# 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 September 20, 2011

on:**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%

V_{0}=I*PVIFA(K_{d}, n) + F*PVIF(K_{d}, 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: **

** **

V_{0 }or P_{0 }= ∑^{n}_{t=1 }I/2/(I+K_{d}/2)^{n} +F/(I+K_{d}/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

### 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 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.

1 | Dane Braxton

September 24, 2011 at 2:34 am

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!