IEB Wireframe
1 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
7.8
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
bond investors.
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.
Page 231
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?
Section 7.1
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?
Section 7.3
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?
7/31/2016 2:27 PM
IEB Wireframe
2 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
Section 7.4
What type of bonds is most apt to have a “collar”?
Section 7.6
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?
Section 7.7
The term structure of interest rates is based on what type of bonds?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
7.1
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?
7.2
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
7.1
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.
Page 232
7.2
7/31/2016 2:27 PM
IEB Wireframe
3 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
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 following:
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
7/31/2016 2:27 PM
IEB Wireframe
4 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
curve?
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?
Page 233
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
bond market?
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
BASIC
(Questions 1–17)
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?
4.
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?
5.
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?
7/31/2016 2:27 PM
IEB Wireframe
5 of 11
6.
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
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?
Page 234
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.
INTERMEDIATE
(Questions 18–31)
7/31/2016 2:27 PM
IEB Wireframe
6 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
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?
21.
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?
Page 235
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?
Company (Ticker)CouponMaturity
Last PriceLast YieldEST Vol (000s)
7/31/2016 2:27 PM
IEB Wireframe
7 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
IOU (IOU)
5.7
Apr 19, 2028 108.96
27. Bond Prices versus Yields [LO2]
??
1,827
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
compounding periods.
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
prefer? Why?
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?
Page 236
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?
7/31/2016 2:27 PM
IEB Wireframe
8 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
CHALLENGE
(Questions 32–38)
32.
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 pays $1,400 every six
months over the last six years. Bond N also has a face value of $20,000 and a maturity of 20 years; it
makes no coupon payments over the life of the bond. If the required return on both these bonds is 5.6
percent compounded semiannually, what is the current price of bond M? Of bond N?
35. Valuing the Call Feature [LO2] At one point, certain U.S. Treasury bonds were callable. Consider the
prices in the following three Treasury issues as of May 15, 2014:
5/15/20206.500 106.31250106.37500−.312505.28
5/15/20208.250 103.43750103.50000−.093755.24
5/15/202012.000134.78125134.96875−.468755.32
The bond in the middle is callable in February 2015. What is the implied value of the call feature?
Assume a par value of $1,000. (Hint: Is there a way to combine the two noncallable issues to create an
issue that has the same coupon as the callable bond?)
Page 237
36. Treasury Bonds [LO2] The following Treasury bond quote appeared in The Wall Street Journal on
May 11, 2004:
5/15/20099.125100.09375100.125000−2.15
Why would anyone buy this Treasury bond with a negative yield to maturity? How is this possible?
7/31/2016 2:27 PM
IEB Wireframe
9 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
37. Real Cash Flows [LO4] When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh
flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of
fresh flowers that the former baseball player thought appropriate for the star cost about $7. Based on
actuarial tables, “Joltin' Joe” could expect to live for 30 years after the actress died. Assume that the
EAR is 7.3 percent. Also, assume that the price of the flowers will increase at 3.7 percent per year,
when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value of
this commitment? Joe began purchasing flowers the week after Marilyn died.
38. Real Cash Flows [LO4] You are planning to save for retirement over the next 30 years. To save for
retirement, you will invest $800 per month in a stock account in real dollars and $400 per month in a
bond account in real dollars. The effective annual return of the stock account is expected to be 11
percent, and the bond account will earn 7 percent. When you retire, you will combine your money into
an account with a an effective return of 9 percent. The returns are stated in nominal terms. The inflation
rate over this period is expected to be 4 percent. How much can you withdraw each month from your
account in real terms assuming a 25-year withdrawal period? What is the nominal dollar amount of
your last withdrawal?
EXCEL MASTER IT! PROBLEM
Companies often buy bonds to meet a future liability or cash outlay. Such an investment is called a
dedicated portfolio because the proceeds of the portfolio are dedicated to the future liability. In such a case,
the portfolio is subject to reinvestment risk. Reinvestment risk occurs because the company will be
reinvesting the coupon payments it receives. If the YTM on similar bonds falls, these coupon payments will
be reinvested at a lower interest rate, which will result in a portfolio value that is lower than desired at
maturity. Of course, if interest rates increase, the portfolio value at maturity will be higher than needed.
