Chapter 5: Bond and Stock (Equity) Valuation

1
Chapter 5 Bond and Stock (Equity) Valuation

• Bond valuation
• Zero coupon bond valuation and introduction to
  interest rate/bond price changes.
• Valuation of coupon paying bonds, annual and
  semiannual
• Yield-to-Maturity (YTM) calculation
• Bond terms and types
• Basics concerning stock valuation
• Valuation of constant growth (mature) stocks.
• Valuation of nonconstant growth stocks.
• Corporate value or Free Cash Flow model

2
Bond basics

• A bond is a debt security, where money/capital is
  borrowed and is to be paid back along with
  interest.
• More specifically, bonds mature in more than 10
  years, notes in less than 10 years, and bills in
  less than one year. In this presentation we will
  use the term bond to refer to all maturities.
• Bonds are known as fixed income securities.
• All of the future payments to be made on the bond
  are fixed or predetermined, as stated in the bond
  contract.
• The current value of a bond is defined as the
  Present Value of all the future cash flows to be
  received by the bondholder.
• A bond promises to pay a predetermined stream of
  future cash flows.

3
Example of a two-year zero coupon bond

• Three years ago, a 5-year bond was issued.
  Today, this bond matures in 2 years. The par
  value is 100. Currently, this bond sells for
  84.17 in the market. What annual rate of return
  do investors currently require on this two year
  bond?
• This bond must be competitively priced in the
  market with similar bonds. This bonds time line
  appears below

t0
t2
t1
FV2 100 par
PV0 84.17
4
Example of a two-year zero coupon bond, continued

• From Chapter 4, we have the time value of money
  formulas that relate the PV0 and FVn for
  multiperiod applications
• PV0 FVn/(1r)n, rearrange as ? r FVn/PV01/n
  1
• For this example, PV084.17, FVn100, and n2
• r FVn/PV01/n 1 100/84.171/2 1 0.09
  or 9.0
• On a financial calculator, enter FV100,
  PV-84.17, N2, P/Y1, and compute the I/Y8.

5
Example of a 10 year bond that pays annual coupons

• Assume that 10 years ago, a 20-year bond was
  issued. Today, this bond now matures in 10
  years. The par value is 1000. It promises to
  pay the owner 9 (fixed rate) coupon interest
  each year. What is todays bond price?
• This bond will pay (0.09)(1000) 90 coupon
  interest each year, and will also pay off the
  1000 par value at t10 years from today.
• Currently, lets assume that the 10 year market
  required rate of interest or return on this and
  comparable bonds is r8.5 per year. Anyone that
  buys this bond today will expect to earn this
  rate over the next 10 years. The bonds time
  line appears below

kD8.5
t0
t1
t9
t10
1000 par 90 coupon 1090
PV0 ?
90 coupon
90 coupon
6
Example of a 10 year bond that pays annual
coupons, continued

• The 10 year, 9 annual fixed coupon, 1000 par
  bond promises to pay the following bundle of cash
  flows
• 10 coupons, paid annually, of (0.09)(1000)90
  each.
• The par value amount of 1000 in 10 years.
• From a Chapter 4 TVM perspective, the bonds
  promised cash flows can be represented as
• A 10-year ordinary annuity of 90 annual cash
  flows.
• One lump sum cash amount of 1000 in 10 years.

7
Example of a 10 year bond that pays annual
coupons, continued

• The bonds current price or value is thus the PV
  of all the promised future cash flows, discounted
  at r8.5 per year.
• To calculate this bonds current price, add
  together the PVs of the annuity of coupons and
  the PV of the par value lump sum.
• The coupon stream annuity PV0590.52 and the lump
  sum PV0442.29, and both sum up to 1032.81,
  which is therefore the bonds current value or
  price. The TVM formulas are shown below

8
Example of a 10 year bond that pays annual
coupons, continued

• On a financial calculator (or on the appropriate
  MS Excel function), the following items must be
  entered
• A 10 year annuity of 90 annual cash flows.
• A lump sum of 1000 in 10 years.
• On a financial calculator, enter FV1000, PMT90,
  N10, I/Y8.5, P/Y1, and compute the
  PV-1032.81.

9
Bond prices and market interest rate changes,
using the ten year bond

• Interest rates (yields) and bond prices will
  change as time passes and economic conditions
  change.
• What will happen to this ten year bonds price if
  the one year market required yield suddenly
  either (1) decreases to r8.0 or (2) increases
  to r9.0?
• NOTE the coupon rate and payment do not change
  and thus the cash flows paid by this bond will
  never change however, the price that investors
  are willing to pay today will always change
  whenever current market interest rates or yields
  change.

