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 Post subject: Bond questionPosted: Fri, 13 Nov 2009 04:48:11 UTC
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Joined: Thu, 18 Jun 2009 10:22:43 UTC
Posts: 44
Hi,
Iâ€™m having trouble with this question about bonds:

What is the market price of a 12% p.a. semi-annual coupon bond with a face value of \$100, 10 years to go until maturity when the current market yield is 10% p.a. compounded quarterly?

Since the timing of the rates donâ€™t match, Iâ€™m confused as to whether I find the effective rates for both and then work it out?

I found the effective rate for the coupon to be 12.36% and the Effective rate for the yield to be 10.38%.
Then to work out the interest payment, I did:
(0.1236/2) x \$100 = \$6.18

I also divided 10.38% by 2 to get 5.19% for the semi-annual yield rate.
Then I plugged the numbers into the following formula:
D = F/r[1 â€“ (1+r)^-n] + B/[(1+r)^n]
Where F = interest payment
B = face value of bond
And I got \$112.14.

I wasnâ€™t provided with a solution for that but I donâ€™t think my method for working it out is correct.
Any help would be appreciated. Thank you.

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 Post subject: Posted: Fri, 13 Nov 2009 05:51:40 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3688
Location: Ottawa Ontario
112.14 is close; I make it 111.62.

Convert 10% cpd quarterly to cpd semiannually (to match coupon frequency):
1.025^4 = (1 + i)^2 : i = .050625

Use that rate to calculate:
PV of \$100 : 37.243...
PV of flows : 74.378...
Total: 111.62 (rounded)

By the way, on these, the "coupon rate" is simply to determine the cash
flow amounts; no need to worry further.

With your problem, these flows were \$6 (half of 100 * .12) semiannually.
Looks like this:
PV?...[1]6...[2]6...[3]6...............................[18]6...[19]6...[20]6 + 100

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 Post subject: Thank you!Posted: Fri, 13 Nov 2009 08:58:03 UTC
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Joined: Thu, 18 Jun 2009 10:22:43 UTC
Posts: 44
Thank you so much for your replies.

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