1. Chapter 6
Bonds

2. Chapter Outline Why Issue Debts? Bond Basics Interest Rate
Yield Curve
Bond Valuation
Zero-Coupon Bonds
Coupon Bonds
Why Bond Price Changes
Premium, Discount, Par
Capital gain / loss yield, Current yield, Yield to Maturity
Interest Rate Sensitivity
Bond Credit Risk
Credit Spread and Credit Rating 2

3. Why Issue debt?

4. Investing in Bonds

5. Advantage of Debt over Equity
Interest expense is tax-deductible but dividend is not.
Avoid earning/ownership dilution
Avoid a high flotation cost for issuing stock.
Flotation cost = Underwriting fee, Fee to investment banker
Income Statement
Revenue
-COGS
Profit Margin30 cents tax saving for each dollar of interest
- Op. Cost Firm w/o Debt Firm w/ Debt
EBIT $5 $5
-Int. Exp
EBT
-Tax (30%)
Net Income

6. Example of Tax Saving with Debt
Income Statement
Revenue
−COGS
Profit Margin
− Op. Cost Firm w/o Debt Firm w/ Debt EBIT $5 $5
−Int. Exp
EBT
−Tax (30%)
Net Income
30 cents savings for every dollar of interest expense

7. Disadvantage of Debt
A high level of debt increases credit / default risk.
Interest payments can be a burden, while dividend payments can be skipped or reduced.
A high level of debt may make it difficult to obtain additional funding.
Debt covenants can be a burden.

8. Bond basics

9. Types of Bonds Domestically, Internationally,
Treasury bill, note, or bond: Issued by federal government, Called “risk-free” securities, about $4 trillion market
Municipal bond: “munis”
Corporate bond: 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

10. Types of Bonds
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

11. AMD Bonds

12. Bond Pricing: Cash Flow
Coupons at t=1,2, …. T
AMD
(Issuer, Seller, or
Borrower)
Investor
(Buyer, Lender)
Face Value at T
Price?
Main Question: At how much would a buyer be willing to pay for this bond?

13. Elements of Bond Pricing
Par value (par): Face amount. paid at maturity. Assume $1,000.
Coupon interest rate: Stated interest rate on the bond certificate. Multiply by par value to get dollars of interest to be paid. Generally fixed.
3. Maturity: Years until bond must be repaid. Declines over time.
4. Yield-to-Maturity (YTM): The current market interest rate that is used to discount the future coupon payments and face amount. Or, the required rate of return to be earned from other bonds with same level of risk.

14. Interest rates - Review

15. U.S. Interest Rates and Inflation Rates, 1955–2009
INTEREST rates are very low around the developed world; near-zero in nominal terms and negative in real terms. This is part of a deliberate policy by central banks to discourage saving and encourage borrowing. It has also been seen as a way of boosting the stockmarket and thus as creating a wealth effect for individuals, and boosting confidence.

16. The Determinants of Interest Rates
The Yield Curve and Discount Rates
Term Structure
The relationship between the investment term and the interest rate
Yield Curve
A plot of bond yields as a function of the bonds’ maturity date
Risk-Free Interest Rate
The interest rate at which money can be borrowed or lent without risk over a given period.

17. Term Structure of Risk-Free U. S
Term Structure of Risk-Free U.S. Interest Rates, November 2006, 2007, and 2008

18. The Determinants of Interest Rates
The Yield Curve and Discount Rates
Present Value of a Cash Flow Stream Using a Term Structure of Discount Rates
(Eq. 5.7)

19. Using the Term Structure to Compute Present Values
Compute the present value of a risk-free five-year annuity of $2,500 per year, given the following yield curve for July 2009.
Term
Date
Years
July-09 1
0.54% 2
1.05% 3
1.57% 4
2.05% 5
2.51%
$2,500 1 2 3 4 5

20. Using the Term Structure to Compute Present Values
The yield curve tells us the market interest rate per year for each different maturity.
In order to correctly calculate the PV of cash flows from five different maturities, we need to use the five different interest rates corresponding to those maturities.
Note that we cannot use the annuity formula here because the discount rates differ for each cash flow.
However, in a typical finance class like this one, we assume that interest rates will remain the same, and this assumption allows us to use one interest rates for all different maturities. Then we can use the annuity formula.

