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Summary and Conclusions
This chapter has explored bonds, bond yields, and interest rates:
1. Determining bond prices and yields is an application of basic discounted cash flow principles.
2. Bond values move in the direction opposite that of interest rates, leading to potential gains or losses for
3. Bonds have a variety of features spelled out in a document called the indenture.
4. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have no risk of
default, whereas so-called junk bonds have substantial default risk.
5. A wide variety of bonds exist, many of which contain exotic or unusual features.
6. Almost all bond trading is OTC, with little or no market transparency in many cases. As a result, bond
price and volume information can be difficult to find for some types of bonds.
7. Bond yields and interest rates reflect the effect of six different things: the real interest rate and five
premiums that investors demand as compensation for inflation, interest rate risk, default risk, taxability,
and lack of liquidity.
In closing, we note that bonds are a vital source of financing to governments and corporations of all types.
Bond prices and yields are a rich subject, and our one chapter, necessarily, touches on only the most
important concepts and ideas. There is a great deal more we could say, but, instead, we will move on to
stocks in our next chapter.
CONNECT TO FINANCE
Connect Finance Do you use Connect Finance to practice what you
learned? If you don’t, you should - we can help you master the topics presented in this material. Log on to
connect.mheducation.com to learn more!
Can you answer the following Connect Quiz questions?
An 8 percent, semiannual coupon bond has a face value of $1,000 and a current market value of
$1,030. What is the current yield?
The 10-year bonds issued by KP Enterprises were rated as BBB and Baa last year. This year, the bonds
are rated as CC and Ca. What term best applies to these bonds today?
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What type of bonds is most apt to have a “collar”?
Kate wants to earn a 4 percent real rate of return. To do this, what nominal rate must she earn if the
inflation rate is 3.6 percent?
The term structure of interest rates is based on what type of bonds?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
Bond Values A Microgates Industries bond has a 10 percent coupon rate and a $1,000 face value.
Interest is paid semiannually, and the bond has 20 years to maturity. If investors require a 12 percent
yield, what is the bond’s value? What is the effective annual yield on the bond?
Bond Yields A Macrohard Corp. bond carries an 8 percent coupon, paid semiannually. The par value is
$1,000, and the bond matures in six years. If the bond currently sells for $911.37, what is its yield to
maturity? What is the effective annual yield?
ANSWERS TO CHAPTER REVIEW AND SELF-TEST PROBLEMS
Because the bond has a 10 percent coupon yield and investors require a 12 percent return, we know
that the bond must sell at a discount. Notice that, because the bond pays interest semiannually, the
coupons amount to $100/2 = $50 every six months. The required yield is 12%/2 = 6% every six
months. Finally, the bond matures in 20 years, so there are a total of 40 six-month periods.
The bond’s value is thus equal to the present value of $50 every six months for the next 40 six-month
periods plus the present value of the $1,000 face amount:
Notice that we discounted the $1,000 back 40 periods at 6 percent per period, rather than 20 years at 12
percent. The reason is that the effective annual yield on the bond is 1.062 − 1 = 12.36%, not 12 percent.
We thus could have used 12.36 percent per year for 20 years when we calculated the present value of
the $1,000 face amount, and the answer would have been the same.
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The present value of the bond’s cash flows is its current price, $911.37. The coupon is $40 every six
months for 12 periods. The face value is $1,000. So the bond’s yield is the unknown discount rate in
The bond sells at a discount. Because the coupon rate is 8 percent, the yield must be something in
excess of that.
If we were to solve this by trial and error, we might try 12 percent (or 6 percent per six months):
This is less than the actual value, so our discount rate is too high. We now know that the yield is
somewhere between 8 and 12 percent. With further trial and error (or a little machine assistance), the
yield works out to be 10 percent, or 5 percent every six months.
By convention, the bond’s yield to maturity would be quoted as 2 × 5% = 10%. The effective yield is
thus 1.052 − 1 = 10.25%.
CONCEPTS REVIEW AND CRITICAL THINKING QUESTIONS
1. Treasury Bonds [LO1] Is it true that a U.S. Treasury security is risk-free?
2. Interest Rate Risk [LO2] Which has greater interest rate risk, a 30-year Treasury bond or a 30-year
BB corporate bond?
