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confused_college_student · Feb 7, 2008, 07:38 PM

General Toys, Inc. sold five year bonds having a face value of $100,000 and a coupon rate of 7% when the market rate was 9%. The present value of $1 at 9% for five periods is $0.6499. The present value of a $1 annuity for 5 periods at 9% is $3.8897. At what price did these bonds sell?

I came up with $93,690, but I'm not sure. Can someone please rework and correct me if I'm wrong? Thanks.

morgaine300 · Feb 10, 2008, 12:29 AM

Can you please include calculations of how you're getting your answers. Don't know about anyone else, but I'd much prefer see your work and tell you where you went wrong, rather than just showing you the correct answer. I think you'll learn better that way.

You're really close.

ddrahota · Feb 11, 2008, 08:45 PM

You are half right. You do take the PV of the 100,000 at 9% for five periods giving you the multiplier of .64993 and take that times 100,000 and it gives you the present value of the principal payment when the obligation becomes due in five years 100,000 in five years is worth $64993 if the market rate is 9%. Where you went wrong was using the market rate to figure out the present value of the interest payments. The coupon rate is what you will be paid as per the bonds, so use 7% and since you are being paid every year, it is an ordianry annuity. 5 years at 7% under the present value of an ordianry annuity gives the multiplier 4.1002. You multiply that by the amount of the annual interest payment. In this case it is easy to figure out since it is based upon 100,000 at 7%= 7,000 and take that times 4.1002 and you get $28,701.40 You add the two PV numbers together: $64993
+$28701.40
$93694.40
$93,694.40 is the answer

morgaine300 · Feb 11, 2008, 09:16 PM

I beg to differ, but you do use the market rate to figure out the present value of the interest payments.

You use the contract rate (7%) to figure out the actual interest payment the bonds will be paying, i.e. $7000 per year. But to figure the present value of those payments, you use the market rate (9%). The 3.8897 factor is accurate. (And also appears to have been given in the problem.) The whole point of doing the present value is to figure out what it would take in the market to gain those same $7000 payments, so you have to use the rate from the market.

That is not where the original poster went wrong. I tried several common errors to come up with her/his answer and cannot get it. I don't know where s/he went wrong without seeing the work.