0. Chapter 6
Interest Rates and Bond Valuation

1. Issues in Chapter 6 Financial Markets Bond market Bond valuation
Finding a price (annual vs. semiannual)
Finding a yield (annual vs. semiannual)
Premium, discount, and par bonds
A relationship between price and yield
Reading Wall Street Journal corporate bond quotation
Assessing risk
Default risk, interest rate risk, and reinvestment risk
Types of bonds
The Fisher Effect
Term structures

2. Financial Markets
Financial markets exist in order to allocate the supply of savings in the economy to the demanders of those savings.
Financial markets are institutions and procedures that facilitate transactions in all types of financial claims. A securities market is simply a place where you can buy and sell securities (example, New York Stock Exchange)

3. Public Offerings Versus Private Placements
Public Offering – Both individuals and institutional investors have the opportunity to purchase securities. The securities are initially sold by the managing investment bank firm. The issuing firm never actually meets the ultimate purchaser of securities
Private Placement (direct placement) – The securities are offered and sold to a limited number of investors
The New York Stock Exchange (NYSE), nicknamed the "Big Board", is a stock exchange based in New York City. It is the largest stock exchange in the world by dollar volume and has 2,764 listed securities.[1]

4. Primary Versus Secondary Market
Primary Market (initial issue)
Market in which new issues of a security are sold to initial buyers. This is the only time the issuing firm ever gets any money for the securities.
Example: Google raised $1.76 billion through sale of shares to public in August 2004.
Secondary Market (subsequent trading)
Market in which previously issued securities are traded. The issuing corporation does not get any money for stocks traded on the secondary market.
Example: Trading among investors today of Google stocks.
Since September 30, 1985, the NYSE trading hours have been 9:30–16:00 ET on all days of the week except Saturdays, Sundays and holidays declared by the Exchange in advance.[5]
open outcry auction market environment
The Black Thursday crash of the Exchange on October 24, 1929, and the sell-off panic which started on Black Tuesday, October 29, are often blamed for precipitating the Great Depression of In an effort to try to restore investor confidence, the Exchange unveiled a fifteen-point program aimed to upgrade protection for the investing public on October 31, 1938.
On October 1, 1934, the exchange was registered as a national securities exchange with the U.S. Securities and Exchange Commission, with a president and a thirty-three member board. On February 18, 1971 the non-profit corporation was formed, and the number of board members was reduced to twenty-five.
On October 19, 1987, the Dow Jones Industrial Average (DJIA) dropped 508 points, a 22.6% loss in a single day, the biggest one-day drop the exchange had yet experienced, prompting officials at the exchange to invoke for the first time the "circuit breaker" rule to halt all trading. This was a very controversial move and led to a quick change in the rule; trading now halts for an hour, two hours, or the rest of the day when the DJIA drops 10, 20, or 30 percent, respectively. In the afternoon, the 10% and 20% drops will halt trading for a shorter period of time, but a 30% drop will always close the exchange for the day. The rationale behind the trading halt was to give investors a chance to cool off and reevaluate their positions. Black Monday was followed by Terrible Tuesday, a day in which the Exchange's systems did not perform well and some people had difficulty completing their trades.

5. Money versus Capital Market
Money Market
Market for short-term debt instruments (maturity periods of one year or less). Money market is typically a telephone and computer market (rather than a physical building)
Examples: Treasury bills (issued by federal government), commercial paper, negotiable CDs, bankers’ acceptances.
Capital Market
Market for long-term securities (maturity greater than one year).
Examples: Corporate Bonds, Common stocks, Treasury Bonds, term loans and financial leases

6. Classifying Securities
Basic Types
Major Subtypes
Interest-bearing, or
Debts
Money market instruments
Fixed-income securities
Equities
Common stock
Preferred stock
Derivatives
Futures
Options

7. Interest-Bearing Assets
Pay interest, as the name suggests.
The value of these assets depends, at least for the most part, on interest rates.
They all begin life as a loan of some sort, so they are all debt obligations of some issuers.
Relatively low risk and often large denominations

8. Interest-Bearing Assets
Money market instruments are short-term debt obligations of large corporations and governments.
These securities promise to make one future payment.
When they are issued, their lives are less than one year.
Relatively more liquid than longer-term fixed-income securities.
Fixed-income securities are longer-term debt obligations of corporations or governments.
These securities promise to make fixed payments according to a pre-set schedule.
When they are issued, their lives exceed one year.
Less liquid.

