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Chapter 5
Bonds, Bond Valuation, and Interest Rates
ANSWERS TO END-OF-CHAPTER QUESTIONS
5-1 a. A bond is a promissory note issued by a business or a governmental unit. Treasury
bonds, sometimes referred to as government bonds, are issued by the Federal
government and are not exposed to default risk. Corporate bonds are issued by
corporations and are exposed to default risk. Different corporate bonds have different
levels of default risk, depending on the issuing company's characteristics and on the
b. The par value is the nominal or face value of a stock or bond. The par value of a
bond generally represents the amount of money that the firm borrows and promises to
repay at some future date. The par value of a bond is often $1,000, but can be $5,000
or more. The maturity date is the date when the bond's par value is repaid to the
c. In some cases, a bond's coupon payment may vary over time. These bonds are called
floating rate bonds. Floating rate debt is popular with investors because the market
value of the debt is stabilized. It is advantageous to corporations because firms can
d. Most bonds contain a call provision, which gives the issuing corporation the right to
call the bonds for redemption. The call provision generally states that if the bonds are
called, the company must pay the bondholders an amount greater than the par value, a
e. Convertible bonds are securities that are convertible into shares of common stock, at a
fixed price, at the option of the bondholder. Bonds issued with warrants are similar to
convertibles. Warrants are options which permit the holder to buy stock for a stated
f. Bond prices and interest rates are inversely related; that is, they tend to move in the
opposite direction from one another. A fixed-rate bond will sell at par when its
g. The current yield on a bond is the annual coupon payment divided by the current
market price. YTM, or yield to maturity, is the rate of interest earned on a bond if it is
h. Corporations can influence the default risk of their bonds by changing the type of
bonds they issue. Under a mortgage bond, the corporation pledges certain assets as
security for the bond. All such bonds are written subject to an indenture, which is a
i. A development bond is a tax-exempt bond sold by state and local governments whose
proceeds are made available to corporations for specific uses deemed (by Congress)
to be in the public interest. Municipalities can insure their bonds, in which an
insurance company guarantees to pay the coupon and principal payments should the
issuer default. This reduces the risk to investors who are willing to accept a lower
j. The real risk-free rate is the rate that a hypothetical riskless security pays each
moment if zero inflation were expected. The real risk-free rate is not constant—r*
changes over time depending on economic conditions. The real risk-free rate could
also be called the pure rate of interest since it is the rate of interest that would exist on
k. The inflation premium is the premium added to the real risk-free rate of interest to
compensate for the expected loss of purchasing power. The inflation premium is the
average rate of inflation expected over the life of the security. Default risk is the risk
that a borrower will not pay the interest and/or principal on a loan as they become
l. Interest rate risk arises from the fact that bond prices decline when interest rates rise.
Under these circumstances, selling a bond prior to maturity will result in a capital
loss, and the longer the term to maturity, the larger the loss. Thus, a maturity risk
m. The term structure of interest rates is the relationship between yield to maturity and
n. When the yield curve slopes upward, it is said to be “normal,” because it is like this
5-2 False. Short-term bond prices are less sensitive than long-term bond prices to interest
5-3 The price of the bond will fall and its YTM will rise if interest rates rise. If the bond still
has a long term to maturity, its YTM will reflect long-term rates. Of course, the bond's
5-4 If interest rates decline significantly, the values of callable bonds will not rise by as much
5-5 From the corporation's viewpoint, one important factor in establishing a sinking fund is
that its own bonds generally have a higher yield than do government bonds; hence, the
company saves more interest by retiring its own bonds than it could earn by buying
On balance, investors seem to have little reason for choosing one method over the
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
5-1 With your financial calculator, enter the following:
N = 12; I/YR = YTM = 9%; PMT = 0.08 1,000 = 80; FV = 1000; PV = VB = ?
Alternatively,
5-2 With your financial calculator, enter the following:
5-3 With your financial calculator, enter the following to find the current value of the bonds,
so you can then calculate their current yield:
Alternatively,
r = r* + IP + DRP + LP + MRP.
Since these are Treasury securities, DRP = LP = 0.
rT-2 = r* + IP2
rT-3 = r* + IP3
5-5 rT-10 = 6%; rC-10 = 9%; LP = 0.5%; DRP = ?
r = r* + IP + DRP + LP + MRP.
Because both bonds are 10-year bonds the inflation premium and maturity risk premium
on both bonds are equal. The only difference between them is the liquidity and default
risk premiums.
5-6 r* = 3%; IP = 3%; rT-2 = 6.3%; MRP2 = ?
5-7 The problem asks you to find the price of a bond, given the following facts:
5-8 With your financial calculator, enter the following to find YTM:
With your financial calculator, enter the following to find YTC:
5-9 a.
2. 8%: Bond L: From Bond S inputs, change N = 15 and I/YR = 8, PV = ?, PV
Bond S: Change N = 1, PV = ? PV = $1,018.52.
3. 12%: Bond L: From Bond S inputs, change N = 15 and I/YR = 12, PV = ? PV
b. Think about a bond that matures in one month. Its present value is influenced
primarily by the maturity value, which will be received in only one month. Even if
5-10 a. Calculator solution:
b. Yes. At a price of $829, the yield to maturity, 13.98 percent, is greater than your
5-12 a. Using a financial calculator, input the following:
c. YTM = Current Yield + Capital Gains (Loss) Yield
d. Using a financial calculator, input the following:
5-13 The problem asks you to solve for the YTM, given the following facts:
N = 5, PMT = 80, and FV = 1000. In order to solve for I/YR we need PV.
However, you are also given that the current yield is equal to 8.21%. Given this
information, we can find PV.
Now, solve for the YTM with a financial calculator:
5-14 The problem asks you to solve for the current yield, given the following facts: N = 14,
5-15 The bond is selling at a large premium, which means that its coupon rate is much higher
than the going rate of interest. Therefore, the bond is likely to be called--it is more likely
to be called than to remain outstanding until it matures. Thus, it will probably provide a
return equal to the YTC rather than the YTM. So, there is no point in calculating the
YTM--just calculate the YTC. Enter these values:
5-16
Price at 8% Price at 7% Pctge. change
10-year, 10% annual coupon $1,134.20 $1,210.71 6.75%
10-year zero 463.19 508.35 9.75
