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Bond Valuation & Interest Rates
±
Bond
²
Bond valuation
²
Bond features and types
Prof. Q. Ma
HADM 2222: Bond Valuation
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²
Bond market
±
Interest rate
Bond Example
Marriott International issues bonds to
finance its expansion into emerging markets.
From each bond issued, it borrows a face
value of $1,000 for 20 years. The coupon
Prof. Q. Ma
HADM 2222: Bond Valuation
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rate is 10 percent. Marriott will thus pay
$100 in interest every year for 20 years. At
the end of 20 years, Marriott will repay the
$1,000. The yield to maturity for similar
bonds is quoted at 8%.
Bond Definition
±
Bond
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Par value or face value (F)
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Coupon rate
Prof. Q. Ma
HADM 2222: Bond Valuation
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²
Coupon payment (C)
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Maturity (T)
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Yield to maturity (r)
Bond Pricing Equation
Bond Value = PV of coupons + PV of par
1
⎤
⎡
Prof. Q. Ma
HADM 2222: Bond Valuation
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T
T
r)
(1
F
r
r)
(1

1
C
Value
Bond
+
+
⎥
⎥
⎥
⎥
⎦
⎢
⎢
⎢
⎢
⎣
+
=
Discount Bond
Consider a bond with a coupon rate of 10% and
coupons paid annually. The par value is $1000
and the bond has 20 years to maturity. The yield
to maturity is 12%. What is the value of the bond?
±
Formula
Prof. Q. Ma
HADM 2222: Bond Valuation
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²
B = PV of annuity + PV of lump sum
²
B = 100[1 – 1/(1.12)
20
] / .12 + 1000 / (1.12)
20
±
Calculator
²
N = 20; I/Y = 12; PMT = 100; FV = 1000
²
CPT PV =
– 850.61
Premium Bond
Consider a bond with a coupon rate of 10% and
coupons paid annually. The par value is $1000
and the bond has 20 years to maturity. The yield
to maturity is 8%. What is the value of the bond?
±
Formula
Prof. Q. Ma
HADM 2222: Bond Valuation
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²
B = PV of annuity + PV of lump sum
²
B = 100[1 – 1/(1.08)
20
] / .08 + 1000 / (1.08)
20
±
Calculator
²
N = 20; I/Y = 8; PMT = 100; FV = 1000
²
CPT PV =
– 1,196.36
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Properties of Bond Price
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Price & yield relationship
²
Everything else the same, higher yield leads to lower
bond price.
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Coupon rate & yield relationship
²
If coupon rate = YTM, then bond price = par value
Prof. Q. Ma
HADM 2222: Bond Valuation
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If coupon rate < YTM, then bond price < par value
²
If coupon rate > YTM, then bond price > par value
Bond Price & Yield
(Par=1,000, Coupon Rate=10%, T=20)
1196.36
1500
2000
2500
d Price
Prof. Q. Ma
HADM 2222: Bond Valuation
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850.61
1000.00
0
500
1000
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
13%
14%
15%
16%
17%
18%
19%
20%
Yield
Bond
Bonds in Reality
±
In practice, bonds issued in the United States
usually make coupon payments twice a year.
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