Chapter 4
Bond Valuation
ANSWERS TO BEGINNING-OF-CHAPTER QUESTIONS
4-1
The
coupon rate
is normally fixed, but it can be indexed so that it
floats with some market rate, such as the T-bill rate.
Currently
(February 2003), new GE bonds would have a coupon rate of about 6% if
they had a long maturity, but more like 4½% if they had a short
maturity.
GE’s currently outstanding bonds would have varying rates,
depending on the level of rates at the time they were issued.
The
current yield
is the annual interest divided by the bond’s
current price.
Since the price changes with changes in the market
rate, the current yield also changes over time.
Even if the market
interest rate remains constant, the current yield will change for a
bond that sells at a premium or discount.
As a discount bond
approaches maturity, its price will rise toward par (baring a strong
possibility of default), and with a rising price and constant interest
payment, the current yield will decline.
The reverse would hold for a
bond selling at a premium. See Figure 4-2 for a picture of this.
For
GE, the current yield would be fairly close to the coupon rate unless
the bond in question is an old one that sells at a large premium or
discount.
The
capital gains yield
is the change in the bond’s price for the
year divided by the beginning price.
Interest rates, hence bond
prices, move somewhat randomly, so bond prices go up and down creating
positive and negative capital gains yields. Also, as discussed above,
premium and discount bonds’ prices move toward par over time, so this
will create a tendency for such bonds to have positive or negative
capital gains yields.
The reverse would hold for a bond selling at a
premium.
The
YTM
is the discount rate that causes the PV of payments
(interest and principal) to equal the current price of the bond.
The
YTM is also the sum of the current yield and the expected capital gains
yield.
Note that virtually all bonds pay interest semiannually, and by
convention yields are quoted on a nominal basis, not an effective
annual rate basis.
See the model for YTM calculations.
The
YTC
is found like the yield to maturity, except (1) for years we
use the time to call and (2) for the final payment we use the call
price.
See the model for YTC calculations.
Brokers typically quote the yield to call
for bonds selling at a
premium because, since a premium means that the coupon rate is above
the current market rate, the bond is likely to be called.
They quote
the YTM on par and discount bonds.
4-2
Interest rate risk
is the risk that a bond’s price will decline due to
an increase n interest rates.
Note, though, that if a bond is not
callable, then its value will rise if rates fall, even though the value
will decline if rates rise.
Reinvestment rate risk
is the risk that
the income produced by a portfolio will decline due to a drop in
interest rates as maturing bonds (and coupon payments) are reinvested
Answers and Solutions:
4 - 1