9. Money Market Securities
Examples:
Treasury bills: Short-term debt of U.S. government
Certificates of Deposits (CDs): Time deposit with a bank
Commercial Paper: Short-term, unsecured debt of a company
Fed Funds: Very short-term loans between banks

10. Fixed-Income Securities
Examples: U.S. Treasury notes, corporate bonds (callable and/or convertible, car loans, student loans. Notes and bonds are generic terms for fixed-income securities.
Potential gains/losses:
Fixed coupon payments and final payment at maturity, except when the borrower defaults.
Possibility of gain (loss) from fall (rise) in interest rates. (Yes, there is an inverse relationship between price and market interest rates.)
Depending on the debt issue, illiquidity can be a problem. (Illiquidity means it is possible that you cannot sell these securities quickly.)

11. Interest rates : Market data from WSJ

12. 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

13. Bonds Quotation

14. Corporate bonds Bonds are debt securities.
When a corporation issues bonds, it is in essence issuing an IOU to bondholders.
The IOU or bond contract sets out the terms, including
the principal that will be owed,
the interest that will be paid, and
the time at which these payments will occur.

15. Largest U.S. Corporate Bond Financings
Issuer GM
Ford Motor Co.
AT&T
RJR Holdings
WorldCom
Sprint
Date
June 2003
July 1999
Mar 1999
May 1989
Aug 1998
Nov 1998
Amount
$16.5 billion
$8.6 billion
$8.0 billion
$6.1 billion
$5.0 billion

16. Who issues a bond? Domestically, Internationally,
Treasury bill, note, or bond: Issued by federal government, Called “risk-free” securities, about $4 trillion market
Municipal bond: Issued by a local government (e.g., state or city), Often called “munis”
Corporate bond: our focus, about $5 trillion market
Internationally,
Euro bond: Dollar-denominated bonds sold in Germany by GM
Foreign bond: “Yankee” bond (dollar-denominated bond sold in U.S. by non-U.S. issuer), “Samurai” bond (Yen bonds sold in Japan by a non-Japanese borrower), etc
T-Bond: denominations of $1,000 or more. The minimum denomination was reduced to $100 in 2008.
As of 2005, the value of outstanding US Treasury Debt was $4.17 trillion and the value of corporate bond market debt was almost $5 trillion.
suppose Disney decides to sell $1,000 bonds in France. These are U.S. denominated bonds trading in a foreign country.
Why they do this?

19. U.S. National Debt

21. Bond Features
Bond - evidence of debt issued by a corporation or a governmental body. A bond represents a loan made by investors to the issuer. In return for his/her money, the investor receives a legal claim on future cash flows from the borrower. The issuer promises to:
Make regular coupon (interest) payments every year or six months until the bond matures, and
Pay the face/par/maturity value of the bond when it matures. That is, principal payment.

22. Bond Pricing: Cash flows
Coupons at t=1,2, …. T
AMD
(Issuer, Seller, or
Borrower)
Investor
(Buyer, Lender)
Face Value at T
Price?

23. Elements of Bond Pricing
Par value (par): Face amount. paid at maturity. Usually $1,000. Entered into FV.
Coupon interest rate (PMT): Stated interest rate on the bond certificate. Multiply by par value to get dollars of interest to be paid. Generally fixed. Entered into to PMT.
3. Maturity (N): Years until bond must be repaid. Declines over time. Entered into N.
4. Yield-to-Maturity (YTM): The required return by investors that is used to discount the future coupon payments and face amount. Entered into I.

