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Chapter 10 Fixed-Income Securities 183
Suggested Answers to Discussion Questions
10.1 a. On average, total returns on bonds were much higher in the 1980s than in the 1970s. Interest
rates in the bond market (i.e., bond yields) generally rose in the 1970s, which kept total bond
b. During the 1990s, interest rates continued to fall, reaching levels not seen in over 30 years. By
c. Table 10.1 shows that by 2014, bond yields were very low, suggesting that there may be little
room for additional interest rate declines, and hence little room for more capital gains on bonds.
d. Answers will vary with the student’s degree of risk aversion. When students first graduate, they
are 40 years from retirement. Over this time period, extremely good years in the stock market
10.2 a. Agency bonds: bonds issued by government agencies that are high-quality securities. They
b. Municipal bonds: bonds that are the issues of states, counties, cities, and other political
c. Zero-coupon bonds: bonds that make no payments until maturity. Zero coupon bonds are useful
d. Junk bonds: high-yield bonds that have received low, sub-investment-grade ratings (below
e. Foreign bonds: bonds that are issued in a foreign country and priced in that country’s currency.
f. Collateralized mortgage obligations: payments are based on tranches that are short, medium, or
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184 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
10.3 There are no investment products in the world that are purely risk-free, yet the markets like to think
of a risk-free asset for comparison purposes, especially to determine the risk premium for risky
assets. The closest thing the markets have to a purely risk-free asset are the debt securities of the
10.5 Convertible securities start out as bonds (or even preferred stock) and may end up as shares of
common stock if the conversion value at some point exceeds the bond value. Before conversion, the
bonds are usually unsecured debt obligations and subordinated to other forms of debt. Corporations
10.6 LYONs, or liquid yield option notes, add a conversion feature and put option to a zero coupon. Like
a traditional convertible bond, investors can convert the bonds for shares through the conversion
10.7 Answers will depend on the debentures and preferred stock chosen. It may be advantageous for the
instructor to select securities and to use this question as part of a lecture. Convertible issues are not
Solutions to Problems
10.1 Current yield
Annual interest income
Current market price of bond
10.2 Current yield = coupon / market price
©2017 Pearson Education, Inc.
Chapter 10 Fixed-Income Securities 185
10.3 Interest .075 $1,000 $75
10.4 An investor, comparing municipals to corporates, must convert the municipal yield to its fully
taxable equivalent (FTEY):
Since the fully taxable equivalent yield of 7.3% is less than the 7.5% return on the corporate bond,
Yes, the decision very likely would change if this was an “in-state” bond and the investor lived in a
10.5 After-tax yield Before-tax yield [1 {FTR STR (1 FTR)}]
Where: FTR federal tax rate and STR state tax rate.
10.6 Bond A: AA-rated, in-state muni with 6.375% coupon; exempt from both federal and state income
taxes
a. Calculations for fully taxable equivalent yields (FTEY):
Bond A:
Bond yield
FTEY 1 [Federal tax rate State tax rate (1 FTR)]
6.375 6.375
1 [0.35 0.115(1 0.35)] 1 (0.35 0.0748)
11.08%
=- - -
= =
- + - - +
=
Bond B:
Bond yield 7.125
FTEY 10.96%
1 (Federal tax rate) 1 0.35
= = =
- -
186 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Note: Because the Treasury bond is exempt from state taxes only, the yield is adjusted to
b. Ranking on the basis of fully taxable equivalent yield, best to worst:
Bond Coupon FTEY
10.7 Treasury taxable equivalent yield Treasury yield/(1 State tax rate(1-FTR))
Municipal taxable equivalent yield Muni rate/[1 (FTR STR (1 FTR))]
Sara should purchase the municipal bond, as the tax-adjusted yield is 6.49%, which is better than the
tax-adjusted yield of 5.3% on the Treasury bond.
10.8 Current yield
Annual interest income
Current market price of bond
=
Coupon Interest Market Price Current Yield
95
540
All of the above bonds have a current yield of 9.72% and, as such, are identical.
10.9 a.
Coupon Interest Market Price Current Yield
$75
$962.50
As the price of the bond went up, the current yield dropped to 7.79%.
b. HPR
Annual interest income Capital gains
Purchase price
+
=
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Chapter 10 Fixed-Income Securities 187
$75 $962.50 $850 $75 $112.50
$850.00 $850.00
$187.50 22.06%
$850.00
+ - +
= =
= =
10.10 Price at 5.6% yield ($87.50//0.056) $1,562.50
Price at 6.6% yield ($87.50/0.066) 1,325.76
Loss on sale236.74
Interest income
Net loss $149.24
Caleb lost $149.24 on this investment because interest rates went up.
10.11 a.
Annual interest income + Capital gains
HPR Price at beginning of year
=
(1) (2) (3) (4) (5) (6)
Ending Beginning Capital Annual Total
Year Price Price Gain Income Return HPR
(1) – (2) (3) + (4) (5)
¸
(2)
b. Evaluation of return performance:
Year
High-Rate
d
Corporate T-Bond
Looking at the average HPRs over the five-year period, we can conclude that the high-rated
corporate bond has outperformed Treasury bonds, as would be expected: 13.20% versus 5.9%.
10.12 $20,000. A zero-coupon bond trades at a discount to face value and pays no interest during its
©2017 Pearson Education, Inc.
