2.17 Fixed Income Securities: Dollar Price & Yield-to-Maturity (Solution)

Note that as the discount rate (i.e., the Yield-to-Maturity) increases – going from case 1 to case 2 – the bond’s price/present value decreases. YTM and dollar-price are inversely (or negatively) related.

Imagine that you had purchased a new bond issue some years ago, at which issuance time the coupon was set to equal the market YTM, as would be the case with most investment grade bond issues; the issue price would, of course, be par. Now, with five years to go to maturity, market yields have gone up – to 12% (as in case 2). The market value would have decreased simply due to the mathematics of the time value of money.

Furthermore, bonds that are newly issued today, and which mature in five years, as this “old” one does, would now pay a 12% percent coupon. Wouldn’t you rather have the higher coupon? Shouldn’t the “old,” lower coupon bond be discounted? Its yield, all else equal, is “inferior”! To summarize, there may be two reasons for the discount – one mathematical, the other logical. Of course, there may be another case: what if market yields went down? (See below.)

This illustration assumes no “accrued interest.” Normally, bonds are purchased in between coupon payment periods, and pricing and payment are adjusted accordingly. The formula presented is valid only on a coupon payment date. A bond calculator is therefore useful in other cases!