Price of a zero coupon bond

What does a zero coupon bond mean ?

A bond that does not pay regular and periodic interest or coupon payments and pays a lumpsum amount at maturity is known as a Zero coupon bond.  The lumpsum amount paid at maturity is the face value or par value of the bond.

These bonds are issued at a deep discount on face value and are also known as discount bonds or deep discount bonds.

As there are no Interest or coupon payments made during the term of the bond, the gain for an investor is the difference between the issue price of the bond and the lumpsum amount received at maturity.

What are the distinctive features of a Zero coupon bond ?

Zero coupon bonds are usually issued for period ranging anywhere between 10 – 15 years. From the investors point of view, Zero coupon bonds are a option for long term investment.

Price of a zero coupon bond is linked to its time to maturity. Bonds with a long term to maturity are sold at a deeper discount i.e., there is a higher discount on the face value. Bonds with a shorter term to maturity are issued at comparatively higher price when compared to bonds with longer term to maturity.

They are freely traded on stock exchanges and an investor can sell them before their maturity

As zero coupon bonds do not make any Interest / coupon payments, their duration is equal to their time to maturity.

How is the price of a Zero coupon bond calculated ?

The Price or present value of a zero coupon bond is calculated using the formula

= FV / ( 1 + r ) n

Where

P = Present value of a zero coupon bond ;   FV = Face value of the zero coupon bond ( It is also known as Maturity value of the bond )   r = Discount rate   ;  n = Term to maturity  ;

How do you solve a Zero coupon bond problem ?

Example :

Cash rich Co. has issued a Zero coupon bond with a face value of $ 5,000, term to maturity of 10 years with a discount rate of 6%. Calculate the Price of the Zero coupon bond.

Solution :

The Price or present value of a zero coupon bond is calculated using the formula

= FV / ( 1 + r ) n

Where

P = Present value of a zero coupon bond ;   FV = Face value of the zero coupon bond ( It is also known as Maturity value of the bond )

r = Discount rate   ;  n = Term to maturity  ;

 

As per the information given in the question we have

Face value of the bond = $ 5,000   ;    r = annual discount rate = 6 % = 0.06  ;

n = Term to maturity = 10 years  ;

 

Therefore the price of the zero coupon bond is

= $ 5,000 / ( 1 + 0.06 ) 10

= $ 5,000 / ( 1.06 ) 10

= $ 5,000 / 1.790848

= $ 2,791.973885

= $ 2,791.97  ( when rounded off to two decimal places )

The price of the zero coupon bond = $ 2,791.97

 

Note : ( 1.06 ) 10 = 1.790848 is calculated using the excel function =POWER(Number,Power)

Thus ( 1.06 ) 10 =POWER(1.03,10) = 1.790848.

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