206 Part 3 Financial Assets
7-5 CHANGES IN BOND VALUES OVER TIME
When a coupon bond is issued, the coupon is generally set at a level that causes the
bond’s market price to equal its par value. If a lower coupon were set, investors
would not be willing to pay $1,000 for the bond; but if a higher coupon were set,
investors would clamor for it and bid its price up over $1,000. Investment bankers
can judge quite precisely the coupon rate that will cause a bond to sell at its $1,000
par value.
A bond that has just been issued is known as a new issue. Once it has been is-
sued, it is an outstanding bond, also called a seasoned issue. Newly issued bonds gen-
erally sell at prices very close to par, but the prices of outstanding bonds can vary
widely from par. Except for " oating-rate bonds, coupon payments are constant; so
when economic conditions change, a bond with a $100 coupon that sold at its
$1,000 par value when it was issued will sell for more or less than $1,000
thereafter.
Among its outstanding bonds, Allied currently has three equally risky issues
that will mature in 15 years:- Allied’s just-issued 15-year bonds have a 10% annual coupon. They were
issued at par, which means that the market interest rate on their issue date was
also 10%. Because the coupon rate equals the market interest rate, these bonds
are trading at par, or $1,000. - Five years ago Allied issued 20-year bonds with a 7% annual coupon. These
bonds currently have 15 years remaining until maturity. They were originally
issued at par, which means that 5 years ago the market interest rate was 7%.
Currently, this bond’s coupon rate is less than the 10% market rate, so they sell
at a discount. Using a! nancial calculator or spreadsheet, we can quickly! nd
that they have a price of $771.82. (Set N! 15, I/YR! 10, PMT! 70, and FV!
1000 and solve for the PV to get the price.) - Ten years ago Allied issued 25-year bonds with a 13% coupon rate. These
bonds currently have 15 years remaining until maturity. They were originally
issued at par, which means that 10 years ago the market interest rate must
have been 13%. Because their coupon rate is greater than the current market
rate, they sell at a premium. Using a! nancial calculator or spreadsheet, we
can! nd that their price is $1,228.18. (Set N! 15, I/YR! 10, PMT! 130, and
FV! 1000 and solve for the PV to get the price.)
Each of these three bonds has a 15-year maturity; each has the same credit risk; and
thus each has the same market interest rate, 10%. However, the bonds have differ-
ent prices because of their different coupon rates.
Now let’s consider what would happen to the prices of these three bonds over
the 15 years until they mature, assuming that market interest rates remain constant
at 10% and Allied does not default on its payments. Table 7-1 demonstrates how
the prices of each of these bonds will change over time if market interest rates re-
main at 10%. One year from now each bond will have a maturity of 14 years—that
is, N! 14. With a! nancial calculator, override N! 15 with N! 14 and press the
PV key; that gives you the value of each bond 1 year from now. Continuing, set N
! 13, N! 12, and so forth, to see how the prices change over time.
Table 7-1 also shows the current yield (which is the coupon interest divided by
the bond’s price), the capital gains yield, and the total return over time. For any
given year, the capital gains yield is calculated as the bond’s annual change in price
divided by the beginning-of-year price. For example, if a bond was selling for
$1,000 at the beginning of the year and $1,035 at the end of the year, its capital
gains yield for the year would be $35/$1,000! 3.5%. (If the bond was selling at a
premium, its price would decline over time. Then the capital gains yield would be
negative, but it would be offset by a high current yield.) A bond’s total return is