1. Chapter 7 - Valuation and Characteristics of Bonds

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

3. Example: AT&T 6 ½ 36 Par value = $1,000
Coupon = 6.5% or par value per year,
or $65 per year ($32.50 every six months).
Maturity = 28 years (matures in 2036)
Issued by AT&T. …
$ $ $ $ $ $32.50+$1000

4. Types of Bonds Debentures - unsecured bonds.
Subordinated debentures - unsecured “junior” debt.
Mortgage bonds - secured bonds.
Zeros - bonds that pay only par value at maturity; no coupons.
Junk bonds - speculative or below-investment grade bonds; rated BB and below. High-yield bonds.

5. Types of Bonds
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.

6. 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.

7. Bond Ratings Moody’s Standard & Poor’s Fitch Investor Services
Involve judgment about the future risk potential of the bond
AAA, AA, …, BB, …, CC,…, D

8. Current Yield
The ratio of the annual interest payment to the bond’s market price
Bond with 8 percent coupon interest rate, a par value of 1,000, and a market price of 700, what is its current yield?
Current Yield = (0.08 * 1,000) / 700 = 11.4%

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.

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
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).

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

14. Bond Example
Suppose our firm decides to issue 20-year bonds with a par value of $1,000 and annual coupon payments. The return on other corporate bonds of similar risk is currently 12%, so we decide to offer a 12% coupon interest rate.
What would be a fair price for these bonds?

15.
1000
N = 20
I%YR = 12
FV = 1,000
PMT = 120
Solve PV = -$1,000
Note: If the coupon rate = discount rate, the bond will sell for par value.

16. Bond Example Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
PV = 120 (PVIFA .12, 20 ) (PVIF .12, 20 ) 1
PV = PMT (1 + i)n FV / (1 + i)n i
PV = (1.12 ) / (1.12) 20 = $1000
.12

17. Suppose interest rates fall immediately after we issue the bonds
Suppose interest rates fall immediately after we issue the bonds. The required return on bonds of similar risk drops to 10%.
What would happen to the bond’s intrinsic value?

18. Mode = end
N = 20
I%YR = 10
PMT = 120
FV = 1000
Solve PV = -$1,170.27
Note: If the coupon rate > discount rate,
the bond will sell for a premium.

19. Bond Example Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
PV = 120 (PVIFA .10, 20 ) (PVIF .10, 20 ) 1
PV = PMT (1 + i)n FV / (1 + i)n i
PV = (1.10 ) / (1.10) 20 = $1,170.27
.10

20. Suppose interest rates rise immediately after we issue the bonds
Suppose interest rates rise immediately after we issue the bonds. The required return on bonds of similar risk rises to 14%.
What would happen to the bond’s intrinsic value?

21. Mode = end
N = 20
I%YR = 14
PMT = 120
FV = 1000
Solve PV = -$867.54
Note: If the coupon rate < discount rate, the bond will sell for a discount.

22. Bond Example Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
PV = 120 (PVIFA .14, 20 ) (PVIF .14, 20 ) 1
PV = PMT (1 + i)n FV / (1 + i)n i
PV = (1.14 ) / (1.14) 20 = $867.54
.14

23. Suppose coupons are semi-annual
Mode = end
N = 40
I%YR = 14/2=7
PMT = 60
FV = 1000
Solve PV = -$866.68

24. Bond Example Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
PV = 60 (PVIFA .14, 20 ) (PVIF .14, 20 ) 1
PV = PMT (1 + i)n FV / (1 + i)n i
PV = (1.07 ) / (1.07) 40 = $866.68
.07

25. 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

26. YTM Example
Suppose we paid $ for a $1,000 par 10% coupon bond with 8 years to maturity and semi-annual coupon payments.
What is our yield to maturity?

