[bstewart24]

On January 1, a company issues bonds with a par value of $300,000. The bonds mature in 5 years and pay 8% annual interest each June 30 and December 31. On the issue date, the market rate of interest is 6%. Computer the price of the bonds on their issue date. The following information is taken from the present value tables:

Present value of an annuity for 10 periods at 3%... 8.5302
Present value of an annuity for 10 periods at 4%... 8.1109
Present value of 1 due in 10 periods at 3%... 0.7441
Present value of 1 due in 10 periods at 4%... 0.6756

How would you begin to figure out this problem? I don't want you to figure this out, I just need direction to go in. Do I take 8.5302*.03 then add that number to each new number for the first problem? Then do the same thing for the other 3 problems?

[CB84]

You should find the Present Value of the interest payments and then the Present Value of The Principal Payment at Maturity. Subtract the principal payment form the interest payments.

[bstewart24]

Thank you!

[morgaine300]

The idea in this problem, since they've already given you the factors, is to figure out which factor to use when. It's not uncommon to give both interest rates to make sure you pick out the correct one.

First, figure the interest payments based on the contract rate. That's always a point of confusion. You want the actual interest payments here. I tend to do this first and then leave that rate behind because it won't be used again. Remember they are semi-annual and it has to be calculated by compounding period. i.e. every half year. So interest rates need to be divided in half.

Once you have the actual interest payments, you need to find the present value of both the bond face value and the present value of the series of interest payments. When finding value, always use the market/yield rate. The idea is to find the amount that would yield the amount in the market. That's its "value." If you use the contract rate to do the present values, you'll end up right back at the face value of the bonds. (i.e. the present value using contract will just get you 300,000, which is not the value in the market.)

Then you have to know which is present value of $1, and which is present value of annuity. The key in what I said above is figure the present value of the series of interest payments. i.e. there's a set of payments. An annuity is something that is equal dollar amounts at equal time intervals. The bond is a lump sum payment that will happen in 5 years, at all once.

And then you add the two present values together.