1. CHAPTER 6 Bonds and Their Valuation
Key features of bonds
Bond valuation
Measuring yield
Assessing risk

2. What are Bonds?
bond is a long-term contract under which a borrower agrees to make payments of interest and principal, on specific dates, to the holders of the bond.
Investors have many choices when investing in bonds, but bonds are classified into four main types:
Treasury bonds
Corporate bonds
Municipal bonds
Foreign bonds

3. Treasury bonds
Treasury bonds, sometimes referred to as government bonds, are issued by the U.S. federal government.
It is reasonable to assume that the federal government will make good on its promised payments, so these bonds have no default risk.
However, Treasury bond prices decline when interest rates rise, so they are not free of all risks.

4. Corporate bonds
Corporate bonds, as the name implies, are issued by corporations. Unlike Treasury bonds, corporate bonds are exposed to default risk—if the issuing company gets into trouble, it may be unable to make the promised interest and principal payments.
Different corporate bonds have different levels of default risk, depending on the issuing company’s characteristics and the terms of the specific bond. Default risk often is referred to as “credit risk,” and, as we Know, the larger the default or credit risk, the higher the interest rate the issuer must pay.

5. Municipal bonds
Municipal bonds, or “munis,” are issued by state and local governments.
Like corporate bonds, munis have default risk. However, munis offer one major advantage over all other bonds: the interest earned on most municipal bonds is exempt from federal taxes and also from state taxes if the holder is a resident of the issuing state. Consequently, municipal bonds carry interest rates that are considerably lower than those on corporate bonds with the same default risk.

6. Foreign bonds
Foreign bonds are issued by foreign governments or foreign corporations
Foreign corporate bonds are, of course, exposed to default risk, and so are some foreign government bonds.
An additional risk exists if the bonds are denominated in a currency other than that of the investor’s home currency. For example, if a U.S. investor purchases a corporate bond denominated in Japanese yen and the yen subsequently falls relative to the dollar, then the investor will lose money, even if the company does not default on its bonds.

7. Key Features of a Bond
Par value – face amount of the bond, which is paid at maturity (assume $1,000).
The par value generally represents the amount of money the firm borrows and promises to repay on the maturity date.
Coupon interest rate – stated interest rate (generally fixed) paid by the issuer. Multiply by par to get dollar payment of interest.
For example, MicroDrive’s bonds have a $1,000 par value, and they pay $100 in interest each year.
The bond’s coupon interest is $100, so its coupon interest rate is $100/$1,000 =10 percent.

8. Key Features of a Bond
Maturity date – years until the bond must be repaid.
Bonds generally have a specified maturity date on which the par value must be repaid.
MicroDrive’s bonds, which were issued on January 3, 2003, will mature on January 3, 2018; thus, they had a 15-year maturity at the time they were issued.
Most bonds have original maturities (the maturity at the time the bond is issued) ranging from 10 to 40 years, but any maturity is legally permissible.
Of course, the effective maturity of a bond declines each year after it has been issued. Thus, MicroDrive’s bonds had a 15- year original maturity, but in 2004, a year later, they will have a 14-year maturity, and so on.

9. Key Features of a Bond Issue date – when the bond was issued.
Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”).
Default risk: Risk that issuer will not make interest or principal payments

10. Provisions to Call or Redeem Bonds
Most corporate bonds contain a call provision, which gives the issuing corporation the right to call the bonds for redemption.
The call provision generally states that the company must pay the bondholders an amount greater than the par value if they are called.
The additional sum is termed a call premium,

11. How does adding a call provision affect a bond?
Issuer can refund if rates decline. That helps the issuer but hurts the investor.
If interest rates go up, the company will not call the bond, and the investor will be stuck with the original coupon rate on the bond.
if interest rates fall, the company will call the bond and pay off investors, who then must reinvest the proceeds at the current market interest rate, which is lower than the rate they were getting on the original bond.
Therefore, borrowers are willing to pay more, and lenders require more, on callable bonds.

12. What’s a sinking fund?
Provision to pay off a loan over its life rather than all at maturity.
Similar to amortization on a term loan.
Obviously, a sinking fund can constitute a significant cash drain on the firm.
Reduces risk to investor, shortens average maturity.
But not good for investors if rates decline after issuance.

13. Sinking funds are generally handled in 2 ways
1. Call x% at par per year for sinking fund purposes.
2. Buy bonds on open market.
Company would call if rd is below the coupon rate and bond sells at a premium.
Use open market purchase if rd is above coupon rate and bond sells at a discount.

14. Financial Asset Valuation
The value of any financial asset (a stock, a bond, a lease) or even a physical asset such as an apartment building or a piece of machinery is simply the present value of the cash flows the asset is expected to produce.

15. 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

16. Bond Valuation rd the bond’s market rate of interest
N the number of years before the bond matures
INT dollars of interest paid each year
M the par, or maturity, value of the bond

17. What’s the value of a 10-year, 10% coupon bond if rd = 10%?1 2 10
10%
...
100
V = ?
100
,000 M V  B +   N 1 + r d $1 ,
000 V  + B   10 1 +
.10
= $ = $1,000.

