 ? PVIFA6.2,10 1000/1.06210
  985.41
• Close enough.the semi-annual rate is 6.2, so
  the yield-to-maturity is about 12.4.
• EAR 1.0622 1 12.78

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• Another example
• FV 1000
• C 80, paid annually
• 3.2 years to maturity discount rate 9.
• What is the value of the bond today?
• First, suppose the bond had 4 years to maturity.
• I.e., suppose that it is now 0.8 years ago.
• V-0.8 80?PVIFA9,4 1000/1.094 967.60.
• We are indifferent between holding the bond and
  having received 967.60 in cash 0.8 years ago.
• If we did receive 967.60, we could have invested
  in for 0.8 years to receive 967.60?1.090.8
  1,036.67 today.
• Therefore, the bond is worth 1,036.67 today.

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• Bond Provisions
• Convertibility
• the purchaser can exchange the bond for a
  pre-specified number of shares of stock during a
  pre-specified period.
• Warrants
• often "attached" to a bond
• the purchaser can buy a pre-specified number of
  shares of stock for a pre-specified price during
  a pre-specified period.
• In contrast to a convertible, the warrantholder
  does not give up the bond when warrants are
  exercised.
• Call provision
• the seller can buy back the bond for a
  pre-specified price during a pre-specified period

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• Other Covenants
• force the issuer to maintain a certain level of
  firm stability
• usually specified through financial ratio
  restrictions
• If a covenant is violated, the bond purchaser has
  the right to demand immediate repayment.
• Think about how each of these is likely to affect
  bond values.
• Why would a company choose to issue a bond with
  one of these provisions?

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• Derivatives
• Call option
• The buyer of an American call option has the
  right (but not the obligation) to purchase the
  underlying asset on or before a pre-specified
  date for a pre-specified price.
• The seller (writer) of the option has the
  obligation to sell the underlying asset if the
  buyer chooses to buy it.
• For European options, one can only exercise on
  the expiration date.

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• Put option
• The buyer of an American put option has the right
  (but not the obligation) to sell the underlying
  asset on or before a pre-specified date for a
  pre-specified price.
• The seller (writer) of the option has the
  obligation to buy the underlying asset if the
  buyer chooses to sell it.
• Forward
• The buyer in a forward contract has the
  obligation to purchase the underlying asset from
  the seller for a pre-specified price on a
  pre-specified date.

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• When would a firm want to use derivative
  securities?
• Primarily, derivatives are used to reduce price
  risk.
• Example Suppose a gold mine is planning to
  produce 10,000 ounces of gold next quarter.
• It might lock in a price for those ounces by
  selling a forward contract.
• Alternatively, it might buy put options that
  allow the firm to sell at a pre-specified price
  if need be.
• In both cases, the firm is using derivatives as
  insurance against declines in price.
• In contrast, the buyer of a commodity might buy
  forward or buy call options to hedge the risk.

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• How does a firm choose between forwards and
  options?
• Generally speaking,
• forwards are preferred when the firm wants to
  hedge a certain cash flow.
• e.g., the firm has a contract in place that will
  require the firm to pay 100,000,000 in one year.
  The firm might buy yen forwards to hedge that
  risk.
• options are preferred when the firm wants to
  hedge an uncertain cash flow.
• e.g., the firm is negotiating a deal in which the
  firm would have to manufacture a product. The
  manufacturing process requires oil. The firm
  might buy call options on oil to hedge the risk.

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• Stocks
• definition A residual claim on firm cash flows.
• Notation
• R required rate of return on the stock
• Dt dividend paid at date t
• Pt price of the stock at date t
• g expected rate of growth in dividends
• Definitions
• dividend yield D1/P0
• capital gains yield (P1 - P0)/P0
• total return dividend yield capital gains
  yield.
• Note that this is analogous to bond returns

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• Valuation Basics
• In theory, the value of a share of stock should
  be equal to the present value of the expected
  dividend payments.
• V0 D1/(1R) D2/(1R)2
• Note We will discuss the estimation of R later
  in the course.
• For now, think of it as the return shareholders
  need in order to be compensated for risk.
• Problems
• We cant estimate dividends forever
• Some companies dont pay dividends.

