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					Introduction to Investment Analysis

         Valuation of Bonds
                  What are Bonds?
• Bonds are a form of long-term debt (Will mature in one year or less)
  that usually is secured by property, usually with an original maturity
  of twenty to thirty years. Also could be for five years, such as Emirates
• Unsecured bonds are called debentures. Maturity refers to the length
  of time that the bond will be outstanding.
• For coupon bonds, the issue promises to pay:
   – a fixed amount of interest periodically, annually or semi-annually
       if it is a coupon bond.
   – repay the principal on a specific date of maturity.
• For zero-coupon bonds, the issuer promises to pay:
   – only the face value at maturity.
   – There are no periodic interest payments for zero-coupon bonds.
        Who issues bonds?
• Bonds could issued by various levels
  of the government: At the Federal (no
  bonds in the UAE issued yet) and
  Emirate levels (Dubai 2003 will issue a
  AED 1.5 Billion bond), and by
  business corporations (e.g., Emirates
       Characteristics of Bonds
• The Par value, also known as the face value or
  maturity value, MV, of a bond or debenture and is
  a fixed amount (we will assume it to be AED
  1,000 always). This is the amount of principal to
  be repaid at maturity for each bond. The Par value
  of Emirates Airlines is equal to AED 100,000.
• The coupon interest rate, CR, is the stated annual
  rate of interest on the bond. A bond’s coupon rate
  never changes over the life of the bond, unless it is
  a floating rate bond such as that of Emirates
Characteristics of Bonds (Cont’d)
• When the annual interest of a bond is stated in
  Dirham terms, it is called the coupon payment
    CP  CR  MV
• For example, an offering of AED 400 million of
  30-year debentures that carries a coupon interest
  rate of 12.25% has an annual coupon payment per
  bond as follows:
•   CP         1000  AED122.5
                     Valuation of a bond
• Because the cash flows of a bond are a contractual payment of a fixed amount of
  interest (CP) over a certain number of years, plus the maturity value (MV), the
  formula to value a bond is as follows:

           D  CP ( PVIFA)  MV ( PVIF )
            0                  Kd ,n                     Kd ,n

 D = current market price of the bond.

CP= Periodic coupon interest at the end of the period
  K = required rate of return on the debt instrument

  n = number of periods remaining before the bond is redeemed
MV= Principal or face value or maturity value of the bond
           Valuation Example
• Page 29 of text.
• If the required rate of return is less than the
  coupon rate (the rate offered by the issuing
  company), the bond sells for less than par value.
• Bonds that sell at less than par value are said to be
  selling at a discount.
• Bonds that sell for less than par value are said to
  be selling at a premium.
         Some relationships

Relationship among required rates of return,
       Coupon rates, and Bond Prices
          If                  Then
                      Bond Sells at a
K  Coupon Rate
                      Bond will sell at par
K  Coupon Rate

K  Coupon Rate       Bond will sell at a
            Yield to Maturity
• The yield to maturity of a bond is that discount
  rate that equates the present value of the bond’s
  cash flows to the market price. It is the same as
  the bond’s internal rate of return (IRR).
• To illustrate, assume that a 10-year, AED 1,000
  year par value bond has an annual coupon rate of
  8%. If the bond’s current price is AED 935.80,
  what is the bond’s yield to maturity?
             YTM Calculation
• From the valuation model:

  D  CP ( PVIFA )  MV ( PVIF
     0             Kd , n               K d ,n

AED 935.80  100( PVIFA ) 1000( PVIF )
                              K d ,10
                                                  K d ,10

• Because the price is less than the par value, the
  YTM must be more than 8%.
• Use the IRR function in Excel to get a YTM =
 Valuation of Semi-annual Coupons
• Up to this point, our examples of bond price calculations
  assumed that interest is paid annually, but many bonds pay
  interest semiannually. The procedure discussed above to
  value bonds can still be used but with three modifications:
   – Convert the annual coupon payment to semiannual payment, by
     dividing it by 2.
   – Convert the number of years to maturity, n, to the number of six-
     month periods to maturity, by multiplying n by 2.
   – Convert the required return from an annual rate,K   d
                                                          to a
     semiannual rate, by dividing it by 2.
 Valuation of Semi-annual Coupons

