CHAPTER 15
GOVERNMENT SECURITIES
Teaching Guides for the Questions and Problems in the Text
QUESTIONS
15-1. The federal government has the constitutional right to tax and to create money. Thus,
there should be no question of the ability of the federal government to pay interest and
15-2. Treasury bills are short-term federal government debt. Bills are issued in minimum
denominations of $10,000 and are auctioned off at a discount, which establishes their yield.
Series EE bonds are also sold at a discount, but the units are very small (e.g., $50 for $100
15-3. The prices of all debt instruments are sensitive to changes in interest rates. When
interest rates rise, the market prices of both federal government and state and local
15-4. a. A bond secured by full faith and credit is supported by the taxing authority of the
issuing government. The government is obligated to raise revenues to service the debt.
A bond secured by a moral obligation is not supported by taxing authority. Some federal
government agency bonds (but not all) are supported by the full faith and credit of the
federal government.
Federal agency bonds that lack full faith and credit backing are supported by the revenues
generated by the projects they financed. If the revenues are insufficient, the federal
b. A revenue bond (e.g., a bond issued to finance the construction of a toll road) is similar
to a bond supported by a moral obligation. If revenues are insufficient, there is no
A general obligation is similar to a bond secured by full faith and credit because it must be
paid from all sources of revenues available to the borrower, especially the taxing authority
5. a. Sources of risk to investors owning federal government bonds are (1) fluctuations in
the market price caused by changes in interest rates, (2) reinvestment rate risk, and (3) loss
b. Owners of municipal debt also must bear the risks enumerated above. In addition, these
investors must bear the risk associated with default (i.e., government specific or
unsystematic risk). This source of risk may be reduced by purchasing bonds with high
6. This question continues the previous question. Treasury inflation-indexed bonds have a
7. A term bond issue matures at a specified date. A serial bond issue has a specified amount
of debt maturing each year. Many governments use serial bonds to finance capital
8. A mortgage pass-through bond is a long-term security used to finance purchases of
home. Payments are made to the holders of the bonds as the mortgages are paid off. Each
payment consists of both interest and principal repayment. Ginnie Mae bonds are
9. a. If interest rates increase, the market prices of Ginnie Mae and municipal bonds will
fall.
b. During periods of higher interest rates, homeowners will in the aggregate tend to retard
the retirement of principal paid on their mortgages. Fewer homes will be purchased so
fewer existing mortgages will be retired. Any slowdown in principal repayments will
Municipal bond interest (the coupon) will not be affected by the higher interest rates, so
bondholders should continue to receive the same periodic payments. However, there is no
incentive for the municipalities to refinance the debt since interest rates have increased, so
the bondholders cannot anticipate early retirement of the debt.
The answer to (a) suggests that the prices of both types of bonds respond in the same way
10. a. Retired couples seeking income should prefer government securities that generate a
b. An investor in the highest tax bracket who wants a liquid investment would prefer a
c. Since the investment is being placed in an IRA, there is no reason to include a
d. A child with a modest amount to invest may acquire series EE bonds, which are sold in
small denominations and offer competitive, short-term yields that will adjust if interest
rates rise. The tax on the income is also deferred, which may be desirable if the child’s
e. A corporation seeking to invest a substantial amount for a short period of time would
f. A church is tax-exempt institution, so there is no need to consider tax-exempt securities.
An endowment fund should generate income, so the funds should be invested in safe
11. and 12. These questions request the student to obtain current data concerning the yields
PROBLEMS
15-1. The T-bill is purchased for $96,750 and will pay $100,000 when retired.