27. YTM Example
Mode = end
N = 16
PV =
PMT = 50
FV = 1000
Solve I%YR = 6%
6%*2 = 12%

28. Bond Example Mathematical Solution:
PV = PMT (PVIFA k, n ) + FV (PVIF k, n )
= 50 (PVIFA k, 16 ) (PVIF k, 16 ) 1
PV = PMT (1 + i)n FV / (1 + i)n i
= (1 + i ) / (1 + i) 16
i solve using trial and error

29. Bond Example Mathematical Solution: 10%  5 %  1000 14%  7%  811.06
10%  5 %  1000
14%  7% 
We know i is between 10% and 14%, because is between and 1000.
Then we try 11% and 13%....
Finally we try 12% to get the correct answer.

30. Zero Coupon Bonds No coupon interest payments.
The bond holder’s return is determined entirely by the price discount.

31. Zero Example
Suppose you pay $508 for a zero coupon bond that has 10 years left to maturity.
What is your yield to maturity?
-$ $1000

32. Zero Example Mode = End N = 10 PMT = 0 PV = -508 FV = 1000
Solve: I%YR = 7%

33. Mathematical Solution:
Zero Example
PV = FV = 1000
Mathematical Solution:
PV = FV (PVIF i, n )
508 = 1000 (PVIF i, 10 )
.508 = (PVIF i, 10 ) [use PVIF table]
PV = FV /(1 + i) 10
508 = 1000 /(1 + i)10
= (1 + i)10
i = 7%

34. The Financial Pages: Corporate Bonds
Cur Net
Yld Vol Close Chg
Polaroid 11 1/ /
What is the yield to maturity for this bond?
N = 10, FV = 1000,
PV = $ ,
PMT =
Solve: I/YR = 13.24% *2 = 26.48%

35. The Financial Pages: Corporate Bonds
Cur Net
Yld Vol Close Chg
HewlPkd zr /2 +1
What is the yield to maturity for this bond?
N = 16, FV = 1000,
PV = $-515,
PMT = 0
Solve: I/YR = 4.24%

36. The Financial Pages: Treasury Bonds
Maturity Ask
Rate Mo/Yr Bid Asked Close Yld
9 Nov : : /
What is the yield to maturity for this Treasury bond? (assume 35 half years)
N = 35, FV = 1000,
PMT = 45,
PV = - 1, ( % of par)
Solve: I/YR = 2.728%*2 = 5.457%

37. Five Relationships
Value of bond is inversely related to changes in the investor’s present required rate of return
Interest rate increases, bond value decreases

38. Five Relationships
Market value of bond will be less than the par value if investor’s required rate is above the coupon interest rate

39. Five Relationships
As maturity date approaches, the market value of bond approaches its par value

40. Five Relationships
Long-term bonds have greater interest rate risk than do short-term bonds

41. Five Relationships
The sensitivity of bond’s value to changing interest rate depends not only on length of time to maturity, but also on the pattern of cash flows provided by the bond

42. Five Relationships
Duration: weighted average of time to maturity in which the weight attached to each year is the present value of the cash flow for that year

43. Five Relationships
A, B mature in 3 years, present value $1000, par value $1000, market interest is 10%
A: coupon $100 per year
B: pay whole interest $331 at the end of year 3
The duration of the two bonds?

44. Five Relationships Duration for A:
[(1) * 100 /(1.1) + (2) * 100 /(1.1)^2 + (3) * 1,100 / (1.1)^3] / 1000 = 2.74
Duration for B:
[(1) * 0 /(1.1) + (2) * 0/(1.1)^2 + (3) * 1,331 / (1.1)^3] / 1000 = 3

45. Five Relationships If interest rate falls to 6% from 10%
Value of A = $1,106
Value of B = $1,117
B’s cash flows are received in more distant future, and change in interest rate has a greater impact on the present value of later cash flow

46. Five Relationships Conclusion:
-- the longer the duration, the greater the relative percentage change in bond price in response to a given percentage change in the interest rate
-- duration is more proper than term to maturity in measuring bond’s sensitivity to interest rate change