• Substituting these changes into the equation
  D     ( PVIFA) MV ( PVIF )   kd

                kd                    ,2n
                     ,2n         2
   Value of a 30-year bond paying a
       4% semi-annual Coupon
b               Present value  Present
eSemi-annual    of coupon      value of   Price of
rrequired yield payments       principal  bond
             0%           2400       1000      3400
             2%    1390.435467  304.7823   1695.218
             4%     904.939599    95.0604      1000
             6%    646.4571082  30.31434   676.7714
             8%    495.0620729  9.875854   504.9379
            10%    398.6862919    3.28427  401.9706
            12%    332.9619714  1.114086   334.0761
Relationship between Price and yield

                     Relationship Between Price and Yield


          2000                                                        Series1
                 0   0.02    0.04   0.06   0.08   0.1   0.12   0.14
                            Semiannual Required Yield
Relationship between Price and yield

• when the required rate of return rises (falls),
  the value of the bond falls (rises).
• This inverse relationship is illustrated in the
  Graph above.
           Types of Bond Yields
•    There are five types of bond yields.

    1.   Coupon rate (also called the nominal yield),
    2.   Current yield,
    3.   Effective yield
    4.   Yield to maturity
    5.   Yield to call for callable bonds.
                   Coupon Rate
• The coupon rate is the interest rate used to calculate the
  periodic interest payment on the bond. It is set at the time
  the bond is issued and remains the same until the bond
  matures or is called back. It is calculated as follows:
   CR 

• CR = Coupon rate
• CP = Annual coupon or interest payment
• FV (MV) = Face value of the bond.
       Coupon rate Example
• suppose the annual coupon payment is AED
  100 and the face value is AED 1,000. The
  annual coupon rate would be:

   CR         0.10  10%
                  Current Yield
• The current yield is the ratio of the annual interest income
  to the current price of the bond. Unlike the coupon rate,
  the current yield varies with the price of the bond. Since it
  measures the interest per Dirham of investment of the
  bond, it is a better indicator of yield than the coupon rate.

• The current yield is calculated as follows:

    CY 
         Pr ice of bond
       Current Yield Example
• Assume that the annual interest payment is
  AED 100 and the current price of the bond
  is AED 980. The current yield would be:

Current yield       0.1010  10.10%
                    Effective Yield

• While the current yield is a better indicator of yield than the coupon
  rate, it is not an adequate measure of yield because it does not reflect
  capital gains or losses.
• The effective yield reflects not only the interest income from the bond
  but also any capital gains or losses.
                                       CP  ( P  P )
• One year effective Yield:      OEY                            1     0

                                            P                0
OEY = One-year effective yield
CP = Coupon Payment
P  Price of the bond at the beginning of the year

P  Price of the bond at the end of the year
        Effective Yield Example
• Assume the following data:             P  AED 970

Interest paid last year =AED 100 and     P  AED 990

• The One year effective yield is calculated as follows:

• OEY= 100  (990  970)  0.1237  12.37%

• Also referred to as the Annual Holding Period Return
Yield to maturity(Annual Coupon)

• The yield to maturity is the true yield if the bond is held until maturity.
• The true yield to maturity takes into consideration all the cash flows of
  the bond as well as the time value of money.
• The true yield to maturity for an annual coupon bond is calculated
  using the following equation:

                 CP         CP         CP                      FV
   Pr ice                                  .........
            (1  YTM ) (1  YTM ) (1  YTM )
                      1              2             3
                                                          (1  YTM )      n

• YTM= Yield to maturity
• N= number of years to maturity
• FV = Face Value
Yield to maturity(Semi-Annual Coupon)

              CP         CP            CP
               2          2             2                             FV
Pr ice                                        ............ 
          YTM   YTM   YTM                                   YTM 
                    1             2              3                           2n

         1       1       1                              1     
               2        2           2                           2 
• You need Excel or a financial calculator to solve for the Yield to
   maturity of a bond.

                 The End
• Long-term debt generally refers to debt that
  will mature in a year or more.

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