12.7 The True Price of a Bond
Once again, it may be said that the “true price” of a bond is its yield-to-maturity. YTM is the means by which the bond’s cash flows are discounted or “priced.”
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, the market yields today are the same for both.
To illustrate this, solve the following problem for two bonds. You will note that the YTMs and TTMs for each of the two bonds in the example are the same, but the coupons differ, causing the dollar prices to differ. We assume equal creditability for each.
YTM = 4%
N = 10
P = 2
Cpn. Bond #1 = 4%
Cpn. Bond #2 = 0%
Solve this without glancing at the solutions.
Price Bond #1 = ($20) (16.3514) + ($1,000) (0.6730) = 100%
You should have known that the price would be Par- without having to calculate.
Price Bond #2 = ($00) (16.3514) + ($1,000) (0.6730) = 67.30%
We now also see, that as the coupon rises, so too does the dollar price.
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