Need help with bond pricing formulas

After reading an article on advanced bond concepts I find myself a bit confused with a formula they are using. Any help would be greatly appreciated.

Quote:

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Fundamentally, however, the price of a bond is the sum of the present values of all expected coupon payments plus the present value of the par value at maturity. Calculating bond price is simple: all we are doing is discounting the known future cash flows. Remember, to calculate present value--which is based on the assumption that each payment is re-invested at some interest rate once it is received--we have to know the interest rate that would earn us a known future value. For bond pricing, this interest rate is the required yield.

Here is the formula for calculating a bond's price, which uses the basic present value (PV) formula:

Bond Price = C / (1 + i) + C / (1 + i)².. C / (1 + i)ⁿ + M / (1 + i)ⁿ

C = coupon payment
n = number of payments
i = interest rate, or required yield
M = value at maturity, or par value

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Why would the interest rate have to be factored in? The coupon is the interested rate paid (typically semiannually).

This is interest over interest from another year.
Example:
100 over 2 years with interest rate of 10% is now worth: 100/(1+0.10)^2 = 82.64.
next year you get 10% interest, 82.64 will be 82.64*(1+ 0.1) = 90.91, and over 2 years 90.91 * (1 + 0.1) = 100

I hope this helps.

Pieter

Another way to look at it is to multiply the whole thing through by (1+i)^n.

Then you are saying effectively that the price of the bond scaled up by the interest n times should be equal to the first payment + the second payment scaled once + the third payment scaled twice +...+ the value at maturity. Which of course is the case, because you get paid a certain value each time (including one lot, two lots etc of interest) plus the final lump sum at the end.

zaza

Ok got it. Thanks guys. :thumb: