freaked out by bonds maths!

[Simonsky]

Have been trying to read a book on bonds and the maths connected with it. I understand the basics of bonds but got puzzled by this:

This is a case where the interest rate is 8% but the yield is 9% and you have to calculate the price where the par value is £1,000 with a four years to maturity:

Annual interest is 0.08 x 1000 = 80 and n(period in years)=4

So to work out price the book says: PV (present value) = 80/(1.09)^1 + 80/(1.09)^2 + 80/(1.09)^3 + 1,000/(1.09)^4 = 976.40

So I don't quite get why that process gives us the new price although I understand that the lower the price the higher the yield because the initial interest rate as an absolute value is £80 and if the price lowers that £80 will represent a bigger yield. But I still don't get the formula which divided the interest rate by 1.09 compounding each of three years then adding the par amount plus interest divided by 1.09 compounded for 4 years.

Any help appreciated.

 

[JeffM]

We discount the cash flows after first separating them into two seperate, logically distinct pieces, one being the four annual payments of interest of 80 and one being the payment of the face value of the bond at maturity. We could just as well treat the cash flows as four payments, namely as three annual payments of interest and a final payment of interest and principal. Mathematically they are the same.

[MATH]\left (\dfrac{80}{1.09^1} + \dfrac{80}{1.09^2} + \dfrac{80}{1.09^3} + \dfrac{80}{1.09^4} \right ) + \dfrac{1000}{1.09^4} =\\ \dfrac{80}{1.09^1} + \dfrac{80}{1.09^2} + \dfrac{80}{1.09^3} + \dfrac{1080}{1.09^4}.[/MATH]Does this answer your question?

 

[Simonsky]

Thanks JeffM-that seems to have given me the necessary light bulb moment. Seeing the two separate processes (discounting interest and discounting face value).

Many thanks.