2.10 The True Price of a Bond

Once again, it may be said that “true price” of a bond is its yield-to-maturity. YTM is the manner in which the bond’s cash flows are discounted or “priced.” For each future cash flow, a bond produces, how much does a buyer pay (or a seller get)?

Two bonds may have the same credit rating and maturity but may have been issued at different times and thus will have different coupon rates, and therefore will be valued at different dollar prices even though market yields are the same.

To illustrate this, solve the following problem for two bonds. You will note that the YTM for each of the two bonds in the example are the same, but the coupons differ, therefore the dollar prices will differ. We assume equal creditability for each.

YTM = 4%
N = 10
P = 2
Cpn. _{Bond #1} = 0%
Cpn. _{Bond #2} = 4%

Price _{Bond #1} = ?
Price _{Bond #2} = ?

We now also see, assuming you solved this problem, that as the coupon rises so does the dollar price.