10
Case 1 market interest rates (yields) decrease
from 8.5 to 8.0

• What are investors now willing to pay for a 10
  year bond that pays 90 annual coupons and 1000
  par value exactly ten years from today at t10,
  after rates (yields) fall today by 0.5?
• On a financial calculator, enter FV1000, PMT90,
  N10, I/Y8, P/Y1, and compute the
  PV-1067.10. Bond price rises by 34.29
• When market interest rates or yields decrease,
  the price of all existing fixed rate coupon bonds
  will rise.

11
Case 2 market interest rates (yields) increase
from 8.5 to 9.0

• What are investors now willing to pay for a 10
  year bond that pays 90 annual coupons and 1000
  par value exactly ten years from today at t10,
  after rates (yields) rise today by 0.5?
• On a financial calculator, enter FV1000, PMT90,
  N10, I/Y9, P/Y1, and compute the PV-1000.
  Bond price falls by 32.81
• When market interest rates or yields increase,
  the price of all existing fixed rate coupon bonds
  will fall.

12
Finding the Yield-to-Maturity or YTM of an
existing bond (not in lecture notes)

• An existing bond matures in 5 years. The par
  value is 1000. It pays an annual coupon payment
  of 8 or (0.08)(1000) 80 each year.
  Currently the bond sells for 1050.
• What must r be, here called the YTM?
• On a financial calculator, enter FV1000, PMT80,
  PV-1050, N5, P/Y1, and compute the I/Y6.787.
• Note the FV and PMT are of opposite sign than the
  PV!!!

13
Yield to Maturities of bonds, continued

• What we actually observe in the bond market are a
  bonds current price, and also the promised
  future coupon and par value payments. The bonds
  yield (YTM) or r is something that is calculated
  or extrapolated from these observable items.
• This is where the bond yields (YTMs) we see in
  the financial press, e.g., Wall Street Journal,
  come from they are extrapolated from the bond
  market data.
• In these notes, my use of the term yield is
  synonymous with YTM, not the term current yield
  or CY as sometimes mention the textbooks.
  CY(coupon payment/bond price).

14
Bonds that pay semiannual coupon interest payments

• Most coupon paying bonds pay the interest every
  six months or semiannually.
• An example a U.S. government Treasury Bond
  matures 11.5 years from today. The par value is
  1000. The coupon interest is 14 per year
  (always stated on annual basis), paid
  semiannually.
• Currently, on such bonds, the r or YTM is 8 per
  year. What is this bonds current value?
• Here, we return to the Chapter 4 section on other
  than annual compounding of interest.

15
Bonds that pay semiannual coupon interest
payments, continued

• The fixed semiannual coupon payments
• The 14 annual coupon is (0.14)(1000) 140 per
  year, actually paid as (140/2) 70 each six
  months.
• There are 23 of these semiannual payments of 70
  each over the following 11.5 years (23 semiannual
  periods).
• The par value consists of the 1000 payment in
  11.5 years (at maturity).
• With semiannual bonds, the YTM of 8 means 8
  annual nominal, compounded semiannually.
• The bonds true effective yield is actually
  (8/2) or 4 semiannually or every six months.

16
Bonds that pay semiannual coupon interest
payments, continued
YTM8
t0
t0.5
t11
t11.5
PV0 ?
70 coupon
70 coupon
70 coupon and 1000 par

• On a financial calculator, enter FV1000, PMT70,
  N23, I/Y8, P/Y2, and compute the PV-1445.71.
• The coupon annuity must be entered as done above,
  23 payments of 70 each (never as 11.5 payments
  of 140 each). The par value repayment occurs 23
  semiannual periods from today.
• The calculator takes I/Y, divides by P/Y, and
  solves the problem using a semiannual effective
  rate of 8/2 4.

17
Types and terms of bonds

• Callable bond the issuer has right to retire
  the bond before maturity, at a predetermined
  price that is always specified in the bond
  contract.
• Almost all corporate bonds are callable. If
  interest rates then fall in the future, firms can
  retire these existing bonds and replace them with
  new lower rate bonds.
• Callable bonds will command a higher interest
  rate or yield (lower price) than a comparable
  risk non-callable bond.
• Mortgage bond bond is secured or collateralized
  by some physical asset in case the issuer
  defaults.
• Commonly used in the transportation industry.

