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Coupon-Bearing Bonds

Think now of a coupon-bearing instrument like a Treasury bond that matures in, say, n years. For example, assume that you are considering a bond that matures in n years with yield r, face value M, and certain (that is, riskless) annual coupon payments equal to C. You want to find the value (the fundamental price) of this stream of cash flows accruing over an n-year period. By lending P, you will receive the stream of cash flows:

. You wish to value this stream. To do so, you need to discount this stream at a rate that makes the price paid for the bond, P, just equal to the present value of this stream of cash flows. That is, r, which is the bond yield, or yield to maturity, solves

Since this is a constant coupon, then and so , or more compactly as

Solving for the bond's yield is an iterative procedure that uses some variation of Newton's method. Note: . Here, the function ...