Yield to Maturity + Bond Amortization + Excel by cwq19948

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									Interest Rates and Bond
Valuation
  Chapter 6
Key Concepts and Skills
   Know the important bond features and
    bond types
   Understand bond values and why they
    fluctuate
   Understand bond ratings and what they
    mean
   Understand the impact of inflation on
    interest rates
   Understand the term structure of interest
    rates and the determinants of bond yields
                                                2
Chapter Outline
 Bonds and Bond Valuation
 More on Bond Features
 Bond Ratings
 Some Different Types of Bonds
 Bond Markets
 Inflation and Interest Rates
 Determinants of Bond Yields


                                  3
Issuer (Seller) of Bonds (Borrower) = “Bond
Issuer”
   Bonds = Debt = Liability = Long-term debt
       1 Bond usually means the corporation borrows
        $1000 (face value)
       Corporations usually issue many Bonds
            Bond Issue:
               The total number of bonds that a corporation issues
                at the same time, in denominations of $1,000 or
                $5,000 each
   Like any contractual debt:
       Bond issuer pays periodic interest to the
        bondholder
       Bond issuer pays the face value back at the end
        of the bond term
                                                                  4
Issuer (Seller) of Bonds (Borrower) = “Bond
Issuer”
   When you issue a bond, you borrow the
    money, then use the money to buy assets
    that earn more cash than the cash you have
    to pay out to the bondholder
   Leverage
      Example:
         Borrow money at 8% interest and buy a
          machine that earns the corporation 13%
         The difference between 13% and 8%, or 5%,
          is left for the stockholders

                                                  5
Buyer of Bonds (Lender) = “Bondholder”
    Bonds = Asset
        1 Bond usually means the borrow lends
         money to the corporation or government
    Like any contractual debt:
        Bondholders are paid periodic interest for
         loaning money to the corporation and are
         paid back the face value at the end of the
         bond term
    When you buy a bond you are paying
     for a future steam of cash flow


                                                      6
Bond Vocabulary:
   Face value = par value = loan repayment at maturity =
    FV
   Annual interest payments = “annual coupon”
       Coupon is from the days when you presented coupon to get
        paid interest
   Annual interest rate (not discount rate) = coupon rate =
    annual interest rate for calculating interest payments =
    annual coupon/face value
   Number of interest payments per year = n
   Periodic rate (not discount rate) = periodic coupon rate
    = (annual coupon rate)/n
       The book is inconsistent with the use of “coupon” (sometimes
        annual, sometimes semi-annual)
   Periodic interest payment = periodic rate*face = PMT
   Years until maturity = term of bond = years until paying
    back face value and last periodic interest payment = x
   Maturity = specified date on which principal is repaid

                                                                   7
Bond Vocabulary:
   Yield To Maturity (YTM) = discount rate
    used to value bond = i = YTM
       YTM = Bond Yield = Required Return =
        Market Rate = Rate required in the market on a bond
   YTMs are quoted like APRs
       YTM = (Period Discount Rate) * n

   Example: YTM = 10% and bond pays
    semiannual interest payments, then
    period discount rate = YTM/n = .10/2
    =.05
       Effective Annual Yield on the Bond =
        (1+.10/2)2 = .1025

                                                              8
Bonds
   Bonds are interest only loans
      Corporations/Governments borrow money,
       pay interest each period, then pay back face
       amount at end of bond term
   Corporations/Governments plan to issue bonds
    and then set the coupon rate, but by the time
    they actually issue the bond the financial
    markets have already calculated a discount rate
    for the future values that is often different than
    the coupon rate
   Corporations/Governments issue bonds and get
    the “cash in” (Bonds sold in primary market)
   Many Bonds from Corporations/Governments
    can be traded in the financial markets (Bonds
    sold in the secondary market)
                                                         9
Bonds
   Each bond has a price expressed as a
    percentage of the face value:
     For example, 103 means 1.03 times the
      face value of the bond
     When the corporation issues the $1,000
      face-value bond, it receives $1,030
     At maturity, the corporation pays back
      only the face value of $1,000
     103 and 103% and 1.03 all convey the
      same meaning  The bond is selling for
      3% above the face value

                                               10
    Example 1
   On January 1, Cox Construction Corp. issues 750
    10-year bonds with a face of $1000 with a coupon
    rate of 9% at 103, with interest payable
    semiannually, on June 30 and December 31


