Introduction:

Bond a fixed income security, is debt security instrument issued by borrower for the purpose of raising capital and subscribed by the lender or investor.

Following are the characteristics of bonds:

1. It is a long-term financial instrument,
2. It is a negotiable instrument,
3. It is a capital market instrument,
4. Government and Corporations borrow money by selling bonds to the investors,
5. It represents loan,
6. In return company provides fixed interest payment each year (except in case of floating rate bonds) until maturity date. Such payment is coupon,
7. Interest is paid annually or semi-annually,
8. On maturity debt is repaid,
9. Bonds have a fixed maturity period, fixed maturity value. Maturity date of the bond is usually specified at issue time except in case of perpetual bonds.
10. Bonds are generally redeemed at par.
11. Bonds may be issued at par or discount or premium,
12. Bonds are traded in stock market.
13. Bonds are negotiable promissory notes that can be used by individuals, business firms, Governments or Government agencies. Bonds issued by the Government or Public sector companies are generally secured. Private sector companies can issue secured or unsecured bonds.
14. Difference between bonds and debentures is that bonds are issued by Public Sector undertakings whereas debentures are issued by Private sector undertakings, bonds are secured debt instruments i.e. bondholders have access to the assets of company in case of default but debentures are generally unsecured i.e. debenture holders do not have recourse to assets in case of default by company, there is no default risk in case of bonds but there is always a default risk in case of debentures, bonds are generally issued for a period of 10-30 years but the debentures are issued for a period not less than 20 years.
15. The par value is the face value of the bond
16. Interest is calculated of the par value of the bond
17. Bond has a fixed maturity value known as redeemable value.
18. Discounting rate /cost of capital is a rate of discount at which the present value of bond is calculated. It is the rate at which the present value of cash inflows and outflows are traded off. Discounting rate is normally the bank rate or the market rate of interest.

Types of Bonds:

1. Straight bonds: Those bonds having fixed rate of interest, fixed maturity date, fixed maturity value.
2. Extendable Bonds: these bonds have no fixed maturity date and can be extended on the demand of the buyer.
3. Zero coupon bonds: Zero coupon bonds are those bonds which are issued at discount but redeemed at par; no interest is paid to bond holder. The merit of this bond is that the company does not have burden of servicing debt during execution period of the project. The origin of this type of bond can be traced in U.S. security market. In such types of bonds, the maturity date is far, issued at deep discount on the nominal value of the bond, redeemed at par in single installment at the time of maturity. In India various public sector banks like ICICI, IDBI etc. have issued such type of bonds.
4. Deep discount bonds: It is a form of zero coupon bonds. Interest rate of such bonds is less than prevailing rate of fixed income securities with similar risk profile and issued at discount on the nominal value but redeemed at par. The maturity period may range from 3 years to 25 years or more. IDBI was first to issue deep discount bonds in India in 1992.
5. Floating rate bonds: coupon rate can change as it has a relationship with current market rates but the par value of the bond remains same.
6. Convertible bonds: Bonds can be converted into shares at latter specified date and this option provides the opportunity to bond investor to participate in equity, if company is a progressing company.
7. Callable bonds: Issuer company reserve right to call back bonds and pay fixed price at pre mature date.
8. Retractable Bonds: is a bond in which there is an option for the holder to force the issuer to redeem the bonds before maturity at par value.
9. Secured bonds and Unsecured Bonds: Those bonds which are secured by a charge on the assets of the company. Those bonds, the repayment of which is not secured by any asset.
10. Perpetual bonds and Redeemable bonds: perpetual bonds are those bonds which do not carry any fixed maturity period and redeemed only at the time of winding up of the company. Redeemable bonds are those bonds which are redeemed after a fixed period of time.

• Relationships

• The relationship between the market rate of interest/YTM and price of the bond is inverse i.e. if the market rate of interest/YTM increases, price of the bonds decreases and vice versa.

• Longer the period of maturity, greater will be the risk and so price of the bond will be less as compared to the bond with shorter maturity period.
• As the bond reaches the maturity, its price will be more.

Types of risks involved in bond valuations:

1. Price risk: uncertainty of change in price of bond which an investor is holding. Longer the period of maturity, more will be the risk.
2. Default risk: uncertainty regarding non payment of interest and principle obligation amount by Issuer Company.
3. Interest rate risk: uncertainty of change in rate of interest affecting price of the bonds. If market interest rate falls, price of bond rises.

Present Value:

The present value of the bond is the defined as the present value of future interest payments and present value of the maturity value discounted at appropriate discounting rate i.e. k_d.

Coupon₁ + Coupon₂ +_ _ _ _ _ _ (Coupon_n + Maturity Value)

 (1+k_d)¹            (1+k_d)²                             (1+k_d)ⁿ

^{Where, K}_d ^{is the Discounting rate/Cost of capital}

In case of semi annually interest:

Coupon/2 + Coupon/2 + ­_ _  _ _ _ (Coupon/2 +Maturity Value)

 (1+k_d/2)¹            (1+k_d/2)²                             (1+k_d/2)²ⁿ

^{So, in case of semi annual interest payment,}

^{Interest ----- half}

^{Time----- double}

^{Discounting rate----- half.}

e.g. An investor intends purchasing a three-year Rs.1,000 par value bonds having nominal interest rate of 10%. At what price the bond may be purchased now if it matures at par and the investor required a rate of return of 14%.

PV=   100        +           100 +                    100 +1000

   (1+r)¹                       (1+r)²                          (1+r)³       

                 100            100            100+1000

=   -----     +    --------   +   ---------------    

     (1.14)¹         (1.14)²              (1.14)³  

               = 87.719 + 76.947 + 742.469

          = 907.125

Thus, the purchase value of the bond should be Rs. 907.125

e.g. Company issued 10%, 1000/- Bonds issued at 990/- redeemed after 5 years at 1050/-, calculate it’s present value if discounting rate applicable is 15%.

    PV=  100       +    100    +     100    +      100    +  100 + 1050

        (1+r)¹              (1+r)²             (1+r)³             (1+r)⁴            (1+r)⁵

 100          100            100         100              1150

 -----   +    --------   +   -------  +   -------    +   ------     

(1.15)¹         (1.15)²          (1.15)³      (1.15)^4     (1.15)⁵

       = 86.90  + 75.60  + 57.10 + 571.55 

 = 856.85

 So, it is not worth for an investor to invest in such bonds as these are issued at price more than present value.