21. The Determinants of Interest Rates
Interest Rate Determination
Federal Funds Rate
The overnight loan rate charged by banks with excess reserves at a Federal Reserve bank to banks that need additional funds to meet reserve requirements
The Federal Reserve determines very short-term interest rates through its influence on the federal funds rate
If interest rates are expected to rise, long-term interest rates will tend to be higher than short-term rates to attract investors
If interest rates are expected to fall, long-term rates will tend to be lower than short-term rates to attract borrowers.

22. Yield Curve Shapes Steep Inverted
Long-term rates are much higher than short-term rates
Inverted
Long-term rates lower than short-term rates
Check the dynamic yield curve at

23. Short-Term versus Long-Term U.S. Interest Rates and Recessions

24. Bond valuation

25. Financial Asset Valuation1 2 n r
...
CF1
CFn
CF2
Value CF CF CF PV = 1 + 2 + . . . + n .
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?   1   2   n 1 + r 1 + r 1 + r
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. 6.2 Zero-Coupon Bonds Zero-coupon bonds Only two cash flows
The bond’s market price at the time of purchase
The bond’s face value at maturity (n)
Treasury bills are zero-coupon U.S. government bonds with maturity of up to one year.
We often refer to this as the risk-free interest rate for that period (n).
Because a default-free zero-coupon bond that matures on date n provides a risk-free return over that period, the Law of One Price guarantees that the risk-free interest rate equals the yield to maturity on such a bond. 26

27. 6.2 Zero-Coupon Bonds
A one-year, risk-free, zero-coupon bond with a $100,000 face value has an initial price of $96,
If you purchased this bond and held it to maturity, you would have the following cash flows: 27

28. 6.2 Zero-Coupon Bonds Yield to Maturity of a Zero-Coupon Bond
The discount rate that sets the present value of the promised bond payments equal to the current market price of the bond
Yield to Maturity of an n-Year Zero-Coupon Bond:
(Eq. 6.2) 28

29. Example 6.1 Yields for Different Maturities
Problem:
Suppose the following zero-coupon bonds are trading at the prices shown below per $100 face value. Determine the corresponding yield to maturity for each bond.
Maturity
1 year
2 years
3 years
4 years
Price
$96.62
$92.45
$87.63
$83.06 29

30. Example 6.1 Yields for Different Maturities
Solution:
We can use Eq. 6.2 to solve for the YTM of the bonds.
Solving for the YTM of a zero-coupon bond is the same process we used to solve for the compounding rate of return, given the present and future values, by using your financial calculator.
Indeed, the YTM is the rate of return of buying the bond. 30

31. 6.3 Coupon Bonds Coupon bonds
Pay face value at maturity & Also make regular coupon interest payments
Two types of U.S. Treasury coupon securities:
Treasury notes: original maturities from one to ten years
Treasury bonds: original maturities of more than ten years 31

32. Coupon Bond

33. Example 6.3 The Cash Flows of a Coupon Bond or Note
Assume that it is May 15, 2010 and the U.S. Treasury has just issued securities with May 2015 maturity, $1000 par value and a 2.2% coupon rate with semiannual coupons. Since the original maturity is only 5 years, these would be called “notes” as opposed to “bonds”. The first coupon payment will be paid on November 15, What cash flows will you receive if you hold this note until maturity? 33

34. 6.3 Coupon Bonds Yield to Maturity of a Coupon Bond: (Eq. 6.3)
Cash flows shown in the timeline below:
The coupon payments are an annuity, so the yield to maturity is the interest rate y that solves the following equation:
(Eq. 6.3) 34

35. Example 6.4 Computing the Yield to Maturity of a Coupon Bond
Problem:
Consider the five-year, $1000 bond with a 2.2% coupon rate and semiannual coupons described in Example 6.3.
If this bond is currently trading for a price of $963.11, what is the bond’s yield to maturity?
Solution:
Because the bond has ten remaining coupon payments, we compute its yield y by solving Eq.(6.3) for this bond: 35

36. Example 6.4 Computing the Yield to Maturity of a Coupon Bond
(cont’d):
We can solve it by trial-and-error, financial calculator, or a spreadsheet. To use a financial calculator, we enter the price we pay as a negative number for the PV (it is a cash outflow), the coupon payments as the PMT, and the bond’s par value as its FV. Finally, we enter the number of coupon payments remaining (10) as N.
Given: 10 11
1,000
Solve for:
1.50
Excel Formula: =RATE(NPER,PMT,PV,FV)= RATE(10,11, ,1000) 36