                 Cox Construction Corporation
    Face Value = 750 * $1,000 =               $750,000.00
    Bond Annual Interest Rate                     9%
    Years Until Maturity                           10
    Percentage Of Face Value                      1.03
    Semiannually (2 Times A Year)                   2
    Interest Payment Date                       June 30
    Interest Payment Date                     December 31
                                                            11
This Bond with its 9% coupon, is priced to yield 8.74%
at $1,030
             Amount Of Cash Bondholder Pays Bond Issuer
      Face Value = 750       Percentage Of
                         x                    =      Bond Price
          * $1,000 =           Face Value
        $750,000.00      x         1.03       =     $772,500.00
                         Yearly Interest Payment
      Face Value = 750        Bond Annual          Yearly Interest
                         x                    =
          * $1,000 =          Interest Rate           Payment
        $750,000.00      x          9%        =      $67,500.00
       Periodic Cash Interest Payment (Due June 30 & Dec. 31)
                                                   Periodic Cash
       Yearly Interest      Semiannually (2      Interest Payment
                         ÷                    =
           Payment           Times A Year)        (Due June 30 &
                                                       Dec. 31)
         $67,500.00      ÷           2        =      $33,750.00
                 Total Number Of Payments To Be Made
         Years Until        Semiannually (2       Total Number Of
                         x                    =
           Maturity          Times A Year)            Payments
              10         x           2        =          20
                                                                     12
But If The Loan Has A Face
Value Of $750,000, Why Did
The Bondholder Pay
$772,500?

                             13
   If a corporation offers a rate of interest that is
    higher than the market rate for similar securities,
    investors may be willing to pay a premium for the
    bond
   If a corporation offers a rate of interest that is
    lower than the market rate for similar securities,
    investors will demand a discount on the bond
            YTM (Market) Rate For Similar Securities
           6%                8%                 10.0%



                       Interest Rate On Bond
           8%                    8%                 8.0%



      Record Bond At       Record Bond          Record Bond At
         Premium         Without Pre. Or Dis.      Discount
                                                                 14
What Are Similar Securities?
   Similar securities are bonds or other
    investment vehicles issue by other
    corporations (different than the one being
    considered) that have similar business
    and financial risks

   The similarities could be:
     Similar credit ratings
     Similar business activities
     Similar capital structure


                                             15
Bond Prices
                        Selling Price For Bond
    Below 1.00                    100                 Above 1.00
(Example: 93 or 0.93)      (Example: 1.00)       (Example: 107 or 1.07)



  Record Bond At        Record Bond With No         Record Bond At
     Discount           Premium Or Discount            Premium




YTM > Coupon Rate                                YTM < Coupon Rate




                                                                     16
Definitions
   Premium
     The excess of the price received over
      the face value of a bond
     YTM < Coupon Rate
     “Bond sold at a premium”

   Discount
     The amount by which the issue price is
      less than the face value of a bond
     YTM > Coupon Rate
     “Bond sold at a discount”
                                               17
    The Issuance of Bonds at a
    Discount: Example 2
   On January 1, Muller, Inc., issues 700 6%, 20-year
    bonds with a face value of $1,000, at 96, with
    interest to be paid semiannually, on June 30 and
    December 31
                          Muller, Inc.
        Face Value = 700 * $1,000 =    $700,000.00
        Bond Annual Interest Rate          6%
        Years Until Maturity                20
        Percentage Of Face Value           0.96
        Semiannually (2 Times A Year)        2
        Interest Payment Date            June 30
        Interest Payment Date          December 31
                                                     18
This Bond with its 6% coupon, is priced to yield
6.25% at $960

                    Amount Of Cash Bondholder Pays Bond Issuer
        Face Value = 700 *        Percentage Of Face
                              x                          =       Bond Price
             $1,000 =                      Value
           $700,000.00        x            0.96          =      $672,000.00
                                         Discount
        Face Value = 700 *
                               -       Bond Price        =        Discount
             $1,000 =
           $700,000.00         -      $672,000.00        =       $28,000.00
                                 Yearly Interest Payment
        Face Value = 700 *        Bond Annual Interest         Yearly Interest
                              x                          =
             $1,000 =                      Rate                   Payment
           $700,000.00        x             6%           =       $42,000.00
               Periodic Cash Interest Payment (Due June 30 & Dec. 31)
                                                           Periodic Cash Interest
          Yearly Interest           Semiannually (2
                              ÷                          = Payment (Due June
             Payment                 Times A Year)
                                                               30 & Dec. 31)
            $42,000.00        ÷              2           =       $21,000.00
                        Total Number Of Payments To Be Made
                                    Semiannually (2          Total Number Of
        Years Until Maturity x                           =
                                     Times A Year)                Payments
                20            x              2           =           40
                                                                                    19
                              Bond Valuation

Bond Price (Valuation) from     1) Present Value of Principal Paid at Maturity Date (Bond’s Face
                                   Value):


  Cash Flow Perspective       PV of Lump Sum Deposited (Present Value of Loan Principalor Bond’s
                              Face Value) (Chapter 6)

                                            FVLS
                              PVLS =               n*x
                                          i
                                         1+ 
                                          n
                                2) Present Value of All Future Periodic Interest Payments:

                              PV of regular payments at regular intervals (Valuation for contractual
                              Bond Payments) (Chapter 6)
                                                         -(n*x)
                                                i
                                           1 - 1+ 
                                     = PMT* 
                                                  n
                              PVAn
                                                i
                                                 