18
Types and terms of bonds, continued

• Convertible bond bond can be converted into a
  predetermined number of shares of common stock.
  Investors are willing to accept a lower yield on
  such bonds. The right to convert may become very
  valuable.
• A convertible bond thus has the opportunity to
  become an exciting investment if the firm does
  unexpectedly well.
• Debenture bond bond is backed by the issuers
  ability to generate future cash flow to make the
  promised payments. There is no collateral.

19
Types and terms of bonds, continued

• Subordinated bonds the bonds claim on the
  issuer is junior to one or more senior bond
  issues. The more senior bonds have the higher
  priority in bankruptcy and/or liquidation.
• Sinking fund provision issuer may be required
  to retire a certain amount of an issue each year.
  For example, having to retire 10 of a 20 year
  bond issue each year from year 11 to year 20.
• Bond contract (indenture) a legal contract
  between the issuer and bondholders that specifies
  all of the terms and conditions of the bond issue.

20
Evaluating default riskBond ratings

• Bond ratings are designed to reflect the
  probability of a bond issue going into default.
  The lower the rating (the higher the default
  risk), the higher the required yield.
• AAA or Aaa bonds have the highest rating.
• Depository institutions, e.g., commercial banks
  and Savings Loans may only own Investment Grade
  bonds.

21
Common stock basics

• Common stock represents the ownership of a
  corporation.
• The holders of debt or bonds have a senior claim
  on the firm.
• Stockholders have a residual claim, what remains
  after other obligations met, including any new
  asset investment in the firm.
• Stocks are risky investments however, we seek to
  understand the basics of stock valuation and how
  to price the risk.
• Current stock prices reflect todays expectations
  of future cash flow performance of firms and the
  risk of these cash flows.
• Expectations concerning future performance can
  never be proven in the present.
• Firms pay out excess (residual) cash to
  shareholders primarily as (1) cash dividends
  and (2) share repurchases.

22
Common stock basics

• The primary focus here is placed on Intrinsic
  Value. Intrinsic Value is the Present Value of
  all future forecasted cash flows.
• We define Free Cash Flow to Equity (FCFE) as the
  firms excess cash flow that can be paid out
  through both dividends and stock repurchases.
• We calculate the PV of all future forecasted FCFE
  at a discount rate or cost of equity capital r
  that is (assumed to be) estimated using the
  Capital Asset Pricing Model (CAPM) which will be
  covered in Chapter 10.

23
Common stock basics

• Many tend to either overcomplicate the mechanics
  of stock valuation or unfortunately insert
  misconceptions and/or pseudoscience into the
  analysis.
• For simplicity here, we will assume that all the
  FCFE is paid as a cash dividend, and thus the
  stocks intrinsic value today (V0) is the PV of
  all future forecasted dividends. The timeline
  and TVM valuation equation always resembles the
  following.

t0
t1
t9
t2
t10
t11
V0 ?
D1
D2
D9
D10
D11
24
Intrinsic value (V) versus actual market prices
(P)

• Intrinsic values are usually privately obtained
  estimates of value, here using discounted cash
  flow (DCF) analysis.
• The term V (usually designated as V0) is used
  extensively here since stock valuation is a
  private effort. V0 is thus something we can
  estimate but not prove.
• In efficient capital markets, on average, the
  market value or price P0 should equal the
  intrinsic value V0.
• Note the total value of any firms equity is
  always the value per share times the total number
  of shares.
• Most of our analysis here is done on a per share
  basis.

25
Valuation of a Constant Growth common stock

• The term constant growth indicates that a firm is
  mature and is expected to grow at an assumed
  constant rate g throughout the future.
• The term growth rate typically refers to the
  growth of the firms cash dividends however,
  everything associated with the firm is also
  assumed to grow at the same rate g.
• If a firm is expected to have a variable rate of
  growth in the coming years, then constant growth
  valuation is not appropriate. However, we will
  always assume that constant growth does begin
  somewhere out in the future.

26
Example valuation of a Constant Growth common
stock

• A mature firm just paid a dividend of D05 per
  share today and is expected to have a constant
  growth rate of g5 per year forever. Based on
  the stocks perceived risk, the stock has a
  required return of r14 per year.