24. AMD Bond
6% Coupon
$1,000 Par
7-year Maturity
10% YTM
AMD promises to pay investors $60 (=6% coupon rate of $1,000) per year at year-end for next 7 years and one-time only $1,000 upon maturity.
$60 1 2 7
$ $1,000
V = ?
...

25. Financial Asset Valuation1 2 n r
...
CF1
CFn
CF2
Value CF CF CF PV = 1 + 2 + . . . + n .   1   2   n 1 + r 1 + r 1 + r
Suppose I ask you to lend me a loan of $1,000 at a stated interest of 10% for 1 years. That is, I promise to pay you $100 plus $1,000 at the end of the year. Suppose the current market interest rate is also 10%.
What would be a fair value of this loan? Or what would be the maximum dollar amount you are willing to lend me, given terms defined above?
Or simply how can we know if this is a fair deal to you?
The value of any financial asset (e.g., a bond, a stock, a loan, etc) is simply the present value of the cash flows the asset is expected to produce.

26. AMD Bond Again: What’s the value of a 7-year, 6% coupon bond if YTM (required return) = 10%?60 1 2 7
YTM=10%
,000
V = ?
... ( ) V
YTM B =
$60 $1 , 1
000 7 . +
= $ $ $513.16
= $805.26

27. Bond Valuation Price of a bond
= Present value of coupons and face amount (or par value)
= PV of the coupons (annuity) + PV of par value (usually $1,000)
Remember all CFs are discounted at a required return!!!

28. The bond consists of a 7-year, % annuity of $60/year plus a $1,000 lump sum at t = 7:$
513.16
$805.26
PV annuity
PV maturity value
Value of bond =
INPUTS
N I/YR PV PMT FV
OUTPUT

29. Let’s practice! More Examples
GM Bond
10%, 5-yr, YTM=10%
Price =?
Ford Bond
7%, 5-yr, YTM=10%
Chrysler Bond
15%, 5-yr, YTM=10%

30. Premium, Discount, and Par bond
If coupon rate > YTM, bond sells at a premium. (Price > Par)
The premium price is to compensate the borrower for above-market coupon rate.
If coupon rate = YTM, bond sells at its par value. (Price = Par)
If coupon rate < YTM, bond sells at a discount. (Price < Par)
The discount price is to compensate the lender for below-market coupon rate.

31. Price Changes over Time
10%, 20-year, YTM = 8%
Price today?
Price five years from today?
Price ten years from today?

32. We are dealing with two rates!
Coupon rate = A stated interest rate on the bond at the time of issuance
Yield-to-maturity = YTM is the rate of return earned on a bond held to maturity.
Usually, same as the current market interest rate for a similar investment.
The discount rate that equates a bond’s price with the present value of its future cash flows.

33. YTM = Rate of return on a bond you will earn if you hold the bond until maturity
Suppose you bought an AMD bond for $1, An AMD bond pays 10% and will mature one year from now.
Find the YTM.
PMT =$100 N = 1, FV = 1,000, PV =
YTM = ?
Find the rate of return on this investment.
Rate of Return
= (Future Income – Initial Investment) / Initial Investment
= (1, )/
= ?
From the above example, what rate of return will the investor make? Coupon rate or YTM?
If you say, “Coupon rate” to the question, you are very wrong! Why ???
You paid $1, and you will get paid $1,000 plus $100 in one year.
$1, *(1+ coupon rate) = 1,009.17*1.1 = $1,
$1, *(1+YTM) = 1,009.17*1.09 = $1,100 bingo!
One more example: PV = , N=2, PMT =100, FV =1000, I =?
I=9
So you will pay for this bond
Now you will receive $100 in one year and re-invest it at 9% for one more year. In year 2, you will get
$1,000 plus $100 plus $109.
Now FV=1209, N=2, PV= , I=? I=9 =YTM!!!

