Bond Price Question

Noxi10

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First off Hi guys, :)

Long time viewer of the threads to help get me through some difficult spots in uni and appreciate all the work everyone does.
:)

I have this problem on a current homework sheet that I cannot sort out. I've backtracked and gone over it for hours on end and don't even know where to start. I think I've worked myself up to that point where it's doing my head in. Anyway, here's the problem.

A loan with face value $10,000,000 is issued in bonds each face value $100. The bonds are to be repaid with a bonus of 20%. One fifth of the total capital will be repaid annually with the first payment at the end of the eighth year. Coupons on the outstanding bonds are 8% pa paid semi-annually [ in arrears]. Determine the price at which the bonds should be issued if the loan issue is priced so that an investor who purchased the entire loan would earn 7%pa payable half yearly.

I think there's so much going on that I've confused myself on where to start. My gut tells me to figure out how long it will take to pay back the initial loan first to get a sense for how long it will take to reach the time to maturity for the bonds, but I'm unsure. Then the bonus part screws me over as I don't know where to apply that.

Anyway, any help in getting moving along would be greatly appreciated if it's possible.
Cheers!
 
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A loan with face value $10,000,000 is issued in bonds each face value $100. The bonds are to be repaid with a bonus of 20%. One fifth of the total capital will be repaid annually with the first payment at the end of the eighth year. Coupons on the outstanding bonds are 8% pa paid semi-annually [ in arrears]. Determine the price at which the bonds should be issued if the loan issue is priced so that an investor who purchased the entire loan would earn 7%pa payable half yearly.
Serial Bonds. Google it up.
Accordingly, subject to correction by the indefatigable Sir Denis, the purchase price of the entire serial issue is the sum of the purchase prices of the 5 subissues. The so-called 20% bonus may or may not refer to the redemption rate. If the bonus does refer to the redemption rate then the 2,000,000 bond maturing at the end of the 8th year will be maturing at 120 (or 120%). For the 1st subissue, we would have
2,000,000(.08/2)*[1-(1+.07/2)^(-8*2)]/(.07/2)+2,000,000(120%)(1+.07/2)^(-8*2)
or
\(\displaystyle \left( 2,000,000\times \tfrac{.08}{2} \right)\left( \frac{1-{{\left( 1+\tfrac{.07}{2} \right)}^{-(8*2)}}}{\tfrac{.07}{2}} \right)+2,000,000(1.2){{\left( 1+\tfrac{.07}{2} \right)}^{-\left( 8*2 \right)}}\)

For the 2nd, 3rd, 4th, and 5th subissues, you just change the year from 8 to 9, 10, 11, & 12 respectively.
You should get a sum of $11,717,113.22
 
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