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• The Malkiel Model A solution to the problems?
• We value the stock as if it will be sold at some
  date (T).
• V0 D1/(1R) D2/(1R)2 DT/(1R)T PT
  /(1R)T
• How might we estimate PT (the price at date T)?
• Multiples
• Perpetual growth
• Using multiples.
• 1. Forecast XT, where XT is a cash flow-related
  variable (earnings, sales, etc.) at date T
• 2. Estimate (P/X)T, the price-to-X ratio at date
  T
• 3. PT (P/X)T ? XT
• Perpetual Growth
• 1. Estimate a long-term growth rate (g)
• 2. Use PT DT1/(R-g)

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• Example
• D1 2.20 (expected dividend in one year)
• R 8 (required return on the investment)
• E0 4.50 (current earnings)
• g 4 (expected growth in earnings and dividends
  for, say, 5 years)
• (P/E)5 15 (expected P/E ratio in 5 years)
• What is the value of the stock today?
• D2 2.20?1.04 2.29
• D3 2.20?1.042 2.38
• D4 2.20?1.043 2.47
• D5 2.20?1.044 2.57
• E5 E0?(1g)5 4.50?1.045 4.93
• P5 E5?(P/E)5 73.91
• V0 2.20/1.082.29/1.082 2.57/1.08573.91/
  1.085 59.76

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• Example
• D1 1.00 (expected dividend in one year)
• R 10 (required return on the investment)
• g(4) 15 (expected growth in dividends for 4
  years)
• g(?) 4 (expected long-term growth in
  dividends)
• What is the value of the stock today?
• D2 1.00?1.15 1.15
• D3 1.00?1.152 1.32
• D4 1.00?1.153 1.52
• P4 D5/(R-g) D4(1g)/(R-g)
  1.52?1.04/(0.1-0.04) 26.36
• V0 1/1.081.52/1.1426.36/1.14
  21.90

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• Problems with the Malkiel Model
• Estimating a future multiple is difficult.
• For example, what P/E ratio would you expect for
  the wireless industry in 5 years?
• How might we go about estimating this?
• Estimating the future growth rates is difficult.
• Sustainable growth gives us a starting point.
• What is the likely profit margin for the firm?
• What is the likely asset turnover?
• What is the likely debt ratio?
• What is the likely earning retention rate?
• Caution The firm will only grow at the
  sustainable growth rate if it can find the
  additional sales.
• Note In BUS 365 (Investments), we explore ways
  to minimize these problems.

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• A simple version of Malkiel Comparables
  Analysis (aka, Comps, Trading Comps, )
• One approach (used by investment banks) is to let
  T0 and estimate the market multiple by looking
  at the current average in the industry.
• example Nokia
• Earnings
• The current industry average P/E ratio is 42.86
• Nokia has current earnings of 0.86 per share
• V0 42.86?0.86 36.86
• Sales
• The current industry average P/S ratio is 6.22
• Nokia has current sales of 7.30 per share
• V0 6.22?7.30 45.41
• Average (36.8645.41)/2 41.13.

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• A related technique is called MA Analysis or
  Transaction Comps.
• This is identical to Comps except that- We
  examine historical mergers and acquisitions
  involving similar companies.- In our market
  multiples, we use the transaction purchase price
  instead of the market price
• Problems with Comps
• Ignores growth
• Ignores debt structure
• Biased by our choice of similar companies

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• The Discounted Cash Flow (DCF) Model
• intuition
• forecast the future unlevered free cash flows
  (FCFs) of the firm
• discount them to find firm value today.
• subtract the values of debt and preferred stock
  to find value of equity
• divide by number of outstanding shares to get
  share value today.
• Why use free cash flows?
• They are the actual cash flows of the firm
• Why use unlevered free cash flows?
• simpler to estimate than levered free cash flows
• can take financing cash flows into account
  through the discount rate.

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• Methodology
• Estimate the appropriate discount rate for the
  firm (we will cover this later in the course).
• Forecast the unlevered FCFs.
• Unlevered FCF ? EBIT(1-T) DA CapEx - ?NWC
  OtherEarnings before Interest and Taxes ?
  (1-tax rate) Depreciation and Amortization-
  Capital Expenditures- Increases in Net Working
  Capital Other

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• Estimate the terminal value of the FCFs at the
  end of the forecast period.
• E.g., if we have forecast 5 years of unlevered
  FCFs, we estimate the value at year 5 of the
  unlevered FCFs from years 6 on.
• Discount the expected FCFs to the present using
  the Weighted Average Cost of Capital (WACC).
• This gives us our estimate of Firm Value.
• We will cover the WACC in detail later.
• For now, view it as the weighted average return
  needed by the companys investors.
• Subtract the values of debt and preferred stock
  to get the value of equity.
• Divide by the number of shares outstanding to get
  the per share value.