3. Treasury Pricing [LO1] With regard to bid and ask prices on a Treasury bond, is it possible for the bid
price to be higher? Why or why not?
4. Yield to Maturity [LO2] Treasury bid and ask quotes are sometimes given in terms of yields, so there
would be a bid yield and an ask yield. Which do you think would be larger? Explain.
5. Call Provisions [LO1] A company is contemplating a long-term bond issue. It is debating whether to
include a call provision. What are the benefits to the company from including a call provision? What
are the costs? How do these answers change for a put provision?
6. Coupon Rate [LO1] How does a bond issuer decide on the appropriate coupon rate to set on its
bonds? Explain the difference between the coupon rate and the required return on a bond.
7. Real and Nominal Returns [LO4] Are there any circumstances under which an investor might be
more concerned about the nominal return on an investment than the real return?
8. Bond Ratings [LO3] Companies pay rating agencies such as Moody’s and S&P to rate their bonds,
and the costs can be substantial. However, companies are not required to have their bonds rated; doing
so is strictly voluntary. Why do you think they do it?
9. Bond Ratings [LO3] Often, junk bonds are not rated. Why?
10. Term Structure [LO5] What is the difference between the term structure of interest rates and the yield
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11. Crossover Bonds [LO3] Looking back at the crossover bonds we discussed in the chapter, why do you
think split ratings such as these occur?
12. Municipal Bonds [LO1] Why is it that municipal bonds are not taxed at the federal level, but are
taxable across state lines? Why are U.S. Treasury bonds not taxable at the state level? (You may need
to dust off the history books for this one.)
13. Bond Market [LO1] What are the implications for bond investors of the lack of transparency in the
14. Rating Agencies [LO3] A controversy erupted regarding bond-rating agencies when some agencies
began to provide unsolicited bond ratings. Why do you think this is controversial?
15. Bonds as Equity [LO1] The 100-year bonds we discussed in the chapter have something in common
with junk bonds. Critics charge that, in both cases, the issuers are really selling equity in disguise.
What are the issues here? Why would a company want to sell “equity in disguise”?
QUESTIONS AND PROBLEMS
1. Interpreting Bond Yields [LO1] Is the yield to maturity on a bond the same thing as the required
return? Is YTM the same thing as the coupon rate? Suppose today a 10 percent coupon bond sells at
par. Two years from now, the required return on the same bond is 8 percent. What is the coupon rate on
the bond then? The YTM?
2. Interpreting Bond Yields [LO2] Suppose you buy a 7 percent coupon, 20-year bond today when it’s
first issued. If interest rates suddenly rise to 15 percent, what happens to the value of your bond? Why?
3. Valuing Bonds [LO2] Even though most corporate bonds in the United States make coupon payments
semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German
company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 5.8
percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond?
Bond Yields [LO2] A Japanese company has a bond outstanding that sells for 91.53 percent of its
¥100,000 par value. The bond has a coupon rate of 3.4 percent paid annually and matures in 16 years.
What is the yield to maturity of this bond?
Coupon Rates [LO2] Essary Enterprises has bonds on the market making annual payments, with
eight years to maturity, a par value of $1,000, and selling for $948. At this price, the bonds yield 5.9
percent. What must the coupon rate be on the bonds?
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Bond Prices [LO2] Sqeekers Co. issued 15-year bonds a year ago at a coupon rate of 4.1 percent.
The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is
4.5 percent, what is the current bond price?
7. Bond Yields [LO2] Heginbotham Corp. issued 20-year bonds two years ago at a coupon rate of 5.3
percent. The bonds make semiannual payments. If these bonds currently sell for 105 percent of par
value, what is the YTM?
8. Coupon Rates [LO2] DMA Corporation has bonds on the market with 14.5 years to maturity, a YTM
of 5.3 percent, a par value of $1,000, and a current price of $965. The bonds make semiannual
payments. What must the coupon rate be on these bonds?
