1. Copyright © 1999 Addison Wesley Longman
CHAPTER
CHAPTER 8
Asset Valuation: Bonds
Copyright © 1999 Addison Wesley Longman 1

2. Objectives 1. Understand the valuation concept.
2. Show how bonds are valued
3. Compute yield to maturity

3. The Bond Components
1.Bond: a contractual obligation of a borrower to make periodic cash interest payments to a lender for a fixed number of years
2.Coupon (CF): the periodic interest payment
3.Term to maturity (n): the number of years over which the bond contract extends

4. 4. Par Value (F): the number of dollars
paid to the lender upon maturity
5. Coupon Rate (C/F): the coupon payment
expressed as a percentage of a principal
amount (Par value)
6. Market Rate or Yield (i): the actual rate
paid on the bond by the market

5. The Value of Any Investment:
Is the present value of all future cash flows discounted at an interest rate that reflects the risk of the investment.
Bonds are valued like any other asset

6. The cash flows from a bond:
The equal annual interest payments (an annuity) C = cF
.08 x $1000 = $80
And the final lump sum payment at maturity (F)
$1000

7. The Coupon Bond Price Formula
PB = C C Cn + Fn
(1+i)1 (1+i) (1+i)n
PB = Price of bond = PV of future cash flows
Ct = Coupon pmt. in period t
Fn = par value (amount to be paid at maturity)
i = interest rate (discount rate) or YTM
n = number of periods to maturity

8. Example:
Calculate the price of a 3 year bond with a par value of $1000, a coupon rate of 8% and a discount or market rate of 10%
Step 1: Calculate coupon pmt.
C = cF

9. Step 2: Find the PV of the cash flows which equals the price
t=0 t= t= t= 3
| | | |
$ $ $
PB = ________ ________ ________
( ) ( ) ( )

10. Using the Calculator
[N] =
[I/Y] =
[PV] =
[PMT] =
[FV] =

11. Properties of the Bond Price Formula
1. Case 1: coupon = market rate = PB = par value
bond is selling at par
2. Case 2: coupon < market rate = PB < par value
bond is selling at a discount
3. Case 3: coupon > market rate = PB > par value
bond is selling at a premium

12. The Zero Coupon Bond Price Formula
Zero Coupons:
1. trade at a discount
2. have no coupon reinvestment
risk
3. examples
a. t-Bills
b. savings bonds

13. 4. PB = Fn [ 1/(1+i/k)kn]
PB = Price of bond
Fn = value at maturity
i = interest yield for n periods
n = # of years until maturity
k = # of compoundings annually

14. Example:
Find the price of a 10 yr. Zero coupon bond with a par value of $1000 and a market rate of 12% compounded semi-annually
  Using Calculator
[N] =
[I/Y] =
[PV] =
[PMT] =
[FV] =

15. Example:
What is the price of a bond if it pays interest semi-annually on a 7% coupon and if it has 5 years to maturity, a $1000 face amount and a required return of 10%?
Using Calculator
[N] =
[I/Y] =
[PV] =
[PMT] =
[FV] =

16. As market interest rates rise and fall:
If interest rates increase,
the value of the bond falls.
If interest rates decrease,
the valud of the bond rises.
As maturity decreases, the valud of the bond approaches par.

17. Market Rate Term 9% 10% 11% 1 $1,009.17 $1,000.00 $991.00
TABLE 8.2 Price of $1,000 Par, 10% Coupon Bond with Different Maturities and Market Interest Rates
Market Rate
Term % % 11%
1 $1, $1, $991.00
10 1, ,
20 1, ,

18. FIGURE 8.1 10% Coupon Bond at 9% and 11% Market Rates2

19. Bond Yield Measures A. The actual return on the bond depends on
1. default risk
2. reinvestment risk
3. price risk
B. The ideal measure tries to capture
1. coupon payments
2. reinvestment rate
3. capital gains and losses

20. Yield to Maturity
The investors expected yield if the bond is held to maturity and the cash flows are reinvested at the “Yield to Maturity” for the life of the bond.
1. Yield to maturity varies inversely to bond prices
change in BP
change in YTM
2. When bond is selling at par, the coupon rate should equal the market rate of interest. (Par Bond)
< 0

21. Example: Given a 3 year bond with par=$1000, coupon rate=8%
and a current price = $950.27, what is the bonds YTM?
Using Calculator
[N] =
[I/Y] =
[PV] =
[PMT] =
[FV] =

22. Expected Yield
The ex-ante yield assuming a forecasted sale price prior to maturity based on expected interest rates.

23. Realized Yield
The ex-post actual rate of return given the cash flows actually received and their timing
Realized Yields affected by:
1. change in timing of promised cash flows
2. change in the interest rates
3. sell bond before maturity at different interest rate

24. The Current Yield:
The percentage return earned in a year from interest payments.
CY = Coupon Payment / Market Price

25. Example:
If the current market price is $900, and the coupon payment is $80, then what is the current yield?

26. Even though bonds are called “fixed income securities,”
They are subject to significant price changes when interest rates are volatile.

27. Bond Price Volatility The % change in a bond price for a given
change in yield
1. volatility increases as time to maturity
increases
2. volatility decreases as coupon rates increase
3. for any change in a bond price, short term
rates vary more than term rates

28. Interest Rate Risk 1. Price risk 2. Reinvestment risk
3. Price risk and reinvestment risk partially offset each other.
a. PR up RR down
b. PR down RR up

29. Duration
1. Duration is the investment period necessary for price risk and reinvestment risk to be exactly offset.
2. The weighted average # of years needed to fully recover the present value of principle and coupon payments.

30. Uses of Duration 1. The most important use of duration is for
reducing or eliminating interest risk over a given holding period.
2. Compare sensitivity of bonds with different
coupons and maturities to changes in interest
rates.

31. Duration Equation n CFt(t) D = S t=1 (1+i)t PB PB = Price of bond
  D = Duration
PB = Price of bond
CF = Cash flows or coupon payments
t = Years

32. Example:
Calculate the duration of a bond with 3 years to maturity, a price of $840.17, a coupon rate of 8%, and a current market rate of 15%.
__________ + _________ + __________
D = ( ) ( ) ( )
________________________________
( )

33. Results 1. high coupon rates => shorter duration
low coupon rates => longer duration
2. generally a (+) relationship exists between duration and term to maturity
3. for a zero coupon bond, duration = maturity
4. ceteris paribus : The higher the market rate of interest, the shorter the duration of the bond.