34. What if a price is given?: What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? 1 9 10
YTM=?
... 90 90 90
PV1 .
PV10
PVM
1,000
887
Find YTM that “works”!

35. Computing Yield-to-Maturity
Yield-to-maturity 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)

36. 10-year, 9% annual coupon, $1,000 par value bond that sells for $887
10-year, 9% annual coupon, $1,000 par value bond that sells for $887. YTM = ? 90 90 1 ,
000
...
887  + + + ( ) 1 ( ) ( ) 1 + 1 + 10 1 10
YTM
YTM +
YTM
10 −
N I/YR PV PMT FV
10.91
INPUTS
OUTPUT

37. Annual vs. Semiannual
Find the value of 10-year, 10% coupon, annual bond if YTM = 13%.
Find the value of 10-year, 10% coupon, semiannual bond if YTM = 13%.

38. Semiannual Bonds 1. Multiply years by 2 to get periods = 2n.
2. Divide nominal rate by 2 to get periodic rate = r / 2, or start with 2 Payment Per Year.
3. Divide annual INT by 2 to get PMT = INT/2.
2n r / OK INT/2 OK
N I/YR PV PMT FV
INPUTS
OUTPUT

39. Find the value of 10-year, 10% coupon, semiannual bond if YTM = 13%.
2(10) /2
(2 P)
N I/YR PV PMT FV
INPUTS
OUTPUT
N  Multiply by 2
YTM  2 payments per year
INT  Divide by 2

40. What’s the YTM on a 10-year, 9% semiannual coupon, $1,000 par value bond that sells for $887?1 9
20 6 mth periods
YTM=?
... 45 45 45
PV1 .
PV10
PVM
1,000
887
Find YTM that “works”!

41. Find YTM for Semiannual Bonds45 45 1 ,
000
...
887  + + +   1     1 + 1 + 20 1 20 +
YTM
YTM
YTM
INPUTS
N I/YR PV PMT FV
10.88
(2 P)
OUTPUT

42. Premium, Discount, and Par bond (continued)
Example 1: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 10%.
Example 2: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 13%.
Example 3: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 7%.

43. Graphical Relationship Between Price and Yield-to-maturity
Bond characteristics: Coupon rate = 8% with annual coupons; Par value = $1000; Maturity = 10 years
Price and Yield move in an opposite direction!
If YTM rises, price falls.

44. Premium, Discount, and Par bond
Which of the following bonds would you buy, if you must choose one?
Bond A: 12%, 1-yr, YTM = 10%, PV = 1,018.18
Bond B: 10%, 1-yr, YTM = 10%, PV = 1,000
Bond C: 5%, 1-yr, YTM = 10%, PV =
All of these bonds yield the same 10% return!
Bond A: $1, *(1+YTM) = 1,018.18*1.1 = $1,120
Bond B: $1,000 *(1+YTM) = 1,000*1.1 = $1,100
Bond C: $ *(1+YTM) = *1.1 = $1,050

45. Risks in the bond market
Default risk
“A seller may not pay me coupons and/or principal.”
The failing firm is in a financial difficulty and may not pay coupons or principal.
Interest rate risk
“A volatile interest movement may depress the value of my bonds. (also called price risk)”
Change in price due to changes in interest rates.
Long-term bonds have more price risk than short-term bonds.

46. Bond Ratings Provide One Measure of Default Risk
Low Quality, speculative, Investment-Quality Bond Ratings and/or “Junk”
High Grade Medium Grade Low Grade Very Low Grade
Standard & Poor’s AAA AA A BBB BB B CCC CC C D Moody’s Aaa Aa A Baa Ba B Caa Ca C C
Moody’s S&P
Aaa AAA Debt rated Aaa and AAA has the highest rating. Capacity to pay interest and principal is extremely strong.
Aa AA Debt rated Aa and AA has a very strong capacity to pay interest and repay principal. Together with the highest rating, this group comprises the high-grade bond class.
A A Debt rated A has a strong capacity to pay interest and repay principal, although it is somewhat more susceptible to the adverse effects of changes in circumstances and economic conditions than
debt in high rated categories.

