Bond by wanghonghx

VIEWS: 13 PAGES: 14

									                    Bond Valuation
Coverage
 Terms

 Calculations
   Bond Price and coupon
   Bond Yield


 Bond Price Relationship
   Price, Coupon rate, Interest rate, Maturity



                                                  1
                Issuer and Holder

                   Price of Bond
     Received                         Paid out

 Bond                                            Bond
Issuer                                           Holder
                   Periodic Coupon
                      Payments
Paid out
                                           Received


                        +
                   Principal Amount


                                                      2
                Bond Price

                Price of Bond
     Received                      Paid out

 Bond                                         Bond
Issuer                                        Holder
                Periodic Coupon
                   Payments
Paid out
                                        Received


                     +
                Principal Amount


                                                   3
                           Bond Price
      Because what you paid should be what you get, therefore;



                                              Periodic Coupon
                                                 Payments
Price of Bond


                                                    +
                                               Principal Amount

                             OR

Vb = PV of expected periodic coupon payment + PV of bond’s principal



                                                                       4
                Bond Terminology (1)
 Price (Vb)
   Value or price of bond
 Par Value
   The stated value, face value, principal, or maturity value
   Usually, par = $1,000
 Coupon Interest Payment (C)
   Issuer pays a specified $ amount of interest each year
    according to the stated coupon rate written on the bond
      Ex. A 6-year bond offers 10% interest rate compounded annually
          The periodic coupon payment would be $1,000 x 10% = $100
          Because the interest is compounded annually, our periodic payment
           will be $100/1 or $100 yearly

                                                                           5
              Bond Terminology (2)
 Rate of Return (Kb)
   Return required by investors on bonds or investments with
    comparable risk.
 Maturity Date
   The date when the principal of bond must be repaid
 Current Yield
   An annualized return of bond
   Ignore capital gain/loss and time value of money
 Yield to Maturity (YTM)
   An ANNUAL RETURN if investors hold bonds till maturity
   The interest rate that will make the present value of all
    cash flows equal to the price of the bond.
                                                            6
                     Bond Calculations
 1A) A 20-yr 10% annual coupon bond with a par value of
  $1,000 and the required yield on this bond is 14%.
     Vb = C(PVA 14%, 20) + M(PV14%, 20)
        = 100 x 6.6231 + 1,000 x 0.0728
        = 662.31 + 72.8
        = $735.11


 1B) A 20-yr 10% annual coupon bond with a par value of
  $1,000 and the required yield on this bond is 8%.

 1C) A 20-yr 10% annual coupon bond with a par value of
  $1,000 and the required yield on this bond is 10%.



                                                           7
                     Bond Calculations
 2A) A 20-yr 10% semi-annual coupon bond with a par value
  of $1,000 and the required yield on this bond is 14%.
      Vb = C(PVA 7%, 40) + M(PV 7%, 40)
        = (100/2) x 13.3317 + 1,000 x 0.0668
        = 666.59 + 66.8
         = $733.39




 2B) A 20-yr 10% semi-annual coupon bond with a par value
  of $1,000 and the required yield on this bond is 8%.

 2C) A 20-yr 10% semi-annual coupon bond with a par value
  of $1,000 and the required yield on this bond is 10%.


                                                         8
               Bond Relationships
 Yield – Price (Inverse relationship)

     Yield     > Price


 Yield – Coupon – Price
      if kb ,> coupon rate = sold at discount
      if kb ,< coupon rate = sold at premium
     if kb ,= coupon rate = sold at par

If you give us more than what we want, we will pay you more
Or coupon rate higher than required return.
                                                              9
                         Bond Relationship
 Bond with more frequent coupon payments
         20-Yr with 10% coupon                        20-Yr with 10% coupon
                     yield = 14%                                  yield = 8%
            Discount Bond                                Premium Bond
Annually                                 Annually
        20       100     14% 662.3131            20         100         8% 981.8147
                1000         72.76172                      1000            214.5482
                             735.0748                                      1196.363
Semi-annually                            Semi-annually
       40         50      7% 666.5854           40           50       4.0% 989.6387
                1000         66.78038                      1000             208.289
                             733.3658                                      1197.928
Quarterly                                Quarterly
        80        25    3.50% 668.7194           80          25       2.0% 993.6128
                1000          63.79285                     1000            205.1097
                              732.5122                                     1198.723

Monthly                                  Monthly
      240        8.33   1.17% 670.1402         240          8.33     0.67% 996.2858
                1000          61.80367                     1000            202.9714
                              731.9439                                     1199.257
                                                                                  10
                  Yield-to-Maturity
 Calculating YTM
      Trial and Error
      Use financial calculators
      Use software functions
      Use formulas (approximation)


YTM - The interest rate that will make the present value of all
         cash flows equal to the price of the bond.




                                                              11
              YTM vs. Current Yield
 YTM - the interest rate that       Current Yield - an
  will make the present value         annualized return of bond
  of all cash flows equal to         Good for person who only
  the price of the bond               concern about annual
 Good for person who                 income because:
  concern about total return            Consider only one source of
  because:                               bond income – annual coupon
    Consider two sources of bond        payment
     income                             Ignore potential capital gain or
    Take into account time value        loss at maturity
     of money                           Ignore time value of money




                                                                      12
       Bond Relationship Summary
 Yield – Price (Inverse relationship)

     Yield    > Price


 Yield – Coupon – Price
      if kb ,> coupon rate = sold at discount
      if kb ,< coupon rate = sold at premium
     if kb ,= coupon rate = sold at par
 YTM – CY – Price
    If YTM>CY = Discount (capital gain is received)
    If CY>YTM = Premium (ignore capital loss at maturity)
                                                             13
                Price vs. Value
 Undervalue vs Overvalue
   A bond is undervalued when the market price is
    lower than the bond value (or calculated value
    (Vb) – you buy it
   A bond is overvalued when the market price is
    higher than the bond value (or calculated value
    (Vb) – you sell it

  Hence, buy low, sell high.


                                                      14

								
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