37. Example 6.4 Computing the Yield to Maturity of a Coupon Bond
(cont’d):
Therefore, y = 1.50%.
Because the bond pays coupons semiannually, this yield is for a six-month period.
We convert it to an APR by multiplying by the number of coupon payments per year.
Thus the bond has a yield to maturity equal to a 3.0% APR with semiannual compounding.
As the equation shows, the yield to maturity is the discount rate that equates the present value of the bond’s cash flows with its price.
Note that the YTM is higher than the coupon rate and the price is lower than the par value. We will discuss why in the next section. 37

38. Example 6.5 Computing a Bond Price from Its Yield to Maturity
Problem:
Consider again the five-year, $1000 bond with a 2.2% coupon rate and semiannual coupons in Example 6.4. Suppose interest rates drop and the bond’s yield to maturity decreases to 2% (expressed as an APR with semiannual compounding). What price is the bond trading for now? And what is the effective annual yield on this bond? 38

39. Example 6.5 Computing a Bond Price from Its Yield to Maturity
Execute:
Using Eq. 6.3 and the 6-month yield of 1.0%, the bond price must be
The effective annual yield corresponding to 1.0% every six months is (1+.01)2-1=0.0201, or 2.01%
Given: 10
1.0 25
1,000
Solve for:
-1,009.47
Excel Formula: = PV(RATE,NPER,PMT,FV)=PV(.01,10,11,1000) 39

40. Example 6.5 Computing a Bond Price from Its Yield to Maturity
Evaluate:
The bond’s price has risen to $ , lowering the return from investing in it from 1.5% to 1.0% per 6-month period. Interest rates have dropped, so the lower return brings the bond’s yield into line with the lower competitive rates being offered for similar risk and maturity elsewhere in the market. 40

41. 6.3 Coupon Bonds Coupon Bond Price Quotes
Prices and yields are often used interchangeably.
Bond traders usually quote yields rather than prices.
One advantage is that the yield is independent of the face value of the bond.
When prices are quoted in the bond market, they are conventionally quoted per $100 face value. 41

42. Why bond price changes

43. 6.4 Why Bond Prices Change
Zero-coupon bonds always trade for a discount.
Coupon bonds may trade at a discount or at a premium
Most issuers of coupon bonds choose a coupon rate so that the bonds will initially trade at, or very close to, par.
After the issue date, the market price of a bond changes over time. 43

44. 6.4 Why Bond Prices Change Interest Rate Changes and Bond Prices
If a bond sells at par the only return investors will earn is from the coupons that the bond pays.
Therefore, the bond’s coupon rate will exactly equal its yield to maturity.
As interest rates in the economy fluctuate, the yields that investors demand will also change. 44

45. 6.4 Why Bond Prices Change Interest Rate Risk and Bond Prices
Effect of time on bond prices is predictable, but unpredictable changes in rates also affect prices.
Bonds with different characteristics will respond differently to changes in interest rates
Investors view long-term bonds to be riskier than short-term bonds.
Investors view low coupon bonds to be riskier than high coupon bonds. 45

46. Figure 6.3 A Bond’s Price vs. Its Yield to Maturity

47. Table 6.3 Bond Prices Immediately After a Coupon Payment47

48. Definitions
Annual coupon pmt
Current price
Current yield =
Capital gains yield =
= YTM =
Change in price
Beginning price
Exp total
return
Exp
Curr yld
Exp cap
gains yld

49. Find current yield and capital gains yield for a 8%, 10-year bond when the bond sells for $ and YTM = 10.91%.
$80
$827.97
Current yield =
= = 9.66%.
divided by 887 = 0.79%

50. YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% %
= 1.25%.
15% % ($1,241.78) % -1.17%
-1.17%
15% % ($1,227.26)
Could also find values in Years 0 and 1,
get difference, and divide by value in
Year 1. Same answer.

51. Premium and Discount Bonds
All 10-year Bonds
Premium
C = 15%
YTM = 10.91%
Discount
C = 8%
Current
Yield
12.08%
9.66%
Capital Gain or Loss Yield
─1.17%
1.25%

52. Example 6.6 Determining the Discount or Premium of a Coupon Bond
Problem:
Consider three 30-year bonds with annual coupon payments.
One bond has a 10% coupon rate, one has a 5% coupon rate, and one has a 3% coupon rate.
If the yield to maturity of each bond is 5%, what is the price of each bond per $100 face value?
Which bond trades at a premium, which trades at a discount, and which trades at par? 52