Suppose Ice Cubes, Inc., has the following liability due in five years. The company is going to buy five-year
bonds today to meet the future obligation. The liability and current YTM are below.
Amount of liability:$100,000,000
Current YTM:
8%
1. At the current YTM, what is the face value of the bonds the company has to purchase today to meet its
future obligation? Assume that the bonds in the relevant range will have the same coupon rate as the
current YTM and these bonds make semiannual coupon payments.
2. Assume that the interest rates remain constant for the next five years. Thus, when the company
reinvests the coupon payments, it will reinvest at the current YTM. What is the value of the portfolio in
five years?
Page 238
3. Assume that immediately after the company purchases the bonds, interest rates either rise or fall by one
percent. What is the value of the portfolio in five years under these circumstances?
One way to eliminate reinvestment risk is called immunization. Rather than buying bonds with the same
maturity as the liability, the company instead buys bonds with the same duration as the liability. If you think
7/31/2016 2:27 PM
IEB Wireframe
10 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
about the dedicated portfolio, if the interest rate falls, the future value of the reinvested coupon payments
decreases. However, as interest rates fall, the price of the bond increases. These effects offset each other in an
immunized portfolio.
Another advantage of using duration to immunize a portfolio is that the duration of a portfolio is simply the
weighted average of the duration of the assets in the portfolio. In other words, to find the duration of a
portfolio, you simply take the weight of each asset multiplied by its duration and then sum the results.
4. What is the duration of the liability for Ice Cubes, Inc.?
5. Suppose the two bonds shown below are the only bonds available to immunize the liability. What face
amount of each bond will the company need to purchase to immunize the portfolio?
Bond A Bond B
Settlement:
1/1/20001/1/2000
Maturity:
1/1/20031/1/2008
Coupon rate:
7.00% 8.00%
YTM:
7.50% 9.00%
Coupons per year:
2
2
MINICASE
Financing S&S Air’s Expansion Plans with a Bond Issue
Mark Sexton and Todd Story, the owners of S&S Air, have decided to expand their operations. They
instructed their newly hired financial analyst, Chris Guthrie, to enlist an underwriter to help sell $35 million
in new 10-year bonds to finance construction. Chris has entered into discussions with Renata Harper, an
underwriter from the firm of Raines and Warren, about which bond features S&S Air should consider and
what coupon rate the issue will likely have.
Although Chris is aware of the bond features, he is uncertain about the costs and benefits of some features, so
he isn’t sure how each feature would affect the coupon rate of the bond issue. You are Renata’s assistant, and
she has asked you to prepare a memo to Chris describing the effect of each of the following bond features on
the coupon rate of the bond. She would also like you to list any advantages or disadvantages of each feature.
