Chapter 6 Chapter 6

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= [(-1 )(Modified Duration)(Yield change in terms of percentage points)}
+ [(C/200) (Yield Chg in terms of percentage points) 2 ]
= [{(-1)( 7.3585)(1)} + {(79.35)/200)(1)}] = 6.96%
New Price of Bond = 1000 – 69.60 = 930.40
• Present value of cash flow method :
New price of bond (YTM 7%) = 60(7.024) + 1000 x 0.508 = 929.44
% Error by duration method = (926.42 – 929.44) / 929.44 = 0.325%
% Error by convexity method = (930.40 – 929.44) / 929.44 = 0.103%
Comment : The new price of bond ( calculated on the basis of changed YTM)
is more accurate when calculated by convexity (rather than by duration)
CONVERTIBLE BONDS
These are the bonds which have / can to be converted into specified number of
equity shares of the company issuing these bonds within a specified period. In
India most of the convertible bonds have been issued on the basis of compulsory
conversion i.e. the bonds are compulsorily convertible into number of specified
number of shares, there is no discretion of the bond holder. In USA and European
countries, convertible bonds are option convertible bonds i.e. conversion takes
place if the bond holder so desire,
An Example of option convertible bond: Suppose a company issues 7%
convertible bonds of $100 each, maturity 7 years, redemption at par. The
bondholder can get his bond converted into 4 equity shares after 2 years of
issuance. Now whether the bond will be converted into equity shares or not, it is
at the discretion of the bond holder. Suppose he gets the bonds converted into
shares, the company’s liability towards principal and interest will extinguish. If
he does not get the bond converted, he will be emitted to receive interest
periodically and on maturity he will get the redemption amount of $100.
The convertibility option lowers the interest rate that the issuer would otherwise
have to pay without this feature, and it appeals to investors who want current
income, but would like to take advantage of any growth in the issuer company.
Let’s understand a few terms related to convertible debentures:
(i) The number of shares that each bond can be converted to is known as the
conversion ratio.
(ii) Conversion price is the exercise price at which the investor converts his
bond into equity shares. It is obtained by dividing the par value of the bond by
the conversion ratio.