The discount yield is
15-2. The formula for determining after-tax equality of yields is ic( 1 – t) = im
If t = .28 and im = 3.3%, then ic(1 – .28) = 0.72 and
Both the corporate and the municipal bonds offer the same after-tax yields. If the bonds are
virtually identical (same rating and same term to maturity), the choice will depend on other
15-4. a. At 4 percent the prices of the bonds (interest
compounded annually) are
Bond A: $1,000/(1 + .04)5 = $1,000(.822) = $822
(N = 5; I = 4; PMT = 0; FV = 1000; PV = ? = -821.93.)
b. At 7 percent the prices of the bonds are
Bond A: $1,000/(1 + .07)5 = $1,000(.713) = $713
c. At 10 percent the prices of the bonds are
Bond A: $1,000/(1 + .1)5 = $1,000(.621) = $621
As interest rates rise, the prices of zero coupon bonds fall dramatically. The longer the firm
to maturity, the more the bond’s price falls (e.g., Bond A’s price decline form $821 to $456
versus Bond C’s price decline from $621 to $149).
15-5. The formula for determining the after-tax equality of yields is
ic( 1 – t) = im
15-6. The discount yield uses a 360-day year and the face amount of the security instead
of the actual price. If the $10,000 bill sells for $9,844, the investor earns $156 in interest
($10,000 – $9,844), and the discount yield is ($156/$10,000) x 360/180 = 3.12%.
If the principal is adjusted downward for a decline in the CPI, the above is correct. Federal
government bonds are not adjusted downward, so the principal in year 2 is $1,000 and the
interest is $30.00. I use the difference in the adjustments to illustrate that a true
inflation-indexed bond’s principal amount could decline.
b. Principal repayment:
c. The annualized return (the internal rate of return):
Traditional bond:
3.465 and 0.792 are the interest factors for the present value of an annuity at 6 percent for
four years and the present value of $1 at 6 percent for four years. Using a financial
calculator, the answer is
d. In this illustration, the traditional bond generated the higher return because the rate of
inflation was insufficient to increase the nominal return on the indexed bond.
15-8. a. Value of the zero coupon bond when originally issued:
b. Value of the bond after three years have passed:
$1,000/(1 + .06)7 = $1,000(.665) = $665
If you buy the bond for $558 and hold it for three years, the annual return is 6 percent.
If you buy the bond for $558 and hold it for six years, the annual return is 6 percent.
If you buy the bond for $558 and hold it for nine years, the annual return is 6 percent.
c. Value of the bond after three years have passed:
Value of the bond after six years have passed:
Value of the bond after nine years have passed:
Notice that as the bond approaches maturity, its yield diminishes so its price rises more that
in part (b).
If the investor sells the bond that was purchased for $558 when it was initially issued, the
annualized returns will be
After three years: $558(1 + r)3 = $711
Return is between 8 and 9 percent.
After six years: $558(1 + r)6 = $855
Return is between 6 and 7 percent.
Notice that selling the bond as it approaches maturity increases the annual return as the
investor rides the yield curve.
d. In this part, the investor rides the yield curve and it shifts down with a general decrease
in interest rates. The total effect is to magnify the yields from riding the curve.
Value of the bond after three years have passed:
years have passed:
Value of the bond after nine years have passed:
If the investor sold the bond that was initially purchased for $558 when it was initially
issued, the annualized returns would be
After three years: $558(1 + r)3 = $760
After nine years: $558(1 + r)9 = $980
IF = $980/$558 = 1.756
Return is between 6 and 7 percent.
e. In this part the investor rides the yield curve but yields rise across the board. The
magnification from riding the yield is reduced.
Value of the bond after three years have passed:
Value of the bond after six years have passed:
Value of the bond after nine years have passed:
If the investor sells the bond that was initially purchased for $558, the annualized returns
will be
f. The returns differ because the structure changes, which affects the price of the bond.
When yields decline, the price rises more and magnifies the return generated by riding the
yield curve. The opposite occurs as interest rates rise, but since the yield curve is generally
positively sloping, this positive slope reduces the impact of higher interest rates.
15-9. To answer the questions, determine the yield to call for years four through seven.
The following answers use a financial calculator,
Four years:
Seven years: 3.63% versus 3.18%.
If the investor can endure the risk associated with the call feature, the return on the
investment is higher for each year. For example, the investor earns 2.35% with certain
Problems 15-10 through 15-13
The value of a mortgage-backed bond depends on the expected cash inflows which are
made by the homeowners, Early repayments, refundings, and increased principal