QUESTIONS
1. The security of the bond—that is, whether the bond has collateral.
2. The seniority of the bond.
3. The presence of a sinking fund.
4. A call provision with specified call dates and call prices.
5. A deferred call accompanying the call provision.
6. A make-whole call provision.
7. Any positive covenants. Also, discuss several possible positive covenants S&S Air might consider.
8. Any negative covenants. Also, discuss several possible negative covenants S&S Air might consider.
7/31/2016 2:27 PM
IEB Wireframe
11 of 11
http://textflow.mheducation.com/parser.php?secload=P3.7.f&fake&print
9. A conversion feature (note that S&S Air is not a publicly traded company).
10. A floating-rate coupon.
7/31/2016 2:27 PM
CHAPTER 7
INTEREST RATES AND BOND VALUATION
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
KEY CONCEPTS AND SKILLS
• Know the important bond features and bond
types
• Understand bond values and why they
fluctuate
• Understand bond ratings and what they
mean
• Understand the impact of inflation on interest
rates
• Understand the term structure of interest rates
and the determinants of bond yields
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-2
CHAPTER OUTLINE
• Bonds and Bond Valuation
• More about Bond Features
• Bond Ratings
• Some Different Types of Bonds
• Bond Markets
• Inflation and Interest Rates
• Determinants of Bond Yields
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-3
BOND DEFINITIONS
• Bond
• Par value (face value)
• Coupon rate
• Coupon payment
• Maturity date
• Yield or Yield to maturity
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-4
PRESENT VALUE OF CASH FLOWS
AS RATES CHANGE
• Bond Value = PV of coupons + PV of par
• Bond Value = PV of annuity + PV of lump
sum
• As interest rates increase, present values
decrease
• So, as interest rates increase, bond prices
decrease and vice versa
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-5
VALUING A DISCOUNT BOND
WITH ANNUAL COUPONS
• Consider a bond with a coupon rate of 10%
and annual coupons. The par value is $1,000,
and the bond has 5 years to maturity. The
yield to maturity is 11%. What is the value of
the bond?
▪ Using the formula:
• B = PV of annuity + PV of lump sum
• B = 100[1 – 1/(1.11)5] / .11 + 1,000 / (1.11)5
• B = 369.59 + 593.45 = 963.04
▪ Using the calculator:
• N = 5; I/Y = 11; PMT = 100; FV = 1,000
• CPT PV = -963.04
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-6
VALUING A PREMIUM BOND
WITH ANNUAL COUPONS
• Suppose you are reviewing a bond that has a
10% annual coupon and a face value of
$1000. There are 20 years to maturity, and the
yield to maturity is 8%. What is the price of this
bond?
▪ Using the formula:
• B = PV of annuity + PV of lump sum
• B = 100[1 – 1/(1.08)20] / .08 + 1000 / (1.08)20
• B = 981.81 + 214.55 = 1196.36
▪ Using the calculator:
• N = 20; I/Y = 8; PMT = 100; FV = 1000
• CPT PV = -1,196.36
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-7
GRAPHICAL RELATIONSHIP BETWEEN
PRICE AND YIELD-TO-MATURITY (YTM)
1400
1300
1200
1100
1000
Bond Price
Bond Price, in dollars
1500
900
800
700
600
0%
2%
4%
6%
8%
10%
12%
14%
Yield-to-Maturity Yield-to-maturity
(YTM)
(YTM)
Bond characteristics:
10 year maturity, 8% coupon rate, $1,000 par value
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-8
BOND PRICES: RELATIONSHIP
BETWEEN COUPON AND YIELD
• If YTM = coupon rate, then par value = bond
price
• If YTM > coupon rate, then par value > bond
price
▪ Why? The discount provides yield above coupon
rate
▪ Price below par value, called a discount bond
• If YTM < coupon rate, then par value < bond
price
▪ Why? Higher coupon rate causes value above par
▪ Price above par value, called a premium bond
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-9
THE BOND PRICING EQUATION
1
1
(1 + r) t
Bond Value = C
r
FV
+
t
(1 + r)
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-10
EXAMPLE 7.1
• If an ordinary bond has a coupon rate of
14 percent, then the owner will get a total
of $140 per year, but this $140 will come in
two payments of $70 each. The yield to
maturity is quoted at 16 percent. The bond
matures in seven years.
• Note: Bond yields are quoted like APRs;
the quoted rate is equal to the actual rate
per period multiplied by the number of
periods.
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
EXAMPLE 7.1
▪ How many coupon payments are there?
▪ What is the semiannual coupon payment?
▪ What is the semiannual yield?
▪ What is the bond price?