47. Bond Ratings (continued)
Baa BBB Debt rated Baa and BBB is regarded as having an adequate capacity to pay interest and repay principal. Whereas it normally exhibits adequate protection parameters, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity to pay interest and repay principal for debt in this category than in higher rated categories. These bonds are medium-grade obligations.
Ba, B BB, B Debt rated in these categories is regarded, on balance, as Caa, CCC predominantly speculative with respect to capacity to pay Ca CC interest and repay principal in accordance with the terms of the C C obligation. BB and Ba indicate the lowest degree of speculation, and Ca, CC, and C are the highest degree of speculation. Although such debt will likely have some quality and protective characteristics, these are outweighed by large uncertainties or major risk exposures to adverse conditions. Some issues may be in default.
D D Debt rated D is in default, and payment of interest and/or repayment of principal is in arrears.
What happen to a bond price if Moodys will downgrade Xerox’s bond? Any influence to Xerox’s stock price?
Bond ratings are like a GPA of the firm.
Go to and find a debt rating of your favorite company.

48. What’s interest rate (or price) risk
What’s interest rate (or price) risk? Does a 1-year or 30-year 10% bond have more risk?
YTM
1-year
Change
30-year 5%
$1,048
$1,769
10%
1,000
+4.8%
+76.9%
15%
956
-4.4%
672
-32.8%
Interest rate risk: Rising YMD causes bond’s price to fall.

50. Does a low coupon or high coupon bond have more risk?
Bond “Stingy Corp” is a 4% coupon bond and Bond “Generous Corp.” is a 10% coupon bond. Both bonds have 12 years to maturity, make semiannual payments, and have a YTM of 9%.
If interest rates rise by 2%, what is the percentage price change of these bonds? What if rates suddenly fall by 2% instead?
What does this problem tell you about the interest rate risk of lower-coupon bonds?
-15% %
19%, %

51. True or False: “All 10-year bonds have the same price risk.”
False! Low coupon bonds have more price risk than high coupon bonds.
If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the value amount to be received at maturity.
Nothing is riskless!

52. In general, Low coupon or
long maturity bonds have a greater interest rate risk.

53. Other Types of Bonds Government bond: Federal government debt
Callable bond: The seller has an option to buy back their bonds from bond investors.
Convertible bond: The seller grant bondholders the right to exchange each bond for a designated number of common stock shares of the issuing firm.
Zero-coupon bonds: “zeros” or “deep discount” bonds
Floating-rate bonds: The coupon payments are adjustable.
Inflation-indexed bonds: Protecting against inflation, Fairly new.
Floating Rate Bonds
Coupon rate floats depending on some index value
There is less price risk and reinvestment risk with floating rate bonds
The coupon floats, so it is less likely to differ substantially from the yield-to-maturity

54. Government Bonds Treasury Securities
Federal government debt issues T-Securities
To control over money supply
To fund national projects
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 – also called “munis”
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

55. Municipal Bond Example
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
You should be willing to accept a lower stated yield on municipals because you do not have to pay taxes on the interest received. You will want to make sure the students understand why you are willing to accept a lower rate of interest. It may be helpful to take the example and illustrate the indifference point using dollars instead of just percentages. The discount you are willing to accept depends on your tax bracket.
Consider a taxable bond with a yield of 8% and a tax-exempt municipal bond with a yield of 6%
At what tax rate would you be indifferent between the two bonds?
8%(1 – T) = 6%
T = 25%
Suppose you own one $1000 bond in each and both bonds are selling at par. You receive $80 per year from the corporate and $60 per year from the municipal. How much do you have after taxes if you are in the 40% tax bracket? Corporate: 80 – 80(.4) = 48; Municipal = 60

56. Callable Bond
Issuer can refund (“buy back”) if rates decline. That helps the issuer but hurts the investor.
Therefore, borrowers are willing to pay more, and lenders pay less, on callable bonds.