27
Example valuation of a Constant Growth common
stock, continued

• Given the dividend growth rate g5 per year, now
  forecast the dividends for the following years
• D0 5.00 (given with example)
• D1 D0(1g) (5.00)(10.05) 5.25
• D2 D0(1g)2 (5.00)(10.05)2 5.5125
• Dn D0(1g)n
• The D05.00 per share has already been paid out
  and is no longer part of the firm.
• The intrinsic value V0 of the stock will be the
  Present Value of all the future forecasted
  dividends, beginning with D1.

28
Example valuation of a Constant Growth common
stock, continued

• We use the Constant Growth model (introduced in
  Chapter 4) to calculate the Present Value. The
  intrinsic value of any currently assumed constant
  growth stock or investment is
• V0D1/(k-g), plugging in the numbers we have
• V0D1/(r-g) 5.25/(0.14 0.05) 5.25/0.09
  58.33
• If D05 has not yet been paid out, then the
  stock value would be 58.33 5.00 63.33 per
  share (cum dividend).
• Thus this stock should be worth 58.33 today if
  the firm is expected to have a permanent growth
  rate of 5 per year and next years dividend at
  t1 years is 5.25 per share.

29
The constant growth model

• A more general form of the constant growth model
  is given below
• VtDt1/(r-g) assuming that capital markets are
  efficient we often reexpress this relation as
  PtDt1/(r-g)
• For the equation to work (1) r must exceed g and
  (2) all dividends following the dividend in the
  equations numerator must grow at a constant rate
  g.
• This equation above will always give you the
  stock value, exactly one year before the dividend
  that you plug into the model. If you plug in the
  dividend expected at t30 years, then the
  equation gives you the value at t29 years.

30
What will be the value of this stock exactly one
year from today?

• From previously, we know that r14, g5, and
  D05, D15.25, and D25.5125.
• The constant growth equation, VtDt1/(r-g),
  calculates the stocks value, exactly one year
  before the dividend that is plugged into the
  equation. The dividend exactly two years from
  today is estimated to be D25.5125 at t2 years.
• V1 D2/(r-g) 5.5125/(0.14-0.05) 61.25
• This stock is predicted to rise in value (or
  perhaps price) from 58.33 today to 61.25 in
  exactly one year (t1 years).
• We thus forecast that in one year (t1), the
  stock will be worth 61.25 per share just after
  it pays out D15.25.

31
What will be the stocks estimated value in
exactly one year? A second approach.

• An alternate method to estimate the future price
  of a constant growth stock Everything
  associated with the firm is expected to grow at
  the rate g5 per year forever, including the
  stocks value!
• Therefore, V1 V0(1g) 58.33(10.05) 61.25

32
The two components of a stocks total return on
investment

• The return on the stock comes in two components
• Cash dividends
• The change in stock price (capital gain or loss)
• Lets assume efficient markets for this case
  (where on average, P0V0,) for any constant
  growth stock we have the following relation P0
  D1/(r-g).
• Rearrange the equation to yield the following
  relation in terms of total return, we have r
  (D1/P0) g
• The first part is D1/P0, the dividend yield
• The second part is g, the capital gains yield

33
The two components of a stocks total return r
(D1/P0) g

• We have the following (previously) D15.25,
  P058/33, and g5. Solving the above equation,
  we have a known result
• k (D1/P0) g (5.25/58.33) 0.05 0.09
  0.05 14
• If we pay 58.33 today for this stock, then the
  expected 14 return comes to us as
• (1) a 9 dividend yield and (2) a 5 capital
  gains yield, which is a 5 increase in stock
  price from 58.33 to 61.25.

34
How todays stock values (or stock prices) can
change

• Example 1 Assume that r increases from 14 to
  16 because investors demand a higher risk
  premium from the stock.
• V0D1/(r-g) 5.25/(0.16 0.05) 47.73
• Example 2 Assume that r decreases from 14 to
  12 because investors demand a lower risk premium
  from the stock.
• V0D1/(r-g) 5.25/(0.12 0.05) 75.00
• What really changed above? It was not the future
  cash flow amounts, but rather the required
  return, due to risk premium changes.

35
The valuation of nonconstant growth stocks (most
stocks!)

• Most stock analysts using an Intrinsic Value
  analysis will forecast the following for most
  stocks that they cover
• Ten (10) future years of individual cash flows
  that can be paid out to stockholders. Refer to
  the valuation model at bottom of slide.
• A terminal value, i.e., what the stock will be
  worth in exactly 10 years (V10), assuming
  constant growth (maturity) at rate g following
  year 10.
• The stocks intrinsic value is then the sum of
  the PVs of D1 through D10 and the PV of the
  terminal value V10D11/(r-g).
• A good approximation for the constant growth g
  (at maturity) for a firm is expected future
  inflation plus the real expected rate of economic
  growth in GDP.

