Bonds Question

gammy_knees

Give me a little help with this one.

A company issues a 12 year bond of €1500 that pays €50 at the end of every six month period for the 12 years. If the current market AER is 6.75%, with interest added every 6 months, what is the fair market value of the bond?

I've attached the way I'm approaching the question. Get the present value of the €1500 and the PV of each €50 over the 12yrs at 6 month intervals and used sum of a geometric to total that and then add the two.
My result is €1503.30. Recommended answer is €1836.58(tried different ways but wondering if that might be incorrect!!). I think my compounding is accurate.
A second/third opinion appreciated.
With thanks.

Yakuza

For what it's worth, I agree with your answer.
The coupon rate (.033333% per 6 months) is very close to the 6-monthly yield (1.0675^(1/2) or .03319), so it makes sense that the price of the bond is close to the nominal value.

If the AER is less than the coupon rate, then a bond will be valued more than the nominal value (using goal seek in Excel, I worked out that the AER should be around 4.3% for the bond to have a value of 1836.58). I'm guessing there's a typo somewhere in either the book or the solution.

gammy_knees

Yakuza, thanks for your answer and it does have a lot of worth!
You're going into more detail than what is required when you mention the 'coupon rate'. I only need to work with the AER. As you said, the recommended answer must be faulty.
Thanks for the affirmation!