6-0
The Valuation of Bond using
DCF
6-1
The Size of Bond vs. Stock Markets
• Daily trading volume of
• US stock markets: $10 billion
• Treasury Bond : $300 billion
• Foreign exchange: $ 1.8 trillion
– US GNP in 2005 was $11 trillion
6-2
Valuation of Bonds
• First Principles:
– Value of financial securities = PV of expected future
cash flows
• To value bonds and stocks we need to:
– Estimate future cash flows:
• Size (how much) and
• Timing (when)
– Discount future cash flows at an appropriate rate:
• The rate should be appropriate to the risk presented by the
security.
6-3
Definition and Example of a Bond
• A bond is a legally binding agreement between a
borrower and a lender:
– Specifies the principal amount of the loan.
– Specifies the size and timing of the cash flows:
• In dollar terms (fixed-rate borrowing)
• As a formula (adjustable-rate borrowing): ex:
LIBOR+50 bps (basis points); T-Bond+30 bps
6-4
Definition and Example of a Bond
• Consider a government bond listed as 6 3/8 of
December 2009.
– The Par Value of the bond is $1,000.
– Coupon payments are made semi-annually (June 30 and
December 31 for this particular bond).
– Since the coupon rate is 6 3/8, the payment is $31.875.
– On January 1, 2002 the size and timing of cash flows are:
$31.875 $31.875
$31.875
$1,031.875
6 / 30 / 09
12 / 31 / 09

1 / 1 / 02
6 / 30 / 02
12 / 31 / 02
6-5
How to Value Bonds
• Identify the size and timing of cash flows.
• Discount at the correct discount rate.
– If you know the price of a bond and the size and
timing of cash flows, the yield to maturity is the
discount rate.
6-6
Pure Discount Bonds
Information needed for valuing pure discount bonds:
– Time to maturity (T) = Maturity date - today’s date
– Face value (F)
– Discount rate (r)
$0
$0
$0
$F
T 1
T

0
1
2
Present value of a pure discount bond at time 0:
F
PV 
T
(1  r )
6-7
Pure Discount Bonds: Example
Find the value of a 30-year zero-coupon bond
with a $1,000 par value and a YTM of 6%.
$0
$0
$0
$1,000
29
30

0
1
2
F
$1,000
PV 

 $174.11
T
30
(1  r )
(1.06)
6-8
Level-Coupon Bonds
Information needed to value level-coupon bonds:
– Coupon payment dates and time to maturity (T)
– Coupon payment (C) per period and Face value (F)
– Discount rate
$C
$C
$C
$C  $F
T 1
T

0
1
2
Value of a Level-coupon bond
= PV of coupon payment annuity + PV of face value
C
1 
F
PV  1 

T 
T
r  (1  r )  (1  r )
6-9
Level-Coupon Bonds: Example
Find the present value (as of January 1, 2002), of a 6-3/8 coupon
T-bond with semi-annual payments, and a maturity date of
December 2009 if the YTM is 5-percent.
– On January 1, 2002 the size and timing of cash flows are:
$31.875 $31.875
$31.875
$1,031.875
6 / 30 / 09
12 / 31 / 09

1 / 1 / 02
6 / 30 / 02
12 / 31 / 02
 $1,000
$31.875 
1
PV 
1

 $1,049.30

16 
16
.05 2  (1.025)  (1.025)
6-10
How to Calculate Rate of Return of
Bonds?
• Traditional way of thinking
– Two-period investment: C0 and C1,
rate of return: r = C1/(-C0) -1
– Three-period investment : C0, C1 and C2 ???
• Alternative way of thinking
– Calculate the discount rate that produces a zero
NPV
NPV = C0 + C1/(1+r) = 0, r = C1/(-C0) -1
6-11
What is Yield to Maturity?
• YTM: the rate that produces zero NPV for
bond
NPV = -B + { F / (1 + r)T +  [Ci / (1+r)i] }= 0 ,
B = F / (1 + r)T +  [Ci / (1+r)i]
• The Yield Curve
6-12
Bond Concepts
1. Bond prices and market interest rates move in
opposite directions.
2. When coupon rate = YTM,
When coupon rate > YTM,
(premium bond)
price = par value.
price > par value
When coupon rate < YTM,
price < par value
(discount bond)