188 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
10.13 Nate probably purchased an asset-backed security. These securities pay a portion of principal with
10.14 a. Total return in Swiss francs:
Ending value of bond in CHF + Interest in CHF
Total return 1
Beginning value of bond in CHF
11,750 CHF + 950 CHF 1
11,000 CHF
15.45%
= -
= -
=
b. Total return in U.S. dollars:
Ending value of bond in CHF + Interest in CHF
Total return Beginning value of bond in CHF
Exchange rate at end of holding period 1
Exchange rate at beginning of period
(11,750 CHF + 950
r
Total eturn
= ´
-
=CHF) 0.8000 1
11,000 CHF 0.6329
1.4594 1
45.94%
´-
´
= -
=
(Students sometimes ask why CHF is used for Swiss currency. Actually, Fr and SFr are also
commonly used, but CHF is used by financial institutions. Because French, German, Italian and
Romansh are all official languages in Switzerland, the Latin for Swiss Republic Confoederatio
Helevetica skirts the problem of choosing one of the spoken languages.)
10.15 a. If you buy each for $10,000 and sell each for $10,000, the profit will be the interest you earn,
b. The original purchase will be $10,000/1.11 9,009 euros
10.16 Conversion equilvalent= Current Market Price of convertible bond/conversion ratio
Chapter 10 Fixed-Income Securities 189
10.17 If you spend $800 by purchasing shares, you will have 32 shares. If those shares increase in value to
$33, you will earn a profit of $8 per share or $256. That represents a 32% return on your $800
investment.
10.18 Convertible bond: $1,000 face value, 6% coupon, 20-year maturity, convertible into 20 shares;
current price of the convertible is $800, current stock price is $35.
c. Conversion value Conversion ratio Market price of the stock
d. Conversion
premium Current market price of convertible Conversion value
e.
Payback period =
Conversion premium (in $)
Annual interest Annual dividend
income from income from
convertible bond underlying CS
-
=
$100 $100
$60 (20 0.75) $60 $15
=
- ´ -
2.2 years
Investment value Value as a straight (nonconvertible) bond
So the convertible is selling near its floor, or its value as a bond.
10.19 Price of convertible in one year will be 10% over the conversion value.
Conversion value (end of year) Price of stock Conversion ratio
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190 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
Now with $5,000, an investor can buy five bonds priced at $1,000 each. Therefore:
One-year holding period return $3,650/$5,000 73%
Given the convertible is selling at a price of $1,000, which includes a 25% conversion premium:
(A factor of 1.25 is used in this formula since, with a 25% conversion premium, the price of the
convertible will be equal to 125% of the conversion value.)
Conversion value
Price of underlying common stock Security's conversion ratio
$800/20 $40/share
=
= =
Note: This problem shows that, while the price of the convertible went up by 65% over the course
of the year (from $1,000 to $1,650), the price of the underlying common stock went up even more:
10.20 The investment value of a convertible bond is done by pricing the bond at a rate equal (or close) to
10.21 Conversion value Conversion ratio Price of common stock
Conversion premium Market price Conversion value
So there is a conversion premium of $18 or 25% ($18/$72).
Conversion parity
Market price of convertible
Conversion ratio
$90 $50
1.8 =
Conversion parity is the price the common stock would have to sell for in order to make the
Chapter 10 Fixed-Income Securities 191
Solutions to Case Problems
Case 10.1 Max and Veronica Develop a Bond Investment Program
This simple case requires the student to choose a fixed-income investment strategy for a couple who hope
to invest on a long-term basis. In particular, the student must review and consider the applicability of
several kinds of issues as they relate to the investment needs of this couple.
a.Max and Veronica don’t rely on the income from their investments for their day-to-day needs. They have
an adequate income, and given that they say that the want to achieve some capital appreciation while
b.Max and Veronica could consider a variety of issues. For example, Treasury obligations maturing in 20
years or more would be one option. Treasury obligations have low risk, are noncallable or have very
long call deferment periods, and are exempt from state and local taxes. Agency issues are another
Case 10.2 The Case of the Missing Bond Ratings
In this case, the student relates various financial ratios to bond ratings in order to assign a bond rating to a
particular issue. The student should review the financial ratios presented in Chapter 6 before solving this
case.
a.Bonds issued by Companies 2, 3, and 6 are investment grade issues. The bonds issued by the other three
(1, 4, and 5) are in the junk bond category. Comparing the various financial ratios, we see that
b.AAA is the highest rating for a bond, while B is the one of the lowest rating for speculative
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192 Smart/Gitman/Joehnk • Fundamentals of Investing, Thirteenth Edition
c.Company 6 ranks second in terms of financial ratios; its current ratio is slightly better than
Companies 1 and 5 are fairly similar with respect to the financial ratios. Even though Company 5 has a
Answer to Chapter-Opening Problem
a. Both upgrades and downgrades are generally trending up over time. The main reason for this is that
b. Downgrades outnumber upgrades in most years. In part, this is because firms typically issue debt
when their credit ratings are high rather than low. That is, if a firm is having financial difficulties and
would have to issue a low-rated bond if it borrowed, the firm is less likely to issue the bond. Instead,
c. The ratio of downgrades to upgrades was relatively high in 1990, 1991, 2001, 2002, 2008, and 2009.
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