9. Zero Coupon Bonds [LO2] You find a zero coupon bond with a par value of $10,000 and 17 years to
maturity. If the yield to maturity on this bond is 4.9 percent, what is the price of the bond? Assume
semiannual compounding periods.
10. Valuing Bonds [LO2] Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of
4.9 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 3.8
percent. What is the price of the bond?
11. Valuing Bonds [LO2] Union Local School District has a bond outstanding with a coupon rate of 3.7
percent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 3.9 percent,
and the bond has a par value of $5,000. What is the price of the bond?
12. Calculating Real Rates of Return [LO4] If Treasury bills are currently paying 5.1 percent and the
inflation rate is 2.2 percent, what is the approximate real rate of interest? The exact real rate?
13. Inflation and Nominal Returns [LO4] Suppose the real rate is 1.9 percent and the inflation rate is 3.1
percent. What rate would you expect to see on a Treasury bill?
14. Nominal and Real Returns [LO4] An investment offers a total return of 11.5 percent over the coming
year. Janice Yellen thinks the total real return on this investment will be only 9 percent. What does
Janice believe the inflation rate will be over the next year?
15. Nominal versus Real Returns [LO4] Say you own an asset that had a total return last year of 11.65
percent. If the inflation rate last year was 3.4 percent, what was your real return?
16. Using Treasury Quotes [LO2] Locate the Treasury issue in Figure 7.4 maturing in February 2038.
What is its coupon rate? What is its bid price? What was the previous day’s asked price? Assume a par
value of $10,000.
17. Using Treasury Quotes [LO2] Locate the Treasury bond in Figure 7.4 maturing in August 2039. Is
this a premium or a discount bond? What is its current yield? What is its yield to maturity? What is the
bid–ask spread in dollars? Assume a par value of $10,000.
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18. Bond Price Movements [LO2] Bond X is a premium bond making semiannual payments. The bond
pays a coupon rate of 8.5 percent, has a YTM of 7 percent, and has 13 years to maturity. Bond Y is a
discount bond making semiannual payments. This bond pays a coupon rate of 7 percent, has a YTM of
8.5 percent, and also has 13 years to maturity. What is the price of each bond today? If interest rates
remain unchanged, what do you expect the price of these bonds to be one year from now? In three
years? In eight years? In 12 years? In 13 years? What’s going on here? Illustrate your answers by
graphing bond prices versus time to maturity.
19. Interest Rate Risk [LO2] Both Bond Sam and Bond Dave have 6.5 percent coupons, make
semiannual payments, and are priced at par value. Bond Sam has 3 years to maturity, whereas Bond
Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percentage
change in the price of Bond Sam? Of Bond Dave? If rates were to suddenly fall by 2 percent instead,
what would the percentage change in the price of Bond Sam be then? Of Bond Dave? Illustrate your
answers by graphing bond prices versus YTM. What does this problem tell you about the interest rate
risk of longer-term bonds?
20. Interest Rate Risk [LO2] Bond J has a coupon rate of 3 percent. Bond K has a coupon rate of 9
percent. Both bonds have 19 years to maturity, make semiannual payments, and have a YTM of 6
percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds?
What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate
risk of lower-coupon bonds?
Bond Yields [LO2] Bourdon Software has 6.4 percent coupon bonds on the market with 18 years
to maturity. The bonds make semiannual payments and currently sell for 106.8 percent of par. What is
the current yield on the bonds? The YTM? The effective annual yield?
22. Bond Yields [LO2] Chamberlain Co. wants to issue new 20-year bonds for some much-needed
expansion projects. The company currently has 7 percent coupon bonds on the market that sell for
$1,083, make semiannual payments, and mature in 20 years. What coupon rate should the company set
on its new bonds if it wants them to sell at par?
23. Accrued Interest [LO2] You purchase a bond with an invoice price of $1,035. The bond has a coupon
rate of 5.9 percent, and there are four months to the next semi-annual coupon date. What is the clean
price of the bond?
24. Accrued Interest [LO2] You purchase a bond with a coupon rate of 4.7 percent and a clean price of
$951. If the next semiannual coupon payment is due in two months, what is the invoice price?