▪ B = 70[1 – 1/(1.08)14] / .08 + 1,000 / (1.08)14 =
917.56
▪ Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT
PV = -917.56
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-12
INTEREST RATE RISK
• Price Risk
▪ Change in price due to changes in interest rates
▪ Long-term bonds have more price risk than shortterm bonds
▪ Low coupon rate bonds have more price risk than
high coupon rate bonds
• Reinvestment Rate Risk
▪ Uncertainty concerning rates at which cash flows
can be reinvested
▪ Short-term bonds have more reinvestment rate risk
than long-term bonds
▪ High coupon rate bonds have more reinvestment
rate risk than low coupon rate bonds
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-13
FIGURE 7.2
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-14
COMPUTING YIELD TO MATURITY
• Yield to Maturity (YTM) is the rate implied by
the current bond price
• Finding the YTM requires trial and error if you
do not have a financial calculator and is
similar to the process for finding r with an
annuity
• If you have a financial calculator, enter N,
PV, PMT, and FV, remembering the sign
convention (PMT and FV need to have the
same sign, PV the opposite sign)
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-15
YTM WITH ANNUAL COUPONS
• Consider a bond with a 10% annual coupon
rate, 15 years to maturity and a par value of
$1,000. The current price is $928.09.
▪ Will the yield be more or less than 10%?
▪ N = 15; PV = -928.09; FV = 1,000; PMT = 100; CPT I/Y
= 11%
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-16
YTM WITH SEMIANNUAL
COUPONS
• Suppose a bond with a 10% coupon rate
and semiannual coupons, has a face value
of $1,000, 20 years to maturity and is selling
for $1,197.93.
▪ Is the YTM more or less than 10%?
▪ What is the semiannual coupon payment?
▪ How many periods are there?
▪ N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT I/Y
= 4% (Is this the YTM?)
▪ YTM = 4%* 2 = 8%
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-17
TABLE 7.1
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-18
CURRENT YIELD VS. YIELD TO
MATURITY
• Current Yield = annual coupon / price
• Yield to maturity = current yield + capital gains yield
• Example: 10% coupon bond, with semiannual
coupons, face value of 1,000, 20 years to maturity,
$1,197.93 price
▪ Current yield = 100 / 1,197.93 = .0835 = 8.35%
▪ Price in one year, assuming no change in YTM = 1,193.68
▪ Capital gain yield = (1,193.68 – 1,197.93) / 1,197.93 = -.0035
= -.35%
▪ YTM = 8.35 - .35 = 8%, which is the same YTM computed
earlier
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-19
BOND PRICING THEOREMS
• Bonds of similar risk (and maturity) will be
priced to yield about the same return,
regardless of the coupon rate
• If you know the price of one bond, you can
estimate its YTM and use that to find the
price of the second bond
• This is a useful concept that can be
transferred to valuing assets other than
bonds
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-20
BOND PRICES WITH A
SPREADSHEET
• There is a specific formula for finding
bond prices on a spreadsheet
▪ PRICE(Settlement,Maturity,Rate,Yld,Redemption,
Frequency,Basis)
▪ YIELD(Settlement,Maturity,Rate,Pr,Redemption,
Frequency,Basis)
▪ Settlement and maturity need to be actual dates
▪ The redemption and Pr need to be input as % of
par value
• Click on the Excel icon for an
example
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-21
DIFFERENCES BETWEEN
DEBT AND EQUITY
• Debt
▪ Not an ownership interest
▪ Creditors do not have
voting rights
▪ Interest is considered a
cost of doing business
and is tax deductible
▪ Creditors have legal
recourse if interest or
principal payments are
missed
▪ Excess debt can lead to
financial distress and
bankruptcy
• Equity
▪ Ownership interest
▪ Common stockholders
vote for the board of
directors and other issues
▪ Dividends are not
considered a cost of
doing business and are
not tax deductible
▪ Dividends are not a
liability of the firm, and
stockholders have no
legal recourse if
dividends are not paid
▪ An all equity firm can not
go bankrupt merely due
to debt since it has no
debt
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-22
THE BOND INDENTURE
• Contract between the company and the
bondholders that includes
▪ The basic terms of the bonds
▪ The total amount of bonds issued
▪ A description of property used as security, if
applicable
▪ Sinking fund provisions
▪ Call provisions
▪ Details of protective covenants
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-23
BOND CLASSIFICATIONS
• Registered vs. Bearer Forms
• Security
▪ Collateral – secured by financial securities
▪ Mortgage – secured by real property, normally
land or buildings
▪ Debentures – unsecured
▪ Notes – unsecured debt with original maturity less
than 10 years
• Seniority
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-24
BOND CHARACTERISTICS AND
REQUIRED RETURNS
• The coupon rate depends on the risk
characteristics of the bond when issued
• Which bonds will have the higher coupon, all
else equal?