53. Example 6.6 Determining the Discount or Premium of a Coupon Bond
Evaluate:
The prices reveal that when the coupon rate of the bond is higher than its yield to maturity, it trades at a premium.
When its coupon rate equals its yield to maturity, it trades at par.
When its coupon rate is lower than its yield to maturity, it trades at a discount. 53

54. Figure 6.4 The Effect of Time on Bond Prices54

55. 6.4 Why Bond Prices Change Bond Prices in Practice
Bond prices are subject to the effects of both passage of time and changes in interest rates.
Prices converge to face value due to the time effect, but move up and down because of changes in yields. 55

56. Figure 6.5 Yield to Maturity and Bond Price Fluctuations over Time56

57. Changes in Bond Price over Time: Reality

58. Interest rate sensitivity of Bond prices

59. Long-Term versus Short-Term Loans
You work for a bank that has just made two loans. In one, you loaned $ today in return for $1,000 in one year. In the other, you loaned $ today in return for $15, in 30 years. The difference between the loan amount and repayment amount is based on an interest rate of 10% per year.

60. Long-Term versus Short-Term Loans
Imagine that immediately after you make the loans, news about economic growth is announced that increases inflation expectations so that the market interest rate for loans like these jumps to 11%. Loans make up a major part of a bank’s assets, so you are naturally concerned about the value of these loans. What is the effect of the interest rate change on the value to the bank of the promised repayment of these loans?
Note that each of these loans has only one repayment cash flow at the end of the loan. They differ only by the time to repayment.
The effect on the value of the future repayment to the bank today is just the PV of the loan repayment, calculated at the new market interest rate.

61. Long-Term versus Short-Term Loans
The value of the one-year loan decreased by $ $ = $8.19, or 0.9%, but the value of the 30-year loan decreased by $ $ = $216.15, or almost 24%!
The small change in market interest rates, compounded over a longer period, resulted in a much larger change in the present value of the loan repayment.
You can see why investors and banks view longer-term loans as being riskier than short-term loans!
For the one-year loan:
For the 30-year loan:

62. Example 6.8 The Interest Rate Sensitivity of Bonds
Problem:
Consider a 10-year coupon bond and a 30-year coupon bond, both with 10% annual coupons.
By what percentage will the price of each bond change if its yield to maturity increases from 5% to 6%?
The price of the 10-year bond changes by ( ) / = -6.6% if its yield to maturity increases from 5% to 6%.
For the 30-year bond, the price change is ( ) / = -12.3%. 62

63. Example 6.8 The Interest Rate Sensitivity of Bonds
Evaluate:
The 30-year bond is twice as sensitive to a change in the yield than is the 10-year bond.
In fact, if we graph the price and yields of the two bonds, we can see that the line for the 30-year bond, shown in blue, is steeper throughout than the green line for the 10-year bond, reflecting its heightened sensitivity to interest rate changes. 63

64. Example 6.9 Coupons and Interest Rate Sensitivity
Problem:
Consider two bonds, each pays semi-annual coupons and 5 years left until maturity.
One has a coupon rate of 5% and the other has a coupon rate of 10%, but both currently have a yield to maturity of 8%.
How much will the price of each bond change if its yield to maturity decreases from 8% to 7%? 64

65. Example 6.9 Coupons and Interest Rate Sensitivity
Execute:
The 5% coupon bond’s price changed from $87.83 to $91.68, or 4.4%, but the 10% coupon bond’s price changed from $ to $112.47, or 4.0%.
Given: 10 4
2.50
100
Solve for:
-87.83
Excel Formula: =PV(RATE,NPER,PMT,FV)=PV(.04,10,2.5,100) 65

66. Example 6.9 Coupons and Interest Rate Sensitivity
Evaluate:
The bond with the smaller coupon payments is more sensitive to changes in interest rates.
Because its coupons are smaller relative to its par value, a larger fraction of its cash flows are received later.
Later cash flows are affected more greatly by changes in interest rates, so compared to the 10% coupon bond, the effect of the interest change is greater for the cash flows of the 5% bond. 66

67. Credit risk

68. 6.5 Corporate Bonds Credit Risk
U.S. Treasury securities are widely regarded to be risk-free.
Credit risk is the risk of default, so that the bond’s cash flows are not known with certainty
Corporations with higher default risk will need to pay higher coupons to attract buyers to their bonds. 68