                                                n
                                3) Present Value of Principal Paid at Maturity Date & Present Value
                                   of All Future Periodic Interest Payments (Chapter 6):
                                                                                                -(n*x)
                                                 FVLS i                               i
                                                                                 1 - 1+ 
                                       PVLS = 1-(1+n*x)-(n*x)
                                                                           = PMT* 
                                                                                          n
                                   + FV= 1+ n PV+
                              PVLS = PVAn LS PMT* i  i
                                           =                An
                                                                                        i
                                         i         
                                     (1+ )n*x  n  n                                   n
                                                                                                         20
                                        n
Excel
   Bond Valuation from Bondholder’s
    Point of View:
       =PV(rate,nper,pmt,fv,type)
       =PV(YTM/n,n*x,PMT,FV,0)
   Bond Valuation from Bond Issuer’s
    Point of View:
       =PV(rate,nper,pmt,fv,type)
       =PV(YTM/n,n*x,-PMT,-FV,0)

   Finding YTM rate from Bondholder’s
    Point of View:
       =RATE(nper,pmt,pv,fv,type,guess)
       =RATE(n*x,PMT,-PV,FV,0)
                                           21
 Example 3
                                          Assumptions
       # of Bonds                                                                    800
       Face Value                                                   $          1,000.00
       Date Issue                                                               1/1/2004
       Interest Payment Dates                                                  6/30/2004
                                                                              12/31/2004
       Bond Coupon/Interest Rate                                                8.0000%
       Number Of Periods Per Year (semi annual)                                         2
       Years Until Bond Matures                                                       20
       Annual Market Rate = YTM                                                 7.0000%




Bond Valuation: how much cash in will the coporation get when it issues the bond and the
price is 110.68% and the (YTM) Market Rate Per Period (Discount Rate) is 3.50%?

 $885,420.29                                                ……
PV                                                                                           Years
            0             1           2           3           4          39              40
                (32,000.00) (32,000.00) (32,000.00) (32,000.00) (32,000.00)     (32,000.00)
                                                                               (800,000.00)


                                                                                              22
Example 3
                                                           -(n*x)
                         FVLS i                     i
                                               1 - 1+ 
              PVLS = 1-(1+n*x)-(n*x)                n
              FV = 
          + PVAn LS PMT* i  n PV+ An   = PMT*
     PVLS =      =                                    i
                i n*x 1+ n  i
            (1+ )                                   n
               n              n

                              1 - 1+.035
                                                                -(2*20)
       800,000
 =            PV 
            2*20 An = 32,000*
   1+.035                          .035
   = 202,057.97 
      PVLS =                       683, 362.31
   = 885,420.28




                                                                          23
Example 3                                CF Is From Point Of View Of Issuer




         40             0.035        885,420.29      -32,000.00   -800,000.00
                                        PV             PMT            FV
         n             YTM/n



                                Calculated Amounts
Bond Face Value                                                      $800,000.00
Total Periods For Bond (# of PMT)                                             40
Bond Coupon Rate Per Period                                                4.00%
Bond Interest Payments Per Period                                     $32,000.00
(YTM) Market Rate Per Period (Discount Rate)                               3.50%
Price Of Bond                                                        $885,420.29
Premium                                                               $85,420.29

News Paper Price Quote = $885,420.29/$800,000.00                           110.68%


                                                                                24
Bond Values And Why They Fluctuate
 Bond Valuation:
   As time passes, interest rates change
    in the market place
      As new information about the company,
       the industry, the economy comes out,
       interest rates change
   As time passes the amount of cash
    paid out to the bondholder does not
    change
   Because of this the value of the bond
    will fluctuate
   Rates , Bond Value 
   Rates , Bond Value 

                                               25
Graphical Relationship Between
Price and YTM
1500
1400
1300
1200
1100
1000
 900
 800
 700
 600
    0%   2%   4%   6%   8%   10%   12%   14%
                                          26
Valuing a Discount Bond with Annual
Coupons Payments (Example 4)
   Consider a bond with a coupon rate of 10% and coupons paid
    annually. The par value is $1000 and the bond has 5 years left
    until maturity. The yield to maturity is 11%. What is the value
    of the bond  What is the price to you, buying in the
    secondary market?
     Using    the formula:
        B = PV of annuity + PV of lump sum
        B = 100[1 – 1/(1.11)5] / .11 + 1000 / (1.11) 5
        B = 369.59 + 593.45 = 963.04

     Answer:   “You would be willing to pay $963.04
      cash out (negative) for the future cash flows.” or
      said this way: “The bond with a 10% coupon is
      priced to yield 11% at $963.04.”                         27
Valuing a Premium Bond with Annual
Coupons Payments (Example 5)
   Suppose you are looking at a bond that has a 10% annual
    coupon rate and a face value of $1000. There are 20 years
    to maturity and the yield to maturity is 8%. What is the
    value of the bond  what is the price to you?
     Using     the formula:
          B = PV of annuity + PV of lump sum
          B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20
          B = 981.81 + 214.55 = 1196.36
     Answer:  “You would be willing to pay
      $1196.36 cash out (negative) for the future
      cash flows.” or said this way: “The bond
      with a 10% coupon is priced to yield 8% at
      $1196.36.”
                                                             28
Interest Rate Risk
   The risk that arises for bond owners from
    fluctuating interest rates
   How much interest rate risk a bond has
    depends on:
       How sensitive its price is to interest rate
        change
            The sensitivity depends on two things:
               All things being equal, the longer the time to
                maturity, the greater the interest rate risk
               All things being equal, the lower the coupon
                rate, the greater the interest rate risk