36
An example of nonconstant growth valuation

• Cirrus Corp. is expected to pay out the following
  dividends, per share
• D0D1D2D30, D40.50, D50.65, D60.80,
  D70.90, ad D81.00. Timeline appears on next
  slide.
• All dividends following year 8 or D8 will grow at
  g6 per year forever. This means that D9
  D8(1g) 1.00(10.06) 1.06, although this
  amount wont be needed. We are also simplifying
  the example by assuming that maturity begins at
  t8 years.
• Lets just assume here that the firms stock has
  r10 per year.

37
An example of nonconstant growth valuation,
continued

• A timeline of the stocks dividends is shown
  below.
• The salient item here is D8, since all dividend
  growth after t8 years will be at g6 per year
  forever. We can use this information to forecast
  the stocks value exactly three years from now
  (at t7 years).
• V7 D8/(r-g) 1.00/(0.10 0.06) 25.00

t0
t1
t3
t2
t4
t5
t6
t7
t8
D10
D20
D30
D81.00
D50.65
D40.50
D60.80
D70.90
g6
38
An example of nonconstant growth valuation,
continued

• The current intrinsic value V0 will be the
  Present Value of D1, D2, D3, D4, D5, D6, D7 and
  V7 (Terminal Value). As given previously, V7
  D8/(r-g) 1.00/(0.10-0.06) 25.00

39
Nonconstant growth another example

• XYZ Corp. currently pays no dividends.
• XYZs first forecasted dividend is 18 years from
  today at t18 years, and is expected to be
  D186.00 per share. Note that D0 through D17
  are all forecasted to be zero. All dividends
  past t18 years are forecasted to grow at g7
  per year.
• The stock has a required return r14.

t0
t1
t17
t2
t18
t19
D10
D20
D170
D186.00
D19
g7
40
Nonconstant growth another example, continued

• XYZ pays the first dividend at t18 years. Using
  the constant growth formula, we can estimate the
  value of XYZ shares at t17 years, since constant
  growth occurs following year 18.
• Step 1 V17 D18/(k-g) 6.00/(0.14 0.07)
  85.7143
• Step 2 V0 V17/(1k)17 85.7143/(10.14)17
  9.24
• The stock is forecasted to be worth 85.71 per
  share exactly 17 years from today (t17).
  Todays PV0 of this year 17 value of 85.71 is
  9.24

41
The Corporate Valuation Model or Free Cash Flow
(FCF) Model

• Most financial analysts use the FCF model. FCF
  is the cash that can be paid out to the firms
  investors, both the debt and equity holders.
• The FCF model will give a value that is the total
  value of the firms capital, i.e., the sum of
  both debt and equity. Note the following items
• Earnings before interest and taxes EBIT
  Revenues - Costs
• Net operating profit after tax NOPAT EBIT(1 -
  Tax Rate)
• FCF NOPAT - net new investment in operating
  capital.
• The appropriate TVM discount rate is the firms
  total cost of capital both debt and equity. In
  Chapter 12, we will cover the Weighted Average
  Cost of Capital or WACC.

42
The Corporate Valuation Model or Free Cash Flow
(FCF) Model

• The above model looks very similar to the
  dividend model we covered. However, the V0
  estimated here is the total firm value or
  enterprise value of the firm.
• To obtain the equity value, the debt value (and
  preferred stock value) must then be subtracted
  from the total value. To obtain value per share,
  divide by the number of shares.
• Many assumptions enter into valuation, so equity
  estimates using the FCF method may differ from
  those using the FCFE/Dividend model we covered.

43
How new stock is usually issued in the U.S.
capital markets

• The firm usually goes to an Investment Banker
  such as Merrill Lynch, Salomon/Smith Barney, etc.
  
• The investment banker usually underwrites the
  issue purchasing the entire stock issuance from
  the firm and reselling it to the initial
  investors (The markup averages around 7).
• Initial Public Offering (IPO) a privately held
  firm issues publicly traded stock for the first
  time. Needless to say, there is a lot of
  uncertainty in valuing many of IPO firms.
• Seasoned Equity Offering (SEO) an already
  publicly traded firm issues additional stock,
  which we refer to as external equity.