1. Valuation and Characteristics of Bonds
Chapter 7
Valuation and Characteristics of Bonds

2. Chapter 7 Topic Overview
Bond Characteristics
Annual and Semi-Annual Bond Valuation
Finding Returns on Bonds
Reading Bond Quotes
Bond Risk and Other Important Bond Valuation Relationships 2

3. Bond Characteristics
Par Value = stated face value that is the amount the issuer must repay.
Coupon Interest Rate
Coupon = Coupon Rate x Par Value
Maturity Date = when the par value is repaid.
This makes a bond’s cash flows look like this: 3

4. Characteristics of Bonds
Bonds pay fixed coupon (interest) payments at fixed intervals (usually every 6 months) and pay the par value at maturity. n
$I $I $I $I $I $I+$M

5. Types of Bonds Debentures: unsecured debt = bonds.
Subordinated Debentures
Mortgage Bonds
Zero Coupon Bonds: no coupon payments, just par value.
Convertible Bonds: can be converted into shares of stock. 4

6. Types of Bonds(cont.)
Indexed Bonds: coupon payments and/or par value indexed to inflation.
TIPs: Indexed US Treasury coupon bond, fixed coupon rate, par value indexed.
I-Bonds: Indexed US Treasury zero coupon bond.
Junk bonds: speculative or below-investment grade bonds; rated BB and below. High-yield bonds. 4

7. Types of Bonds(cont.)
Eurobonds - bonds denominated in one currency and sold in another country. (Borrowing overseas).
example - suppose Disney decides to sell $1,000 bonds in France. These are U.S. denominated bonds trading in a foreign country. Why do this?
If borrowing rates are lower in France,
To avoid SEC regulations.

8. The Bond Indenture
The bond contract between the firm and the trustee representing the bondholders.
Lists all of the bond’s features:
coupon, par value, maturity, etc.
Lists restrictive provisions which are designed to protect bondholders.
Describes repayment provisions.

9. Value
Book Value: value of an asset as shown on a firm’s balance sheet; historical cost.
Liquidation value: amount that could be received if an asset were sold individually.
Market value: observed value of an asset in the marketplace; determined by supply and demand.
Intrinsic value: economic or fair value of an asset; the present value of the asset’s expected future cash flows.

10. Security Valuation
In general, the intrinsic value of an asset = the present value of the stream of expected cash flows discounted at an appropriate required rate of return.
Can the intrinsic value of an asset differ from its market value?

11. S V = Valuation $Ct (1 + k)t n t = 1
Ct = cash flow to be received at time t.
k = the investor’s required rate of return.
V = the intrinsic value of the asset.

12. Bond Valuation $I $I $I $I $I $I+$M 0 1 2 . . . n
Discount the bond’s cash flows at the investor’s required rate of return.
the coupon payment stream (an annuity).
the par value payment (a single sum). n
$I $I $I $I $I $I+$M

13. S Vb = + Bond Valuation $It $M (1 + kb)t (1 + kb)n
Vb = $It (PVIFA kb, n) + $M (PVIF kb, n)

14. Bond Valuation Example #1
Duff’s Beer has $1,000 par value bonds outstanding that make annual coupon payments. These bonds have an 8% annual coupon rate and 12 years left to maturity. Bonds with similar risk have a required return of 10%, and Moe Szyslak thinks this required return is reasonable.
What’s the most that Moe is willing to pay for a Duff’s Beer bond? 6

15. P/Y = 1 12 = N 10 = I/Y 1,000 = FV 80 = PMT CPT PV = -$863.73
1000
P/Y = 1
12 = N
10 = I/Y
1,000 = FV
80 = PMT
CPT PV = -$863.73
Note: If the coupon rate < discount rate, the bond will sell for less than the par value: a discount.

16. Let’s Play with Example #1
Homer Simpson is interested in buying a Duff Beer bond but demands an 8 percent required return.
What is the most Homer would pay for this bond? 7

17. P/Y = 1 12 = N 8 = I/Y 1,000 = FV 80 = PMT CPT PV = -$1,000
1000
P/Y = 1
12 = N
8 = I/Y
1,000 = FV
80 = PMT
CPT PV = -$1,000
Note: If the coupon rate = discount rate, the bond will sell for its par value.

