208 Part 3 Financial Assets
equal to the current yield plus the capital gains yield. In the absence of default risk
and assuming market equilibrium, the total return is also equal to YTM and the
market interest rate, which in our example is 10%.
Figure 7-2 plots the three bonds’ predicted prices as calculated in Table 7-1.
Notice that the bonds have very different price paths over time but that at matu-
rity, all three will sell at their par value of $1,000. Here are some points about the
prices of the bonds over time:- The price of the 10% coupon bond trading at par will remain at $1,000 if the
market interest rate remains at 10%. Therefore, its current yield will remain at
10% and its capital gains yield will be zero each year. - The 7% bond trades at a discount; but at maturity, it must sell at par because
that is the amount the company will give to its holders. Therefore, its price
must rise over time. - The 13% coupon bond trades at a premium. However, its price must be equal
to its par value at maturity; so the price must decline over time.
While the prices of the 7% and 13% coupon bonds move in opposite directions
over time, each bond provides investors with the same total return, 10%, which is
also the total return on the 10% coupon bond that sells at par. The discount bond
has a low coupon rate (and therefore a low current yield), but it provides a capital
gain each year. In contrast, the premium bond has a high current yield, but it has
an expected capital loss each year.^9
(^9) In this example (and throughout the text), we ignore the tax e! ects associated with purchasing di! erent types
of bonds. For coupon bonds, under the current Tax Code, coupon payments are taxed as ordinary income,
whereas capital gains are taxed at the capital gains tax rate. As we mentioned in Chapter 3, for most investors, the
capital gains tax rate is lower than the personal tax rate. Moreover, while coupon payments are taxed each year,
capital gains taxes are deferred until the bond is sold or matures. Consequently, all else equal, investors end up
paying lower taxes on discount bonds because a greater percentage of their total return comes in the form of
capital gains. For details on the tax treatment of zero coupon bonds, see Web Appendix 7A.
15 12 9 6 3 0
0
1,000
1,250
1,500
500
750
Coupon = 10%
Coupon = 7%
Coupon = 13%
Bond Value
($)
Years Remaining until Maturity
Time Paths of 7%, 10%, and 13% Coupon Bonds When the Market Rate Remains
F I G U R E 7! 2 Constant at 10%