Chapter 5: How to value bonds and stocks

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Chapter 5 How to value bonds and stocks

• Corporate Finance
• Ross, Westerfield, and Jaffe

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Outline

• 5.1 Bonds
• 5.2 Bond pricing
• 5.3 Bond concepts and reporting
• 5.4 Dividend discount model (DDM)
• 5.5 Stock market reporting

3
Announcement

• Cancelled Your group needs to submit a typed
  report for mini-case Stock Valuation at Ragan
  Thermal Systems, p. 159, after we finish this
  chapter.

4
Notations, I

• Bonds debt securities with long-term maturities,
  typically longer than 1 year.
• Coupon, typically C C1 C2 CN the
  stated interest payment made on a bond.
• Par (face) value (FV) the principal value of a
  bond by default, 1,000.
• Maturity (N) specified date on which the
  principal is paid.

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Notations, II

• Coupon rate annual coupon / FV.
• Yield to maturity (YTM) the rate required in the
  market on a bond.
• Market decides.
• Time varying.
• Related to default risk.
• If coupons are paid out annually, i YTM. If
  coupons are paid out semiannually, i YTM/2.

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How to value bonds

• Note that the cash flows of a typical bond
  consists of two cash flow streams (1) an annuity
  of coupon payments, and (2) a final principal.
• Recall that the PV of multiple cash flows is
  simply the sum of individual PVs.
• Thus, for a typical bond, PV PVannuity
  PVprincipal.

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Bond pricing formula

• PV PVannuity PVprincipal C ? 1 1 / (1
  i)N / i FV / (1 i)N.
• Of course, we can also use a financial calculator
  to do the job.
• Note that computation itself is rather
  straightforward. The difficult part is to
  correctly figure out the values of parameters.

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Bond example, I

• Suppose that VTcredit Inc. is going to issue a
  bond. The maturity is 25 years. The average YTM
  on similar issues is 10. A series of 120 as
  coupons is paid out annually. The face value is
  1,000. What is the fair price of the bond?
• Formula PV C ? 1 1 / (1 i)N / i
  FV / (1 i)N 120 ? 1 1 / (1 10)25
  / 10 1,000 / (1 10)25 1,181.54.
• Calculator 120 PMT 1000 FV 25 N 10 I/Y CPT
  PV. The answer is PV -1,181.5408.

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Semiannual payments

• Most corporate bonds pay coupons semiannually.
  The principle of calculation is the same.
• But remember the time frequency of i and N must
  be the same.

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Bond example, II

• Suppose that VTcredit Inc. is going to issue a
  bond. The maturity is 25 years. The average YTM
  on similar issues is 10. A series of 60 as
  coupons is paid out semiannually. The face value
  is 1,000. What is the fair price of the bond?
• Formula PV C ? 1 1 / (1 i)N / i
  FV / (1 i)N 60 ? 1 1 / (1 5)50
  / 5 1,000 / (1 5)50 1,182.56.
• Calculator 60 PMT 1000 FV 50 N 5 I/Y CPT PV.
  The answer is PV -1,182.5593.

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Bond example, III

• Suppose that Northern Inc. bonds have a 1,000
  face value. Annual coupon is 100. The bonds
  mature in 20 years. YTM 10. What is the bond
  price?
• Calculator 100 PMT 1000 FV 20 N 10 I/Y CPT
  PV. The answer is PV -1,000.
• Lesson if payment rate equals to discount rate,
  the bond price is simply the FV.

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YTM example

• Northern Inc. issued 12-year bonds 2 years ago at
  a coupon rate of 8.4. The bonds make semiannual
  payments. If these bonds currently sell for 110
  of par value, what is the YTM?
• Calculator 42 PMT 1000 FV 20 N -1100 PV CPT
  I/Y. The answer is I/Y 3.4966.
• YTM 2 3.4966 6.9932 ().

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Bond price and YTM

• Recall from Chapter 4 Holding time period
  constant the higher the interest (discount)
  rate, the smaller the PV.
• Because YTM is closely related to discount rate,
  one would expect that YTM is negatively related
  to bond price.
• That is, market interest rates rise ? yield (YTM)
  increases ? bond price falls.