18. Let’s Play with Example #1 some more.
Barney (belch!) Barstool is interested in buying a Duff Beer bond and demands on a 6 percent required return.
What is the most Barney (belch!) would pay for this bond? 7

19. P/Y = 1 12 = N 6 = I/Y 1,000 = FV 80 = PMT CPT PV = -$1,167.68
1000
P/Y = 1
12 = N
6 = I/Y
1,000 = FV
80 = PMT
CPT PV = -$1,167.68
Note: If the coupon rate > discount rate, the bond will sell for more than the par value: a premium.

20. Bonds with Semiannual Coupons
Double the number of years, and divide required return and annual coupon by 2.
VB = I/2(PVIFAkb/2,2N) + M(PVIFkb/2,2N) 15

21. Semiannual Example
A $1000 par value bond with an annual coupon rate of 9% pays coupons semiannually with 15 years left to maturity. What is the most you would be willing to pay for this bond if your required return is 8% APR?
Semiannual coupon = 9%/2($1000) = $45
15x2 = 30 remaining coupons 16

22. P/Y = 1 15x2 =30 = N 8/2 = 4 = I/Y 1,000 = FV 90/2 = 45 = PMT
1000
P/Y = 1
15x2 =30 = N
8/2 = 4 = I/Y
1,000 = FV
90/2 = 45 = PMT
CPT PV = -$1,086.46

23. Finding a bond’s rate of return?
Expected Return
In the marketplace, we know a bond’s current price(PV), but not its return.
Yield to Maturity (YTM) = the rate of return the bond would earn if purchased at today’s price and held until maturity.
Annual Actual Return
Current Yield + Capital Gains Yield
I/P0 + (P1 – P0)/P0 = (P1 – P0 + I)/P0 12

24. S P0 = + Yield To Maturity $It $M (1 + kb)t (1 + kb)n
The expected rate of return on a bond.
The rate of return investors earn on a bond if they hold it to maturity.
$It $M
(1 + kb)t (1 + kb)n
P0 = n
t = 1 S

25. Yield to Maturity Example
$1000 face value bond with a 10% coupon rate paid annually with 20 years left to maturity sells for $
What is this bond’s yield to maturity? 13

26. P/Y = 1 -1091.29 = PV 20 = N 1,000 = FV 100 = PMT CPT I/Y = 9% = YTM
1000
P/Y = 1
= PV
20 = N
1,000 = FV
100 = PMT
CPT I/Y = 9% = YTM

27. Let’s try this together.
Imagine a year later, the YTM for the bond on the previous slide fell to 8%.
What is the bond’s expected price?
What is the holding period return, if we sell the bond at this time assuming we bought the bond a year earlier?
PMT =100, FV = 1000

28. Reading Corporate Bond Quotes
Cur Net
Bonds Yld Vol. Close Chg.
IBM 6 ½ /4 -2 1/8
Most info is expressed as % of par value. Par value = 100.
For IBM, 6.5% annual coupon rate, matures in year 2028, Price is 98.25% of par value. 21

29. YTM Estimate for IBM Bond
Assuming $1000 Par (or Face) Value and semi-annual coupons
Price = 98.25% (1000) = , INT/2=1000(6.5%)/2= 32.50, FV = 1000
Assuming N = 26 ( ): YTM?
=32.50(PVIFAYTM/2,2N)+1000(PVIFYTM/2,2N)
Calculator Solution: = PV,1000 = FV, = PMT, 2N = 2(26) = 52 = N, CPT I/Y
I/Y=YTM/2=3.32% YTM(APR) = 2(3.32%)= 6.64% 22

30. The Financial Pages: Treasury Bonds
Maturity Ask
Rate Mo/Yr Bid Asked Chg Yld
6 Feb : :
What is the yield to maturity for this Treasury bond? (assume ( ) 24x2 = 48 half years)
P/Y = 1, N = 48, FV = 1000,
PMT = 1000(6%/2) = 30,
PV = - 1, ( % of par)
Solve: I/Y = ytm/2 = 2.816%, YTM = 5.63%

31. Bond Valuation: What have we learned? 5 Important Relationships
Our Example 1: Duff’s Beer bonds
12-year bond
kb=6%, V = $1,167.68
kb=8%, V = $1,000
kb=10%, V = $863.73
These values illustrate the First & Second Important Relationships