                                                                 29
Interest Rate Risk And Time To Maturity




                                      30
Interest Rate Risk To Loss Of Principal (current price)
     Longer time to maturity
     1.   Small changes in market rate have
          substantial affect on bond value
     2.   Face value is discounted over many periods
          and thus compounding magnifies small
          interest rate changes
     Lower Coupon rate
     1.   Bond with lower coupon rate is
          proportionally more dependent on the face
          value
             (Bond with larger coupon rate has a larger
              cash flow early in life, so value less sensitive
              to discount rate)
                                                                 31
Interest Rate Risk Increases At A
Decreasing Rate
                      12%

                      10%
 Interest Rate Risk




                      8%

                      6%

                      4%

                      2%

                      0%
                            0   5   10    15          20     25   30   35
                                         Years To Maturity




                                                                            32
Computing YTM
 Yield-to-maturity   is the rate implied by the
  current bond price
 Finding the YTM requires trial and error
  (iteration) if you do not have a financial
  calculator and is similar to the process for
  finding i with an annuity
 If you have a financial calculator, enter N, PV,
  PMT and FV, remembering the sign convention
  (PMT and FV need to have the same sign, PV
  the opposite sign)
                                                33
YTM with Annual Coupons (Example 6)
Consider a bond with a 10% annual coupon rate, 15
years to maturity and a par value of $1000. The current
price is $928.09
   Will the yield be more or less than 10%?




                                                          34
YTM with Semiannual Coupons (Example 7)

•Suppose   a bond with a 10% coupon rate and semiannual
coupons, has a face value of $1000, 20 years to maturity
and is selling for $1197.93
     the YTM more or less than 10%?
   •Is

   •What is the semiannual coupon payment?

   •How many periods are there?




                                                      35
Use One Bond YTM To Find Price Of Another
Bond: Example 8
                        Similar Bonds have similar YTM rates
                                              Bond 1       Bond 2
              Settlement date (day sold)       10/22/2005 10/23/2005
  Below       Maturity Date                    10/22/2017 10/23/2017
  Market      Years to Maturity                         12          12
  rate =      Coupon Rate                             10%        12%




                                                                         Above = premium
 discount     Face Value                           $1,000     $1,000
              Semi Annual                                2           2
              Interest Payment                        $50         $60
              Dollar Bond Price                     935.08 $1,066.68
              Bond Price                          0.93508
              Discount Period Rate                  5.49%
              YTM = Discount Period Rate*2
              = 5.49%*2 =                          10.99%     10.99%




                                                                              36
Bonds and Stocks:
   Like stock, bonds bring capital
    (money) into the corporation so that it
    can invest in profitable projects
       Bondholders are creditors
          They have a fixed claim to cash flow
       Stockholders are owners
          They have a residual claim to cash flow




                                                     37
Bonds and Stocks
   Debt is not an ownership interest in the firm
       Creditors do not have voting rights
   Interest is tax deductible
       Dividends are not tax deductible
   Unpaid debt is a liability
       Legal claim against assets
       If debt is not paid creditors have the legal claim to
        assets before shareholders
       One of the costs of issuing debt is the possibility that
        you will not be able to make interest payments 
        creditors force firm into bankruptcy  firm is
        terminated
           This does not arise when equity is issued
       Corporations try to create hybrid financial instruments
        that are Debt/Equity in order to have:
           Tax benefits of debt
           Bankruptcy benefits of equity


                                                                   38
Differences Between Debt and Equity
   Debt                                      Equity
       Not an ownership interest                Ownership interest

       Creditors do not have voting             Common stockholders vote for
        rights                                    the board of directors and other
       Interest is considered a cost of          issues
        doing business and is tax
                                                 Dividends are not considered a
        deductible
                                                  cost of doing business and are
       Creditors have legal recourse if          not tax deductible
        interest or principal payments
        are missed                               Dividends are not a liability of

       Excess debt can lead to                   the firm and stockholders have
        financial distress and                    no legal recourse if dividends
        bankruptcy                                are not paid
                                                 An all equity firm can not go
                                                  bankrupt
                                                                               39
Bond Terms and Types
   Bonds = Long-term debt
       Privately placed
            Directly placed with the lender
       Public-issue bonds
            Offered to the public
   Finance jargon”
       Long-term debt = funded debt
       Short-term debt = unfunded debt
       Example: “A firm planning to fund its debt
        requirements may be replacing short-term
        debt with long-tern debt”
                                                 40
Bond Terms and Types
   Trustee (Investment Bank, other…)
       Appointed by the corporation to
        represent bondholders
         Must make sure terms are obeyed
         Must manage sinking fund

         Must represent bondholders in default

   Indenture
       “The written agreement between the
        corporation and the lender detailing the
        terms of the debt issue”
                                                  41
Bond Types
   Registered Form
       The form of bond issue in which the registrar
        of the company records ownership of each
        bond
            Payment is made directly to the owner of the
             bond
   Bearer Form
       The form of bond issue in which the bond is
        issued without record of the owner’s name
            Payment is made to whoever holds the bond
            Uncommon in the USA