▪
▪
▪
▪
Secured debt versus a debenture
Subordinated debenture versus senior debt
A bond with a sinking fund versus one without
A callable bond versus a non-callable bond
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-25
BOND RATINGS –
INVESTMENT QUALITY
• High Grade
▪ Moody’s Aaa and S&P AAA – capacity to pay
is extremely strong
▪ Moody’s Aa and S&P AA – capacity to pay is
very strong
• Medium Grade
▪ Moody’s A and S&P A – capacity to pay is
strong, but more susceptible to changes in
circumstances
▪ Moody’s Baa and S&P BBB – capacity to pay is
adequate, adverse conditions will have more
impact on the firm’s ability to pay
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-26
BOND RATINGS –
SPECULATIVE GRADE
• Low Grade
▪ Moody’s Ba and B
▪ S&P BB and B
▪ Considered possible that the capacity to pay
will degenerate.
• Very Low Grade
▪ Moody’s C (and below) and S&P C (and
below)
• income bonds with no interest being paid,
or
• in default with principal and interest in
arrears
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-27
GOVERNMENT BONDS
• Treasury Securities
▪ Federal government debt
▪ T-bills – pure discount bonds with original maturity of
one year or less
▪ T-notes – coupon debt with original maturity
between one and ten years
▪ T-bonds – coupon debt with original maturity greater
than ten years
• Municipal Securities
▪ Debt of state and local governments
▪ Varying degrees of default risk, rated similar to
corporate debt
▪ Interest received is tax-exempt at the federal level
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-28
EXAMPLE 7.4
• A taxable bond has a yield of 8%, and a
municipal bond has a yield of 6%.
▪ If you are in a 40% tax bracket, which bond do
you prefer?
• 8%(1 - .4) = 4.8%
• The after-tax return on the corporate bond is 4.8%,
compared to a 6% return on the municipal
▪ At what tax rate would you be indifferent
between the two bonds?
• 8%(1 – T) = 6%
• T = 25%
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-29
ZERO COUPON BONDS
• Make no periodic interest payments
(coupon rate = 0%)
• The entire yield-to-maturity comes from the
difference between the purchase price and the par
value
• Cannot sell for more than par value
• Sometimes called zeroes, deep discount bonds, or
original issue discount bonds (OIDs)
• Treasury Bills and principal-only Treasury strips are
good examples of zeroes
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-30
FLOATING-RATE BONDS
• Coupon rate floats depending on some index value
• Examples – adjustable rate mortgages and inflationlinked Treasuries
• There is less price risk with floating rate bonds
▪ The coupon floats, so it is less likely to differ
substantially from the yield-to-maturity
• Coupons may have a “collar” – the rate cannot go
above a specified “ceiling” or below a specified
“floor”
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-31
OTHER BOND TYPES
• Disaster bonds
• Income bonds
• Convertible bonds
• Put bonds
• There are many other types of provisions that
can be added to a bond and many bonds
have several provisions – it is important to
recognize how these provisions affect
required returns
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-32
SUKUK
• Sukuk are bonds have been created to meet a
demand for assets that comply with Shariah, or
Islamic law
• Shariah does not permit the charging or paying of
interest
• Sukuk are typically bought and held to maturity,
and are extremely illiquid
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-33
BOND MARKETS
• Primarily over-the-counter transactions
with dealers connected electronically
• Extremely large number of bond issues,
but generally low daily volume in single
issues
• Makes getting up-to-date prices
difficult, particularly on small company
or municipal issues
• Treasury securities are an exception
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-34
WORK THE WEB EXAMPLE
• Bond quotes are available online
• One good site is FINRA’s Market Data
Center
• Click on the web surfer to go to the site
▪ Choose a company, enter it in the Issuer Name
bar, choose Corporate, and see what you can
find!