32. First Relationship: Bond Prices and Interest Rates have an inverse relationship!

33. Second Important Relationship
From example 1: The coupon rate was 8%
kb=6%, V = $1,167.68
kb=8%, V = $1,000
kb=10%, V = $863.73
When required rate = coupon rate Bond Value = Par Value (M)
When required rate > coupon rate Bond Value < Par Value (M)
When required rate < coupon rate Bond Value > Par Value (M) 8

34. Bond Value Changes Over Time
Returning to the original example #1, where k = 10%, N = 12, INT(PMT) = $80, M(FV) = $1000, & V = $
What is bond value one year later when N = 11 and k is still = 10%?
VB = $80(PVIFA10%,11) + $1000(PVIF10%,11) = $870.10 9

35. What is the bond’s return over this year. (Proof of YTM = Expected Ret
Total Rate of Return = Current Yield + Capital Gains Yield (C.G.Y)
Beg. V = , End V =
Current Yield = Annual Coupon (INT) divided by Beginning Bond Value
Current Yld = $80/ = 9.26%
C.G.Y.=( )/863.73= 0.74%
Total Return = 9.26% % = 10% 10

36. Third Relationship: Market Value approaches par value as maturity date approaches.11

37. Fourth Relationship: Interest Rate Risk
Measures Bond Price Sensitivity to changes in interest rates.
Long-term bonds have more interest rate risk than short-term bonds.

38. Interest Rate Risk Example
Recall from our earlier example (#1), the 12-year, 8% annual coupon bond has the following values at kd = 6%, 8%, & 10%. Let’s compare with a 2-yr, 8% annual coupon bond.
12-year bond 2-year bond
kb=6%, V = $1, V = $1,036.67
kb=8%, V = $1,000 V = $1,000
kb=10%, V = $ V = $965.29

39. Bond Price Sensitivity Graph

40. Other Bond Risks
Reinvestment Rate Risk = opposite of interest rate risk, greater for short-term bonds, risk that income from bonds will fall.
Default Risk = measured by bond ratings = ability of issuer to fulfill debt obligations
Aaa, AAA, best rating, lowest default risk 20

41. Fifth Relationship
In addition to length of time to maturity, the pattern ( and size) of cash flows affects a bond’s price sensitivity to changes in interest rates.
Duration measures and illustrates this relationship.

42. Duration Weighted average time to maturity.
Higher (longer) duration means greater bond price sensitivity to changes in interest rates.

43. Duration Formula t = year the cash flow is to be received,
n = the number of years to maturity,
Ct = the cash flow to be received at year t,
kb = the bondholder’s required return,
P0 = the bond’s present value (or today’s price).

44. Duration Example
Krusty Burger and Burns Power bonds both have 3 years to maturity, $1,000 par value, and a required return of 8 percent.
However, Krusty Burger makes annual coupon payments of 8%, while Burns Power is a zero coupon bond.
What is the duration of each bond?

45. Suggested Duration Calculation Steps
First, calculate today’s value of the bond.
Second, find the PV today of each time weighted bond CF (CF x time period the CF occurs).
Third, add up all the time weighted PVs
Note: The CF and NPV calculator functions can be used to do steps 2 and 3.
Fourth, divide sum of time weighted PVs by today’s bond value = duration.

46. Krusty Burger Duration
Since Krusty’s required return and coupon rate are equal, today’s value = $1,000.
80 = PMT, 1000 = FV, 8 = I/Y, 3 = N, CPT PV = $1000
t C t x C PV(tC) C C C
NPV: I = 8, CPT NPV = 2783
Krusty Burger Duration = 2783/1000 = 2.783

47. Burns Power Duration
Today’s Burns Power Bond Value: 0 = PMT, 1000 = FV, 8 = I/Y, 3 = N, CPT PV = $793.83
t C t x C PV(tC) C C C
NPV: I = 8, CPT NPV =
Burns Power Duration = / = 3.00
NOTE: Duration for zero coupon bond = time to maturity.

48. Duration Example Conclusion
Krusty Burger Duration = 2.783
Burns Power Duration = 3.000
Burns Power bonds are more sensitive to changes in interest rates.
This is good if interest rates go down, but bad if interest rates go up!
From this example, you can see for bonds with the same time to maturity, lower coupon rate bonds have more interest rate risk.