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Bond markets

• Trading is inactive for corporate bonds
  typically, trading occurs in OTC
  (over-the-counter not exchange) Illiquid.
• Trading is active for U.S. government debt
  instruments. This sector has many international
  participants, e.g., Chinese Central Bank.

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Bond reporting

• WSJ used to publish corporate bond quotation for
  the 40 most active corporate bonds but not
  anymore.
• Bond trading information can be found at FINRA
  (Financial Industry Regulatory Authority)
  http//cxa.marketwatch.com/finra/MarketData/Defaul
  t.aspxority)

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A FINRA bond quotation

• Issue   IBM.GT   IBM 8.375   11/01/2019
• Rating -------------------Last Sale
  ----------------------------
• Moody's/SP/Fitch Date Price
  Yield
• A1 / A / AA- 05/02/2007   125.00
    5.569263
• This TRACE quotation was retrieved on 05/15/2007.
• This issue pays coupons semiannually 05/01 and
  11/01.
• I/Y YTM / 2 2.7846.
• Coupon rate 8.375. So, the semiannual payment
  is 41.875.
• Calculator 25 N 2.7846 I/Y 1000 FV 41.875
  PMT CPT PV. The answer is PV -1,250.2572,
  which is 125.02572 of par.

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Bond features, I

• Indenture The written agreement between the
  corporation and the lender detailing the terms of
  the debt issue.
• Collateral the asset pledged on a debt.
• Debenture (gt 10 years) and note (lt 10 years) an
  unsecured debt.
• Sinking fund an account managed by the bond
  trustee for early bond redemption.

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Bond features, II

• Call bond a bond that allows the firm to
  repurchase or call part or all of the bond
  issue at stated prices over a specific period.
• Put bond a bond that allows the holder to force
  the issuer to buy the bond back at a stated
  price.
• Protective covenant a part of the indenture
  limiting certain actions that might be taken
  during the term of the loan, usually to protect
  the lenders interest.
• Treasury notes (2-10 years) and bonds (gt10
  years) long-term debt securities issued by the
  U.S. federal government.

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Bond features, III

• Municipal bonds (munis) debt securities issued
  by state and local governments.
• Zero coupon bond a bond that makes no coupon
  payments, thus initially priced at a deep
  discount.
• Floating-rate bond a bond whose coupon payments
  are adjustable.
• Convertible bond a bond that can be swapped for
  a fixed number of shares of stock anytime before
  maturity at he holders option.

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Dividends as cash flows

• For bond pricing, we just discounted coupons and
  par (2 types of cash flows) to arrive at the PV.
• For stock pricing, this course focuses on one
  particular type of cash flowscash dividends.
• Discounting dividends makes sense because
  dividends are the only types of cash flows that
  investors can actually receive from the firm.
• When dividends are used as cash flows for
  discounting, we need to use cost of equity, i.e.,
  the required rate demanded by shareholders, as
  the applicable discount rate.

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But the problems are

• Discounting all (possibly infinite terms)
  dividends to arrive at PV (fundamental value of
  the stock) is theoretically correct.
• However, the problems are (1) cash flows are
  uncertain we usually plug in a series of
  estimates as if they were certain, (2) the
  required rate of return is unknown and frequently
  time unstable, (3) the life of the security is
  actually unknown.

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How about those no-dividend firms?

• About 50 of U.S. publicly traded firms do not
  pay dividends.
• However, the valuation concept is the same,
  except that some of the early dividend payments
  are zero. After all, there should be
  expectations that at some point the firm will
  start paying dividends. Otherwise, the
  investment will have no value.
• Of course, it is often difficult to forecast when
  these firms will pay dividends and how much will
  they pay.

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Infinite terms?

• The fundamental value of a stock is the PV of its
  future dividends.
• Because a firm can possibly live forever, thus we
  are discounting an infinite number of cash flows.
• To make the calculation doable, we need to make
  some assumptions.

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Zero-growth DDM

• The easiest assumption one can make is to assume
  that there is no growth in dividends, i.e., D1
  D2 D.
• Because this is a perpetuity, the pricing is
  rather straightforward PV D / i.
• Suppose that GE paid 2 dividend per share last
  year. Investors expect no growth in GEs future
  dividends. The applicable discount rate is 10.
• PV 2 / 10 20.

