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                                    A.     B.     C.

                                             o f 

                              B     O     N     D     S 




1.    What is a bond ?
2.    How are bonds issued and redeemed ? 
3.    How do we calculate the bond Yield ?
4.    Exercise 
5.    How do we calculate the bond Yield to Maturity ? 





1 )   WHAT IS A BOND ? 

A bond, is a receipt given by an institution or a company for a loan that you make to them. A loan always carry an interest rate coupon, and has to be repaid on a specific date, called here the " maturity date ". 

Once issued, bonds can be bought and sold freely on the market. Depending on the price paid for the bond, it is possible to make a profit or loss on the investment, in addition to earning interest.

If the bonds are kept to maturity, it is fairly easy to calculate the yield and the yield to maturity from the date and price when the bonds are bought.




2 )   HOW ARE BONDS ISSUED AND REDEEMED: 

Bonds are usually issued @ $ 1,000 and redeemed at maturity @ $ 1,000. Bonds usually pay interest twice a year except for " Eurobonds " who pay interest once a year.



3 )   BOND YIELD CALCULATIONS:


EXAMPLE: REAL GOOD, COMPANY, 10%, August 10, 2010.


Name of company: REAL GOOD, COMPANY
Coupon rate: 10%
Maturity date: August 10, 2010 


Length of bonds: 

Issue date: August 10, 1990, 
Maturity date: August 10, 2010. 


BOND YIELD:

To calculate the bond yield, we have to take the interest which is $ 100
( 10 % of $ 1,000 ) and divide it by the price of the bond. The bond yield is inversely proportional to the bond price. 

The higher the bond price, the lower the yield.
The lower the bond price, the higher the yield. 


Bond Yield:

Interest   ( $ ) 
-------------------          X  100 %   =   Yield 
Price of bond 


      $   100
      ----------               X  100 %   =   ( 10 % )
      $ 1,000 



The price at which you purchase the bond, as mentioned above, will change the yield of the bond.  Keep in mind that the interest paid by the bond in " dollar ", will never change.   Ie:  in the example $100.



PRICE        INTEREST       YIELD
----------        ---------------        ---------

$2,000             $ 100                 5 %          ($100 / $ 2,000 )   X   100 % 
$1,000             $ 100               10 %          ($100 / $ 1,000 )   X   100 % 
$   500             $ 100                20 %         ($100 / $    500 )   X   100 % 



4 ) EXERCISE:

If you are so incline, try to work out the yield on the bond prices below.
The answers can be found at the end of this article.


PRICE             INTEREST            YIELD
----------             ---------------             ----------

$ 1,800                 $ 100                   ---------- ?

$ 1,600                 $ 100                    ---------- ?

$ 1,400                 $ 100                     --------- ?

$ 1,200                 $ 100                     ---------- ?

$ 1,000                 $ 100                      --------- ?

$ 800                    $ 100                      --------- ?

$ 600                    $ 100                       --------- ?



5 ) BOND YIELD TO MATURITY: 

The bond yield to maturity is a combination of:

a )    The yield of the bond ( Interest )
b)     The Capital gain or loss to maturity,
         ( cost of bond - $ 1000 ) 



CAPITAL GAIN TO MATURITY

Let us say that we buy a bond on August 10, 2000 @ $500.
The coupon is 10 % as above.
There is 10 years left to maturity. 
( August 10, 2000 to August 10, 2010 )


A)     The interest yield of the bond is as we have seen above is 20 %. 
          ( $ 100 / $ 500 ) X 100 %


B)      The capital gain is:
          $ 1,000 less  ( Price paid for the bond ). 

Capital gain to maturity ($)    
( $1,000   -   $500  )  =   $ 500 

Capital gain to maturity (%)
(( $1,000 - $500 ) / $500 ) X 100 % = 100 % 


If we have a Capital gain to maturity of 100 % 
and the maturity is ten ( 10 ) years, 
we have a yearly capital gain of 10 %. 
( 100 % / 10 years )


We can now add our yearly interest yield of 20 % and our yearly Capital appreciation of 10 % for a grand total of a yearly average return of 30 % to maturity. ( 20 % + 10 % ) = 30 %




CAPITAL LOSS TO MATURITY:


Now, if we buy a bond on August 10, 2000 @ $ 2,000,
again the coupon is 10 %.
As above there is 10 years left to maturity. 
( August 10, 2000 to August 10, 2010 )


A)   The interest yield of the bond as we have seen above 
        is 5%.    ( $ 100 / $ 2,000 ) X 100 %

B)    The capital loss is: 
        ( Price paid for the bond less $ 1,000 )

Capital loss to maturity ( $ ) 
$ 2, 000 - $ 1,000   =   ( $ 1,000 )

Capital loss to maturity ( % ) 
(( $ 1,000 / $ 2000 ) X 100 %   =   50 % 


If we have a Capital loss to maturity of 50 % and
the maturity is ten ( 10 ) years, 
we have a yearly capital loss of 5 %.
 ( 50 % / 10 years )  =  5%


We now add our yearly interest yield of 5% and our Capital loss of 5 % for a grand total of a yearly average return to maturity of 0 %. 



By buying bonds below " par " ( $ 1,000 ), we: 

a) Increase the bond yield ( interest ).
b) We acquire a Capital gain, further increasing our returns.


By buying bonds above "par" ( $ 1,000 ), we:

a) Reduce the bond yield ( interest )
b) We acquire a Capital loss, further reducing our returns. 



To have a SAFE and PROFITABLE investment, 

BONDS SHOULD NEVER BE BOUGHT 
ABOVE " PAR ", ( $ 1,000 ).




Answers to the bond yield problems.


PRICE         INTEREST         YIELD
----------         ---------------          ----------

$ 1, 800            $ 100                 5.56 % 

$ 1, 600            $ 100                 6.25 % 

$ 1, 400            $ 100                 7.14 % 

$ 1, 200            $ 100                 8.33 % 

$ 1, 000            $ 100               10.00 % 

$ 800                $ 100                12.50 % 

$ 600               $ 100                 16.67 % 



(ABC-BONDS,14-01-00)