                                                            42
Bond Types
   Security:
     Generic term that means Stocks or
      Bonds or other investment vehicles
      that are backed by an asset
     A document indicating ownership or
      creditorship; a stock certificate or bond

       Dictionary definition of Security:
           Something deposited or given as
            assurance of the fulfillment of an
            obligation; a pledge; collateral

                                                  43
Bond Types
   Debt securities are classified according to the
    collateral and mortgages used to protect the
    bondholder
       Securities Backed By Collateral
          Collateral = any asset pledged on the debt (often
           means assets such as stocks or bonds – financial
           assets)
                   If the borrower does not pay the interest and
                    principal to the bondholder, the bondholder can
                    take the collateral
       Mortgage Securities
          Debt secured by a mortgage on real assets
           (property, but not cash or inventory) of the
           borrower
          Called:
             Mortgage Trust Indenture, or Trust Deed
   Most utility and railroad bonds are secured by a
    pledge of assets

                                                                      44
Bond Types
   Unsecured Debt
       These creditors have a claim on property not
        otherwise pledged
       Debenture
            Unsecured debt (maturity >= 10 years)
            Most financial and industrial companies’ public
             bonds are debentures
       Note
            Unsecured debt (maturity < 10 years)
   Subordinate Debt
       Must give preference to superior debt
       Debt is not subordinate to equity


                                                               45
Bond Types
   Sinking Fund
       An account managed by the trustee for the
        purposed of repaying the bonds, or early
        bond redemption
       Bond Issuer must put away some money each
        period to save up in order to pay off the bond
   Protective Covenant
       A part of the indenture limiting certain actions
        that might be taken in order to protect the
        lender
            Negative (thou shalt not):
               Example: Limit the amount of dividends paid
            Positive (thou shalt):
               Example: CA/CL must be greater than 1.5

                                                              46
Bond Types
   Call Provision
       An agreement giving the corporation the option to
        repurchase the bond at a specific price prior to
        maturity
   Call Premium (Pay for the Option)
       The amount by which the call price > par value
       Example: Bond face = $1,000, Call Price = $1,100
       Call Price goes down over time
   Deferred Call Provision
       Can call only after a certain date
   Call Protected Bond
       Can’t be redeemed by issuer
   Make-Whole Call
       When bond called, bondholder gets PV of future cash
        flows at a reasonable rate
   Derivative security jargon:
       Call = Buy
       Put = Sell
                                                              47
Financial Markets
   Primary Markets
       Original sale of equity or debt
       Corporation issues security
   Secondary Markets
       After original sale of equity or debt
       You sell/buy security
       Dealer Markets (Over-the-counter markets
        (OTC))
            Dealers buy and sell for themselves
            Most debt is sold this way
            Example: NASDAQ
       Auction Markets (Exchanges)
            Brokers and agents match buyers and sellers
            Most of the large firms’ equity is sold this way
            Example: NYSE

                                                                48
Bond Characteristics and Required
Returns
 The  coupon rate depends on the risk
  characteristics of the bond when issued
 Which bonds will have the higher coupon, all
  else equal?
   Secured debt versus a debenture
   Subordinated debenture versus senior debt

   A bond with a sinking fund versus one without

   A callable bond versus a non-callable bond


                                                    49
Bond Ratings And What They Mean
   Bond Rating firms:
       Moody’s
       Standard and Poor’s (S&P)
           They rate:
            1. The likelihood of default
            2. The probability that creditors are protected
           They ask they question: What is the risk associated
            with the firm issuing the debt?
           They do not rate the probability of bond value
            change due to interest rate risk
   The Debt Crisis of 2007 shows that
    Ratings can be less than accurate:
       How do they take risky loans and
        repackage them to get a AAA “Super
        Senior” rating? (That’s what they did!)
                                                              50
Bond Ratings – Investment Quality
   High Grade
     Moody’s Aaa and S&P AAA – capacity to pay is
      extremely strong
     Moody’s Aa and S&P AA – capacity to pay is very
      strong
   Medium Grade
     Moody’s A and S&P A – capacity to pay is strong, but
      more susceptible to changes in circumstances
     Moody’s Baa and S&P BBB – capacity to pay is
      adequate, adverse conditions will have more impact on
      the firm’s ability to pay
                                                          51
Bond Ratings - Speculative
   Low Grade
     Moody’s Ba, B, Caa and Ca
     S&P BB, B, CCC, CC

     Considered speculative with respect to capacity to pay.
      The “B” ratings are the lowest degree of speculation.
   Very Low Grade
     Moody’s C and S&P C – income bonds with no interest
      being paid
     Moody’s D and S&P D – in default with principal and
      interest in arrears
                                                            52
Some Different Types of Bonds
   Government Bonds
     Treasury Bill
        Years < 1
     Treasury Note
        1< years < 7
     Treasury Bonds
        Other
     No default risk
     Treasury issues are exempt from
      state income tax (must pay Fed IT)

