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MB0045 : A company has issued a bond with face value of Rs.1000, with 10% pa coupon rate payable annually and tenure of 10 years to maturity.

Posted on: September 20, 2011

MB0045  : A company has issued a bond with face value of Rs.1000, with 10% pa coupon rate payable annually and tenure of 10 years to maturity. At the end of 10 years, the bond will be redeemed at a premium of 10% to face value.

a) At what price would you buy the bond if the prevailing interest rate is 12% pa on investments of similar risk?

b) What is the YTM of the bond if the prevailing price is same as calculated in a) above.

c) What is the current yield of the bond at the given price?

d) If the coupon rate is paid semi-annually, at what price would you buy the bond at the 12% pa prevailing interest rate?

 

a) At what price would you buy the bond if the prevailing interest rate is 12% pa on investments of similar risk?

Solution:

Interest payable = 1000*10% = Rs. 100

Principal repayment is Rs. 1000

Required rate of return is 12%

V0=I*PVIFA(Kd, n) + F*PVIF(Kd, n)

Therefore,

Value of bond

= 100*PVIFA (12%, 10yrs) + 1000*PVIF (12%, 10yrs)

= 100*5.6502 + 1000*0.3220

= 565.02 + 322

= Rs. 887.02

b) What is the YTM of the bond if the prevailing price is same as calculated in a) above.

Solution:

YTM   = {I + (F – P) / n} / { (F – P) / 2 }

= 100 + {(1000 – 887.02) / 10 / {(1000 + 887.02) / 2}

= {100 + 11.298} / 943.51

= 0.1179 or 11.79%

c) What is the current yield of the bond at the given price?

Solution:

Current Yield (“CY”) = Coupon Interest / Current Market Price

CY      = Coupon Interest / Current Market Price

= 100 / 887.02

= 0.112 or 11.2%

d) If the coupon rate is paid semi-annually, at what price would you buy the bond at the 12% pa prevailing interest rate?

Solution:

 

V0 or P0               = ∑nt=1                  I/2/(I+Kd/2)n +F/(I+Kd/2)2n

= (100/2) / (1 +0.12/2)10 + 1000 / (1 + 0.12/2)10

= 50*PVIF (6%, 20yrs) + 1000*PVIF (6%, 20yrs)

= 50*11.470 + 1000*0.312

= 573.5 + 312

= Rs. 885.50

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3 Responses to "MB0045 : A company has issued a bond with face value of Rs.1000, with 10% pa coupon rate payable annually and tenure of 10 years to maturity."

Thanks for taking time to write down this article. It’s been rather helpful. It couldn’t have arrive at a better time for me!

THANKS A LOT

sowbhagya lakshmi .m.h

thanks a lot for providing the answers it was really difficult to solve without out yours help the answer was really excellent once i thank you for giving the through the website.

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