Question 1201753: Bond XYZ is a $1,000, 4% semi-annual coupon bond issued today on 1 Jan 2023, maturing on 31 December 2032. Coupons are paid on every 30 June and 31 December.
(a) If you bought Bond XYZ today at a yield (YTM) of 3% compounded semiannually, what’s your purchase price? Did you buy the bond at a premium, par or discount? (4 marks)
(b) One year later Bond XYZ’s yield went up to 5% compounded semiannually and you sold it immediately after receiving the coupon.
iii) Assume that you reinvested all coupons at 5% compounded semi-annually. Calculate the total amount of coupon income (coupon payments and reinvestment of coupon payments) at the end of the 1-year holding period.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! first part was already answered from another question, but i'll repeat it here just in case if wasn't also one of your problems.
the calculator at https://exploringfinance.com/bond-price-calculator/ was used to solve this problem.
microsoft excel was also used to provide the same answer.
results from the calculator are shown below:
results from excel are shown below:
one year after you bought bond xyz, the yield to market of bonds went up to 5%.
consequently you sold bond xyz right after receiving the second semi-annual coupon payment.
from what i can understand, the price of the bond on the open market would have had to change because the yield to market rate for bonds of this type had changed.
since the bond yield to market rate was now 5%, and you have a bond that had coupons set to 4% compounded semi-annually, and the remaining term of the bond was now 9 years instead of 10 years because you held the bond for 1 year before selling it, the price the market was willing to pay for your bond becomes $928.23.
that's the price the market was willing to pay for your bond because the new bonds coming out were giving 5% rather than 4%.
i used the bond calculator again, and also repeated the results using excel.
those results are shown below:
results from the calculator are shown below:
results from excel are shown below:
looks like you bought the bond at 1185 when the yield to market rate was 3% and sold it for 928 when the yield to market rate went to 5%.
you did collect two coupons at 20 dollars apiece for the two semi-annual periods you have the bond before you sold it, so you did pick up 40 dollars from them.
the problem did not state that you did nything except sell the 4% bond, so i didn't make any assumption on what you did with the money that you received from selling it.
your part 3 was also a little confusing.
not sure what you wanted there either..
you talk about a one year holding period of which i didn't understand what you were referring to.
going back to your original purchase, you bought a 4% bond with semi-annual coupones worth 20 dollars each for 20 semi-annual periods (10 years).
if you kept that bond and reinvested those coupones at 5% per year, compounded semi-annually, then the semi-annual rate would be 2.5%.
the future value of those re-invested coupons would then be equal to 510.93. at the end of the 10 year invetment period of the bond.
i answered part b and part iii as best i could without actually understanding exactly what it was that you were looking for.
please resubmit your problem with further clarification of what you were looking for if the answers provided didn't address them adequaely.
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