2.9 You Get More, You Pay More: Say What?

So, you say that I am not really getting more from a bond because, after all, I am paying more for it? Precisely. That’s WHY you pay a higher price for a bond with a higher coupon! You are, however, still earning the Market Yield, the YTM, on each dollar, each future cash flow, that you are purchasing. Dollar for dollar paid, you are earning the discount rate regardless of the coupon. Remember that the discount and compound rates are the same. One compounds from the present to the future while the other discounts the future cash flows to the present. Only the “direction” differs.

Let’s say you buy a ten-year bond with a 6% coupon at Par. Payments are semi-annual. You get $30 per $1,000 of Face Value each half-year period. It thus should be inferred that the Yield-to-Maturity too is 6%.

Let’s compare that to an 8% coupon, again with a 10-year maturity, and with a semi-annual payment schedule. We will, again, set the YTM at 6%. This bond pays more coupon cash flow, quite possibly because it was issued sometime in the past, whereas new bonds are issued today with a lower coupon. Remember: this bond pays semi-annually, so the discount rate and the number of periods must be adjusted accordingly. 

You will notice that the PV of the 6% coupon plus the increment of 2% for the higher coupon on the other bond equals the PV of the 8% coupon. Certainly, that should come as no surprise. You get more, you pay more.

Since the present value of the final principal payment has not changed, the difference in the two bond’s prices will depend solely on the coupon cash flows.

Code: PVAF = Present Value Annuity Factor