18. The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at r = 10%:$
385.54
$1,000.00
PV annuity
PV maturity value
Value of bond =

19. If r remained constant at 10 percent, what would the value of the bond be one year after it was issued? d M V  B +   N 1 + r d $1 ,
000 V  + B   9 1 +
.10
= $ = $1,000.

20. Changes in Bond Values over Time
At the time a coupon bond is issued, the coupon is generally set at a level that will cause the market price of the bond to equal its par value.
A bond that has just been issued is known as a new issue (Month from the issue date).
Once the bond has been on the market for a while, it is classified as an outstanding bond.
Newly issued bonds generally sell very close to par, but the prices of outstanding bonds vary widely from par.
IF rd changed, a bond with a $100 coupon that sold at $1000 par when it was issued will sell for more or less than $1,000 thereafter.

21. What would happen if expected inflation rose by 3%, causing r = 13%?M V  B +   N 1 + r d $1 ,
000 V  + B   10 1 +
.13
= $ = $837.
When rd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.

22. What would happen after one year if rd remains 13%?

23. What would happen if expected inflation rose by 5%, causing r = 15%?

24. What would happen if inflation fell, and rd declined to 7% ?M V  B +   N 1 + r d $1 ,
000 V  + B   10 1 +
.07
= $ = $1, -
If coupon rate > rd, price rises above par, and bond sells at a premium.

25. What would happen after one year if rd remains 7%?

26. What would happen if inflation fell, and rd declined to 5% ?

27. Years remaining to Maturity
Bond Value ($)
rd = 7%.
1,211
rd = 10%. M
1,000
rd = 13%.
837
Years remaining to Maturity

28. A par bond stays at $1,000 if rd remains constant.
At maturity, the value of any bond must equal its par value.
Interest rates do change over time, but the coupon rate remains fixed after the bond has been issued.
Whenever the going rate of interest rises above the coupon rate, the price of bond will fall below its par value. Such a bond is called a discount bond.
Discount = Price-Par value = $837 - $1,000 = 163
Whenever the going rate of interest falls below the coupon rate, the price of bond will rise above its par value. Such a bond is called a premium bond.
premium = Price-Par value = $ $1,000 = 211

29. Problem 1 (Bond Value)
Callaghan Motors’ bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8 percent. The bonds have a yield to maturity (market rate) of 9 percent.
What is the current market price of these bonds?

30. Bond Yields
If you examine the any bond market table (e.g The Wall Street Journal) you will typically see information regarding each bond’s maturity date, price, and coupon interest rate. You will also see the Bond’s reported yield.
Bond’s reported yield. Unlike the coupon interest rate, which is fixed, the bond’s yield varies from day to day depending on current market conditions.
Moreover, the yield can be calculated in three different ways, and three “answers” can be obtained.
These different yields are described in the following sections.
Yield to Maturity
Yield to Call
Current Yield

31. What’s “yield to maturity”?
YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.”
The interest rate generally discussed by investors when they talk about rates of return.
The yield to maturity is generally the same as the market rate of interest, r , and to find it, all you need to do is solve the Equation . d

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

33.     Find rd that “works”! + + V  1 + r $1 , 000 887  1 + rM V  B +   N 1 + r d $1 ,
000
887  +   10 1 + r d
That’s need spreadsheet, financial calculator or You could substitute values for r until you find a value that “works”. d
INPUTS
N I/YR PV PMT FV
10.91
OUTPUT

34. Find YTM if price were $1,
INPUTS
N I/YR PV PMT FV
7.08
OUTPUT
Sells at a premium. Because coupon = 9% > rd = 7.08%, bond’s value > par.

35. If coupon rate < rd, bond sells at a discount.
If coupon rate = rd, bond sells at its par value.
If coupon rate > rd, bond sells at a premium.
If rd rises, price falls.
Price = par at maturity.

36. current yield Annual coupon pmt Current price
If you examine brokerage house reports on bonds, you will often see reference to a bond’s current yield.
The current yield is the annual interest payment divided by the bond’s current price.
Current yield=
For example, if MicroDrive’s bonds with a 10 percent coupon were currently selling at $985, the bond’s current yield would be 12 percent ($100/$837).
Annual coupon pmt
Current price

37. 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

38. Find current yield and capital gains yield for a 9%, 10-year bond when the bond sells for $887 and YTM = 10.91%.
$90
$887
Current yield =
= = 10.15%.

39. YTM = Current yield + Capital gains yield.
Cap gains yield = YTM - Current yield
= 10.91% %
= 0.76%.
Could also find values in Years 1 and 2,
get difference, and divide by value in
Year 1. Same answer.

40. What’s interest rate (or price) risk
What’s interest rate (or price) risk? Does a 1-year or 10-year 10% bond have more risk?
Interest rate risk: Rising rd causes bond’s price to fall. rd
1-year
Change
10-year
Change 5%
$1,048
$1,386
4.8%
38.6%
10%
1,000
1,000
4.4%
25.1%
15%
956
749

41. Value
10-year
1,500
1,000
1-year
500 rd 0% 5%
10%
15%