                                           53
   U.S. NATIONAL DEBT CLOCK The Outstanding
    Public Debt as of 13 Nov 2007 at 11:28:01 PM
    GMT is:


                             Debt incurred per   Debt incurred per
            Total                   day              second
    $9,117,654,602,533.09   $1,400,000,000.00      $16,203.70



   The estimated population of the United States is
    303,525,093
    so each citizen's share of this debt is
    $30,039.21. The National Debt has continued
    to increase an average of
    $1.49 billion per day since September 29,
    2006!
                                                                     54
Some Different Types of Bonds
   Municipal Bonds “Munis”
       State and local government debt
            Example: Bond to build Highway
            These do have varying degrees of default risk
            Almost always callable
            Coupons exempt from federal income taxes
             (must pay State IT)
               Attractive to high-income/high-tax bracket
                investors
               Because of this the yields are lower
            Which do you (with 25% Fed tax Bracket)
             prefer: corporate bond that yields 5%, or a
             muni (with comparable risk and maturity) that
             yields 3.90%?
               .039 > .05(1-.25) = .0375

                                                             55
Some Different Types of Bonds
   Zero Coupon Bonds
       A bond that makes no coupon payments, and
        thus is initially priced at a deep discount
       Issuer must deduct interest every year
            Tax Benefit  A deductions for taxes (fewer
             taxes paid  like cash coming in) even though
             no cash going out (interest expense)
       Bondholder must accrue interest revenue
        every year
            Taxes paid on revenue  Cash going out
             (taxes paid) even though cash is not coming in
             (interest revenue)
       Regular amortization table is constructed to
        track interest accrual
                                                              56
Pure Discount Loans (Zero Coupon)
   Borrow an amount today, then pay back
    principal and all interest at the end of the
    loan period
   Example: US Government Treasury Bills,
    or T-bills (government loans < 1year)


                               FV
                      PV =           n*x
                              i
                             1+ 
      Loan amount             n          Payback
     received today                        Amount


                                                     57
Example 9:
Pure Discount Loans (Zero Coupon)




                                    58
Example 10:
Interest Only Bond v. Zero Coupon Bond

                 Interest Only Bond                                   Zero Coupon Bond
  Firm Needs:                     $10,000,000.00       Firm Needs:                   $10,000,000.00
  Years to Maturity                            20      Years to Maturity                          20
  Coupon Rate                                11%       Coupon Rate                              11%
  YTM                                        11%       YTM                                      11%
  Tax Rate                                   35%       Tax Rate                                 35%
  Compounding/year                             1       Compounding/year                           1
  Face Value =                            $1,000       Face Value =                          $1,000
                               1) How many Bonds do we need to issue?
                 Interest Only Bond                              Zero Coupon Bond
  Cash in for 1 bond = PVan +                          Cash in for 1 bond = PVan +
  PVls =                                   1,000.00    PVls =                                124.03
  Number of Bonds =                                    Number of Bonds =
  $10,000,000.00/1000 =                   10,000.00    $10,000,000.00/124.03 =           80,623.12
  Fewer Bonds issued today                             More Bonds issued today

                           2) What is FV and PV of cash flows to bondholder?
                 Interest Only Bond                                 Zero Coupon Bond
  FV = FVan + FV ls =                 $80,623,115.36   FV = FV ls =                  $80,623,115.36

  PV =                                $10,000,000.00   PV =                          $10,000,000.00




                                                                                                       59
 Interest Only Bond v. Zero Coupon
 Bond
                                                   3) Cash Flows

                               Interest Only Bond ==> Cash Flow to Issuers:
PV =$10,000,000                                                     …   …

              0                 1               2               3                        19                 20
                  ($1,100,000.00) ($1,100,000.00) ($1,100,000.00)           ($1,100,000.00)    ($1,100,000.00)
                                                                                              ($10,000,000.00)

                              Zero Coupon Bond ==> Cash Flow to Issuers:
PV =$10,000,000                                                     …   …

              0                1               2               3                        19                  20




                                                                                                       60
Interest Only Bond v. Zero Coupon
Bond
                              4) Actual Cash Going Out For Issuer:
              Interest Only Bond                                Zero Coupon Bond
Yearly Interest PMT                    $1,100,000.00
Years                                             20
Total Interest Paid                   $22,000,000.00
Amount Paid at Maturity               $10,000,000.00
Total Paid Out =                      $32,000,000.00              Total Paid Out =                        $80,623,115.36

                                                 Important Points
              Interest Only Bond                                                 Zero Coupon Bond

                  PV and FV of cash flows are the same, however, the timing of cash flows is different

This option implies that the company has the cash to                This option implies that the company has a lack of
                       pay early                                            cash to pay back until the very end

                                                                    This option allows company to use cash to earn a
   This option requires that the company pays back                 return on the cash it borrowed early, but it must pay
         sooner and will thus pay less interest                       back more cash later and much more interest




                                                                                                                         61
 Interest Only Bond v. Zero Coupon Bond
                                         Interest Expense and Tax Rates
Tax Rate                                           35%