69. 6.5 Corporate Bonds Corporate Bond Yields
Yield to maturity of a defaultable bond is not equal to the expected return of investing in the bond
The promised cash flows used to determine the yield to maturity are always higher than (or equal to, if not defaulted) the expected cash flows investors may receive.
As a result, the yield to maturity will always be higher than the expected return of investing in the bond.
Therefore, a higher yield to maturity does not necessarily imply that a bond’s expected return is higher. 69

70. 6.5 Corporate Bonds Bond Ratings
Several companies rate the creditworthiness of bonds
Two best-known are Standard & Poor’s and Moody’s
These ratings help investors assess creditworthiness
Investment-grade bonds
Speculative bonds
junk bonds
high-yield bonds
The rating depends on
the risk of bankruptcy
bondholders’ claim to assets in the event of bankruptcy. 70

71. Table 6. 6 Bond Ratings and the Number of U. S
Table 6.6 Bond Ratings and the Number of U.S. Public Firms with those Ratings at the End of 2009 71

72. 6.5 Corporate Bonds
Corporate Yield Curves
We can plot a yield curve for corporate bonds just as we can for Treasuries.
The credit spread is the difference between the yields of corporate bonds and Treasuries.
Corporate Yield Curves for Various Ratings, March 2010 72

73. YTM is a function of many factors
YTM = (r* + DRP) + IP + Others.
YTM = Required rate of return on a debt security.
r* = Real risk-free rate. T-bond rate if no inflation; 1% to 4%.
DRP = Default risk premium.
IP = Inflation premium.
Others = Liquidity premium and/or Maturity risk premium.
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.
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
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 $1100 in one year. What’s our return in dollars? In six packs?
A. Dollars. Our return is
($ $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%.

74. Example 6.10 Credit Spreads and Bond Prices
Problem:
Your firm has a credit rating of A.
You notice that the credit spread for 10-year maturity debt is 90 basis points (0.90%).
Your firm’s ten-year debt has a coupon rate of 5%.
You see that new 10-year Treasury notes are being issued at par with a coupon rate of 4.5%.
What should the price of your outstanding 10-year bonds be? 74

75. Example 6.10 Credit Spreads and Bond Prices
Solution:
Plan:
If the credit spread is 90 basis points, then the yield to maturity (YTM) on your debt should be the YTM on similar treasuries plus 0.9%.
The fact that new 10-year treasuries are being issued at par with coupons of 4.5% means that with a coupon rate of 4.5%, these notes are selling for $100 per $100 face value.
Thus their YTM is 4.5% and your debt’s YTM should be 4.5% + 0.9% = 5.4%. 75

76. Bond Risk Premium over Time
Source: Federal Reserve.

77. Table 6.5 Interest Rates on Five-Year Bonds for Various Borrowers, July 2013

78. Risk Premiums of Junk Bonds versus Other Corporate Bonds over Time
Source: Federal Reserve.

79. Example 6.10 Credit Spreads and Bond Prices
Evaluate:
Your bonds offer a higher coupon (5% vs. 4.5%) than treasuries of the same maturity, but sell for a lower price ($96.94 vs. $100).
The reason is the credit spread.
Your firm’s higher probability of default leads investors to demand a higher YTM on your debt.
To provide a higher YTM, the purchase price for the debt must be lower.
If your debt paid 5.4% coupons, it would sell at $100, the same as the treasuries.
But to get that price, you would have to offer coupons that are 90 basis points higher than those on the treasuries—exactly enough to offset the credit spread. 79

80. Credit Rating Example
Andrew Industries is contemplating issuing a 30-year bond with a coupon rate of 7% (annual coupon) and a face value of $1,000.
Andrew believes it can get a rating of A from S&P.
However, due to recent financial difficulties at the company, S&P is warning that it may downgrade Andrew’s bonds to BBB.
Yields on A-rated, long-term bonds are currently 6.70%, and yields on BBB-rated bonds are 7.20%.
What is the price of the bod if Andrew Industries maintains the A rating for the bond issue?
What will the price of the bond be if it is downgraded?

81. Chapter Quiz What types of cash flows does a bond buyer receive?
How are the periodic coupon payments on a bond determined?
Why would you want to know the yield to maturity of a bond?
What is the relationship between a bond’s price and its yield to maturity?
What cash flows does a company pay to investors holding its coupon bonds?
What do we need in order to value a coupon bond? 81

82. Chapter Quiz
Why do interest rates and bond prices move in opposite directions?
If a bond’s yield to maturity does not change, how does its cash price change between coupon payments?
What is a junk bond?
How will the yield to maturity of a bond vary with the bond’s risk of default? 82