25. Finding the Bond Maturity [LO2] Shinoda Corp. has 8 percent coupon bonds making annual
payments with a YTM of 7.2 percent. The current yield on these bonds is 7.55 percent. How many
years do these bonds have left until they mature?
26. Using Bond Quotes [LO2] Suppose the following bond quotes for IOU Corporation appear in the
financial page of today’s newspaper. Assume the bond has a face value of $2,000 and the current date
is April 19, 2015. What is the yield to maturity of the bond? What is the current yield?
Last PriceLast YieldEST Vol (000s)
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Apr 19, 2028 108.96
27. Bond Prices versus Yields [LO2]
1. What is the relationship between the price of a bond and its YTM?
2. Explain why some bonds sell at a premium over par value while other bonds sell at a discount.
What do you know about the relationship between the coupon rate and the YTM for premium
bonds? What about for discount bonds? For bonds selling at par value?
3. What is the relationship between the current yield and YTM for premium bonds? For discount
bonds? For bonds selling at par value?
28. Interest on Zeroes [LO2] Imagination Dragons Corporation needs to raise funds to finance a plant
expansion, and it has decided to issue 25-year zero coupon bonds with a par value of $1,000 each to
raise the money. The required return on the bonds will be 5.8 percent. Assume semiannual
1. What will these bonds sell for at issuance?
2. Using the IRS amortization rule, what interest deduction can the company take on these bonds in
the first year? In the last year?
3. Repeat part (b) using the straight-line method for the interest deduction.
4. Based on your answers in (b) and (c), which interest deduction method would the company
29. Zero Coupon Bonds [LO2] Suppose your company needs to raise $47 million and you want to issue
20-year bonds for this purpose. Assume the required return on your bond issue will be 6 percent, and
you're evaluating two issue alternatives: a semiannual coupon bond with a coupon rate of 6 percent and
a zero coupon bond. Your company’s tax rate is 35 percent. Both bonds will have a par value of $1,000.
1. How many of the coupon bonds would you need to issue to raise the $47 million? How many of
the zeroes would you need to issue?
2. In 20 years, what will your company’s repayment be if you issue the coupon bonds? What if you
issue the zeroes?
3. Based on your answers in (a) and (b), why would you ever want to issue the zeroes? To answer,
calculate the firm’s aftertax cash outflows for the first year under the two different scenarios.
Assume the IRS amortization rules apply for the zero coupon bonds.
30. Finding the Maturity [LO2] You’ve just found a 10 percent coupon bond on the market that sells for
par value. What is the maturity on this bond?
31. Real Cash Flows [LO4] You want to have $2.6 million in real dollars in an account when you retire in
40 years. The nominal return on your investment is 10.8 percent and the inflation rate is 3.7 percent.
What real amount must you deposit each year to achieve your goal?
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Components of Bond Returns [LO2] Bond P is a premium bond with a coupon rate of 10
percent. Bond D has a coupon rate of 4 percent and is currently selling at a discount. Both bonds make
annual payments, have a YTM of 7 percent, and have 10 years to maturity. What is the current yield for
bond P? For bond D? If interest rates remain unchanged, what is the expected capital gains yield over
the next year for bond P? For bond D? Explain your answers and the interrelationships among the
various types of yields.
33. Holding Period Yield [LO2] The YTM on a bond is the interest rate you earn on your investment if
interest rates don’t change. If you actually sell the bond before it matures, your realized return is
known as the holding period yield (HPY).
1. Suppose that today you buy a bond with an annual coupon rate of 7 percent for $1,060. The bond
has 17 years to maturity. What rate of return do you expect to earn on your investment? Assume
a par value of $1,000.
2. Two years from now, the YTM on your bond has declined by 1 percent, and you decide to sell.
What price will your bond sell for? What is the HPY on your investment? Compare this yield to
the YTM when you first bought the bond. Why are they different?
34. Valuing Bonds [LO2] Jallouk Corporation has two different bonds currently outstanding. Bond M has
a face value of $20,000 and matures in 20 years. The bond makes no payments for the first six years,
then pays $1,100 every six months over the subsequent eight years, and finally ...
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