   Total Interest Expense =        After Tax Deduction    +              Tax Shield
            $13.6437               (1 - 0.35)*(13.6437)   +             0.35*13.6437
            $13.6437                       $8.87          +                 $4.78

               Interest Only Bond                                             Zero Coupon Bond
Coupon Rate                                     11.00%        Coupon Rate                        11.00%

Tax Expense                              $1,100,000.00        Principal on books                 $124.03
Tax Shield                                 $385,000.00        Interest Expense                    $13.64
Cash Outflow                               $715,000.00        Tax Sheild                          $4.78
                                                              Implied Cash Outflow                 $8.87
Actual rate given tax benefit of
deduction (compare actual cash
out to principal to show After
Tax Interest Rate ) =
715000/10000000 =                                0.0715       8.87/124.03 =                       0.0715
                 or                                                           or
Interest Rate times one minus
the tax rate = actual rate given
tax benefit of deduction = After
Tax Interest Rate =
0.11*(1 - 0.35) =                                0.0715       0.11*(1 - 0.35) =                   0.0715


                                                                                                 62
Floating-Rate Bonds
1.    Coupon Payments are adjustable
         Rated can be tied to an interest rate index
          such as the Treasury bill interest rate or 30-
          year Treasury bond rate
         Rate and payments are adjusted periodically
2.    Holder may have the right to redeem
      the note at par on the coupon payment
      date after some specified amount of
      time
     1.   This is called a “Put” Provision
3.    The coupon rate has a floor and ceiling
     1.   “Capped” or “Collared” means they have an
          upper and lower barrier
                                                       63
Other Bonds:
   Income Bonds:
       Coupon payments are dependent on the company
        income
   Convertible Bonds
       Debt that can be converted to a fixed amount of equity
        anytime before maturity at the holder’s option
          Half Debt half equity?

          How do you list it on the Balance Sheet?

   Put Bond
       Allows holder to force the issuer to buy the bond back
        at a stated price (reverse of a call)
   CoCo and NoNo Bonds
       These have many features that require complex valuing
        techniques. Because the features can be valuable to
        the bondholder, the YTM could be negative!
                                                                 64
Bond Markets
   Because the bond market is almost entirely OTC,
    it has little or no transparency (can’t see a great
    deal of Buy/Sells to gage market value of bonds)
   US Treasury market is the largest security
    market in the world
   Terminology:
       Bid Price
          The price a dealer is willing to pay for a security

       Ask Price
          The price a dealer is willing to take for a security

       Bid-ask spread
          Bid – Ask = Dealers Profit



                                                                  65
The Impact Of Inflation On Interest
Rates
   Inflation
       Increase in price over time
           Example:
              Price of milk now = $3.39/gal.
              Price of milk in 1 year = $3.56/gal.




                                                      66
Inflation and Interest Rates
   Real Rates
       Base interest rate that does not take inflation
        into consideration
       The percentage change in buying power
       Interest rates or rates of return that have
        been adjusted downward from the nominal
        rate for inflation
   Nominal Rates
       Interest rates or rates of return that have not
        been adjusted downward for inflation
       % change in the number of dollars you have
       The nominal rate of interest includes our
        desired real rate of return plus an adjustment
        for expected inflation                          67
The Fisher Effect (Irving Fisher)
   The Fisher Effect defines the relationship
    between real rates, nominal rates and
    inflation

   R =r + h + r*h
   r = (R-h)/(1+h) = (1+R)/(1+h) - 1
   (1 + R) = (1 + r)(1 + h)

       R = nominal rate
       r = real rate
       h = expected inflation rate

   Approximation
       R=r+h
                                                 68
              Mike Price now                                          3.39
              How many milk do you buy?                                100
              Total price                                         $339.00

              Amount now in bank                                  $339.00
Example 11:

              APR (n=1) = R = Nominal                                10%
              Bank amount in 1 year                               $372.90

              Mike price in 1 year                                    3.56
              Milk Inflation = 3.39/3.56 =                        5.0147%

              Can you buy 10.00% more?                             110.00

              How many can you buy today = $372.90/3.56 =          104.75

              Real Rate = r = (0.1 - 0.050147)/(1 + 0.050147) =   4.7472%

              Real Rate of return is = how much more can we
              buy with our money!!!                               4.7472%
                                                                        69
Example 6.6
 Ifwe require a 10% real return and we expect
  inflation to be 8%, what is the nominal rate?
 R = (1.1)(1.08) – 1 = .188 = 18.8%

 Approximation: R = 10% + 8% = 18%

 Because the real return and expected inflation
  are relatively high, there is significant
  difference between the actual Fisher Effect and
  the approximation.