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Constant-growth DDM

• Another easy assumption one can make is to assume
  that there is a constant growth rate, g, in
  dividends, i.e., D1 D0 (1 g), D2 D0 (1
  g)2, etc.
• That is, this is a growing perpetuity.
• Recall from Chapter 4, the PV of a growing
  perpetuity is PV D1 / (i g).

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Constant-growth DDM example

• Vermont Financial Inc. paid a dividend of 1 last
  year. The constant growth rate of dividends is
  5, and the required rate of return is 10.
• PV D0 (1 g) / (i g) 1 (1 5) /
  (10 5) 21.

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Multiple-stage DDM model

• This model allows different growth rates for
  different stages.
• Typically, it takes care of recent, supernormal
  growth.
• There are formulas for PV. However, they do not
  look neat.
• Let us use Excel to visualize the discounting
  process.

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Multiple-stage example, I

• HP has a cost of equity at 14. HP just paid an
  annual dividend of 2.
• The expected dividend growth rate between year
  1-3 is 25. The expected dividend growth rate
  between year 4-5 is 15. The expected dividend
  growth rate for year 6 and afterwards is 5.

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Multiple-stage example, II
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Quality of inputs

• The above stock pricing examples seem quite
  simple. In reality, stock valuation is extremely
  difficult. The difficulty does not arise from
  the calculation itself, but from the uncertainty
  associated with model inputs (estimates).
• Professional investors compete on the quality of
  inputs.

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Sensitivity

• You should change some of the parameters in the
  previous Excel sheet to see the sensitivity of PV
  with respect to changes in these parameters.
• You would notice that PV is most sensitive to 2
  parameters (1) cost of equity (i), i.e., the
  discount rate, and (2) the long term growth rate,
  i.e., the growth rate (g) after year 5.

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Cost of equity, i

• We will talk about the determination of required
  return (i) in Chapter 10 Risk and Return. The
  cost of equity is directed to the risk level of
  the investment (project) because for a risky
  project one would require a higher return
  risk-return tradeoff.
• In real life, the i estimates from practitioners
  tend not to be too far away from one another.

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Long-term growth rate, g, I

• In contrast, the g estimates from practitioners
  can have a wide range, particularly in the times
  when the market is extremely optimistic or
  pessimistic.
• Empirical evidence indicates that the
  relationship between past and future growth rates
  is weak. This means that it is dangerous to
  simply extrapolate past dividends (earnings, cash
  flows) trends into the future to obtain the
  future growth rate.
• The game of guessing g -- the wild west.
• 2 cents the simple math in p. 141 is probably
  not useful in real life.

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Mad money CNBC and alike
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P/E ratio, I

• The ratio of the current market price per share
  to the expected next-12-month earnings per share
  (or the current annual earnings per share).
• When the expected next-12-month EPS is used, this
  P/E ratio is also called forward P/E ratio.
• The level of P/E ratio is related to growth
  potential. A stock with higher expected growth
  potential tends to have a higher P/E ratio.

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P/E ratio, II

• Embedded in the seemingly high prices of those
  high PE stocks are expectations that in the
  aggregate are unlikely to be met. You should
  expect a high strikeout rate. Example During
  1996-2000, only 1/3 of all high PE, high-tech
  stocks have higher returns than the SP 500 but
  once they beat the SP 500, they tend to have
  extremely good performance.
• An effective, widely-used communication tool
  because of its simplicity.

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Stock market reporting (WSJ), I

• This quotation was retrieved from WSJ on
  05/15/2007.
• STOCK SYM CLOSE NET CHG
• GenMotor GM 30.62 1.16

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Stock market reporting (WSJ), II

• Yesterdays (05/14/2007) closing price 30.62.
• Yesterdays closing price is higher than the
  closing price of the previous trading day by
  1.16.

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Let us work on this

• Q2, P. 154. Microhard has issued a bond with the
  following characteristics (1) par 1000, (2)
  time to maturity 20 years, (3) coupon rate 8
  (4) semiannual payments. What is the price of
  the bond if the YTM is (a) 10, and (b) 6?

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Mini-case report due

• Cancelled Please submit your report for
  mini-case Stock Valuation at Ragan Thermal
  Systems, p. 159, in 1 week.
• For this assignment, you need equation (5.8), p.
  141. The following reading in the textbook will
  help you pp. 136-151.
• Please be prepared to contribute to our
  discussions on this mini-case.