57. 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, or deep discount bonds
Treasury Bills are good examples of zeroes

58. Bond Characteristics, Risk and Return
Secured bond vs. a debenture – Which bond is riskier?
Subordinated (or junior) vs. senior bond – Which bond is riskier?
A callable bond vs. a non-callable bond – Which bond is riskier?
Debenture: secured debt is less risky because the income from the security is used to pay it off first
Subordinated debenture: will be paid after the senior debt
Bond without sinking fund: company has to come up with substantial cash at maturity to retire debt and this is riskier than systematic retirement of debt through time
Callable – bondholders bear the risk of the bond being called early, usually when rates are lower. They don’t receive all of the expected coupons and they have to reinvest at lower rates.

59. Two Kinds of Interest Rates
Real rate of interest
change in purchasing power
the percentage change in the amount of stuff you can actually buy.
Nominal rate of interest
quoted rate of interest, change in purchasing power and inflation
the percentage change in the amount of money you have.
The nominal rate of interest includes our desired real rate of return plus an adjustment for expected inflation
Be sure to ask the students to define inflation to make sure they understand what it is.
Of course, we want to higher real rate and lower inflation.

60. Two Kinds of Interest Rates (continued)
Example:
Suppose we have $1000, and Diet Coke costs $2.00 per six pack. We can buy 500 six packs. Now suppose the rate of inflation is 5%, so that the price rises to $2.10 in one year. We invest the $1000 and it grows to $1100 in one year. What’s our return in dollars? In six packs?
Key issues:
What is the difference between a real return and a nominal return?
How can we convert from one to the other?

61. Two Kinds of Interest Rates (continued)
A. Dollars. Our return is
($ $1000)/$1000 = $100/$1000 = .10.
The percentage increase in the amount of green stuff is 10%; our return is 10%.
B. Six packs. We can buy $1100/$2.10 = six packs, so our return is
( )/500 = 23.81/500 = 4.76%
The percentage increase in the amount of brown stuff is 4.76%; our return is 4.76%.
From the example, the real return is 4.76%; the nominal return is 10%, and the inflation rate is 5%:
(1 + R) = 1.10
(1 + r) ´ (1 + h) = x 1.05 = 1.10

62. 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
The approximation works pretty well with “normal” real rates of interest and expected inflation. If the expected inflation rate is high, then there can be a substantial difference.

63. The Fisher Effect (concluded)
According to the Fisher Effect:
1 + R = (1 + r) ´ (1 + h)
Example: The nominal return is 10%, and the inflation is 5%. Calculate the real turn.
More example: 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%

65. 3-M T-Bill, 30-Y T-Bond, Aaa Corp B, Inflation Rate

66. 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

67. Upward-Sloping Yield Curve

68. Downward-Sloping Yield Curve

69. Factors Affecting Required Return or Yield of Corporate Bonds (rather than T-securities)
Default risk premium – remember bond ratings
Taxability premium – remember municipal versus taxable
Liquidity premium – bonds that have more frequent trading will generally have lower required returns
Anything else that affects the risk of the cash flows to the bondholders, will affect the required returns

70. Quiz 1
Suppose you purchase a zero coupon bond, face value $1,000 maturing in twenty years, for $ If the yield to maturity on the bond remains unchanged, what will the price of the bond be at the end of five years from now?
A) $315.24
B) $387.52
C) $410.91
D) $680.58
E) $1,000.00

71. Quiz 2
If the following bonds are identical except for coupon and price, what is the price of bond B?
Bond A Bond B
Face value $1,000 $1,000
Semiannual coupon $45 $35
Years to maturity
Price $1, ?
$901.03
$925.31
$960.44
$1,037.86
$1,079.63