                                                70
The Fisher Effect
                     3 Components to Nominal
            R        =    r     +         h             +       r*h
                                     compensation
                                                             compensation
                                    for the decrease
                                                                for dollars
                                      in the value of
                                                               earned that
           Nominal       real       money originally
                                                               decrease in
                                          invested
                                                            value because of
                                        because of
                                                                 inflation
                                        inflation, h



   Real rate is hard to observe directly, so
    we observe it indirectly:
       r = (R-h)/(1+h) = (1+R)/(1+h) - 1
   Real Rate is fairly constant
   Take into consideration taxes:
       r (R*(1-taxrate)-h)/(1+h)
                                                                               71
The Term Structure Of Interest Rates
And Determinants Of Bond Yields
   The risks associated with loaning
    money are added into a “base”
    interest rate known as the real rate




                                           72
Bond Yields represent 6 effects:
   Some Components of Interest
    Rates:
    1.   Real Rate
    2.   Inflation Premium
    3.   Interest Rate Risk Premium
    4.   Default Risk Premium
    5.   Taxability Premium
    6.   Liquidity Premium

                                      73
Real Rate
1.   Compensation investors demand
     for foregoing the use of their
     money
2.   Basic component underlying every
     interest rate
3.   When real rate high, all rates tend
     to be high
4.   Doesn’t really determine shape of
     term structure (overall effect)
                                           74
Inflation Premium
1.   The portion of a nominal interest
     rate that represents compensation
     for expected future inflation
2.   Very strongly influences the shape
     of term structure
3.   Inflation expected increase 
     structure upward
4.   Inflation expected decrease 
     structure downward
                                          75
Interest Rate Risk Premium
1. Compensation    demanded for
   bearing interest rate risk
2. longer-term bonds have a much
   greater risk of loss resulting from
   changes in interest rate than so
   short-term bonds
3. This premium increases at a
   decreasing rate

                                         76
Term Structure Of Interest Rates (Based
On Pure Discount Bonds)
1.   This shows the relationship between short and
     long-term interest rates
2.   Tells us what the nominal interest rates are on
     default-free (Treasury), pure discount
     securities of all maturities
3.   This shows the relationship between nominal
     interest rates on default-free, pure discount
     securities and time to maturity
4.   These rates are “pure” because they involve
     no risk of default
5.   The term structure tells us the pure time value
     of money for different lengths of time
    Upward sloping = long-term rates > short-term rates
    Downward sloping = long-term rates < short-term rates
                                                         77
Upward-Sloping Yield Curve




                             78
Downward-Sloping Yield Curve




                               79
Term Structure Of Interest Rates
   Assumes:
     Real Rates remain constant
     Inflation linear

   Rates could be “Humped”
       Rates increase at first, but then decline
        as we look at longer-termed notes




                                                    80
Treasury Yield Curve
 A plot of the yields on Treasury
  Notes and Bonds relative to Maturity
 Treasury Yield Curve and the Term
  Structure Of Interest Rates re
  almost the same thing
       The difference is:
           Treasury Yield Curve
              Based On Coupon Bond Yields
           Term Structure Of Interest Rates
              Based On Pure Discount Bonds

                                               81
Treasury Yield Curve (Coupon Bond Yields)




                                        82
Default Risk Premium
1. Bonds  other than Treasury: Credit
   risk/default risk
2. The portion of a nominal interest
   rate or bond yield that represents
   compensation for the possibility of
   default
3. Lower rated bonds have higher
   yields

                                         83
Taxability Premium
1.   The portion of a nominal interest
     rate or bond yield that represents
     compensation for unfavorable tax
     status
        Remember municipal versus taxable
        Bonds that are taxed at both the state
         and Federal level are less favorable
         than a bond that is only taxed at the
         Fed. level

                                              84
Liquidity Premium
   The portion of a nominal interest rate or
    bond yield that represents compensation
    for a lack of liquidity
       Liquidity:
            How quickly an asset can be converted to cash
       Example:
            Maybe the bond is hard to sell quickly and
             therefore would require a premium for that lack
             of liquidity
   Less liquid bonds have higher yields than
    more liquid bonds
                                                             85
Three Principles in Bond Finance
1.    Rates are inversely related to price
     1.   Market rate , Bond Price 
2.    Par, Discount, Premium
         Market rate = Coupon Rate
             Bond sells at Par or Face Value
         Market rate > Coupon Rate
             Bond sells at a Discount
         Market rate < Coupon Rate
             Bond sells at a Premium
3.    The more years there are to maturity,
      the higher the interest rate risk
      becomes
     1.   “Interest rate risk to loss of principal”

                                                      86
Bond Vocabulary:
   Current Yield =
    Annual Interest Payment/Closing Price
       Not equal to YTM (unless bond sells for par); it
        does not include the capital gain from discounted
        face value (principal)
       Premium Bond
          CY >YTM

       Discount Bond
          CY <YTM

       In all cases (Current Yield) + (Expected
        one-period capital gain/loss yield of the
        bond) must be equal to the YTM
                                                       87
Securitization
   Securitization = “The process of Securitization
    involves the collection or pooling of loans and
    the sale of securities backed by those loans
    (Cash flows in loan)
       Whereas, Banks once made loans and kept them on
        their books, now they can initiate loans and then sell
        the loans to someone else.
   Securitization = packaging a set of cash flows
    and then selling claims (bonds or other) against
    them
      Claims = asset backed securities
            This means that the cash is the asset that backs
             it



                                                                 88

								
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