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-35
TREASURY QUOTATIONS
• Highlighted quote in Figure 7.4
Maturity
yield
5/15/2030
Coupon
6.250
Bid
136.8359
Asked
Chg
Asked
136.9141
-0.7813
3.289
▪ What is the coupon rate on the bond?
▪ When does the bond mature?
▪ What is the bid price? What does this mean?
▪ What is the ask price? What does this mean?
▪ How much did the price change from the previous
day?
▪ What is the yield based on the ask price?
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-36
CLEAN VS. DIRTY PRICES
• Clean price: quoted price
• Dirty price: price actually paid = quoted price plus
accrued interest
• Example: Consider a T-bond with a 4% semiannual
yield and a clean price of $1,282.50:
▪
▪
▪
▪
Number of days since last coupon = 61
Number of days in the coupon period = 184
Accrued interest = (61/184)(.04*1000) = $13.26
Dirty price = $1,282.50 + $13.26 = $1,295.76
• So, you would actually pay $ 1,295.76 for the bond
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-37
INFLATION AND INTEREST RATES
• Real rate of interest – change in
purchasing power
• Nominal rate of interest – quoted rate
of interest, change in actual number of
dollars
• The ex ante nominal rate of interest
includes our desired real rate of return
plus an adjustment for expected
inflation
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-38
THE FISHER EFFECT
• The Fisher Effect defines the relationship
between real rates, nominal rates, and
inflation
• (1 + R) = (1 + r)(1 + h), where
▪ R = nominal rate
▪ r = real rate
▪ h = expected inflation rate
• Approximation
▪R=r+h
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-39
EXAMPLE 7.5
• If we require a 10% real return and we expect
inflation to be 8%, what is the nominal rate?
• R = (1.1)(1.08) – 1 = .188 = 18.8%
• Approximation: R = 10% + 8% = 18%
• Because the real return and expected
inflation are relatively high, there is significant
difference between the actual Fisher Effect
and the approximation.
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-40
TERM STRUCTURE OF
INTEREST RATES
• Term structure is the relationship between
time to maturity and yields, all else equal
• It is important to recognize that we pull out
the effect of default risk, different coupons,
etc.
• Yield curve – graphical representation of the
term structure
▪ Normal – upward-sloping; long-term yields are
higher than short-term yields
▪ Inverted – downward-sloping; long-term yields are
lower than short-term yields
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-41
FIGURE 7.6 – UPWARD-SLOPING
YIELD CURVE
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-42
FIGURE 7.6 – DOWNWARDSLOPING YIELD CURVE
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-43
FIGURE 7.7
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-44
FACTORS AFFECTING
BOND YIELDS
• Real rate of interest
• Expected future inflation premium
• Interest rate risk premium
• Default risk premium
• Taxability premium
• Liquidity premium
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-45
QUICK QUIZ
• How do you find the value of a bond, and
why do bond prices change?
• What is a bond indenture, and what are
some of the important features?
• What are bond ratings, and why are they
important?
• How does inflation affect interest rates?
• What is the term structure of interest rates?
• What factors determine the required return
on bonds? Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-46
ETHICS ISSUES
• In 1996, allegations were made against Moody’s
that it was issuing ratings on bonds it had not been
hired to rate, in order to pressure issuers to pay for
their service.
• The government conducted an inquiry, but charges
of antitrust violations were dropped. Even though
no legal action was taken, does an ethical issue
exist?
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-47
COMPREHENSIVE PROBLEM
• What is the price of a $1,000 par value bond
with a 6% coupon rate paid semiannually, if
the bond is priced to yield 5% and it has 9
years to maturity?
• What would be the price of the bond if the
yield rose to 7%.
• What is the current yield on the bond if the
YTM is 7%?
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-48
CHAPTER 7
END OF CHAPTER
Copyright © 2016 by McGraw-Hill Global Education LLC. All rights reserved.
7-49

Purchase answer to see full
attachment