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**Unformatted text preview: **e bond’s Yield-to-Maturity?
PV Coupon Payments + PV = 60 [1-(1+0.07)3]
0.07 PV Face Value
1000[(1+0.07)-3] PV = 973.76 PV Coupon Payments
PV = 60 [1-(1+0.077)3]
0.077
PV = $955.95 + PV Face Value
1000[(1+0.077)-3] Yield-to-Maturity
§ Illustration: Suppose you decide to buy a 3-year bond
with a 6% coupon rate and face Value of $1,000 for
$960.99. We assume the bond pays coupons annually.
What is the bond’s Yield-to-Maturity?
PV 7% = 973.76 Do not make this gap too wide!! Yunkno =
wn [Pricelow y –
+ Priceunknown y]
Pricelow y –
Pricehigh y Ylow Yunkno =
wn 7% Yunkno =
wn [955.95 - 960.99]
+
955.95 - 973.76 PV 7.7%= 955.95 x x (yhigh y – ylow
y) (7.7% - 7%) 7.5% N=3 PV= -960.99 PMT=60 FV=1,000; CPT I/Y Effective Annual Yield
§ Illustration: Suppose you decide to buy a 30-year bond
with a 8% coupon rate and face Value of $1,000 for
$800. We assume the bond pays coupons semiannually. What is the bond’s Yield-to-Maturity?
PV Coupon Payments + PV = 40 [1-(1+0.05)-60] PV Face Value
1000[(1+0.05)-60] 0.05
PV 10% =
810.71 Do not make this gap too wide!! [Pricelow y –
Yunkno = Ylow
+ Priceunknown y]
Pricelow y –
wn
Pricehigh y
[810.71 - 800]
Yunkno = 5% +
x
810.71 – 795.22
wn
Yunkno =
wn PV 10.2%= 795.22
x (yhigh y – ylow
y) (5.1% - 5%) 5.07% x 2 = 10.14% N=60 PV= -800 PMT=40 FV=1,000; CPT I/Y Effective Annual Yield Illustration: Suppose you decide to buy a 30-year bond
with a 8% coupon rate and face Value of $1,000 for $800.
We assume the bond pays coupons semi-annually. What
is the bond’s Yield-to-Maturity?
Yield = 5.07% x 2 = 10.14% N=60 PV= -800 PMT=40 FV=1,000; CPT I/Y This yield is semiannual, the conventional way is to
double it and get the annual yield; but this ignores TVM
concept!! The best way is to use the EAY approach!! Effective
=
Annual Yield 0.1014
1+
2 2 -1 = 10.4% The Price Behavior of a Bond Interest Rate Sensitivity
§
§
§
§ § § Bond prices and yields are inversely related: as yields
increase, bond prices fall; as yields fall, bond prices rise
An increase in a bond’s yield to maturity results in a smaller
price change than a decrease in yield of equal magnitude
Prices of long-term bonds tend to be more sensitive to
interest rate changes than prices of short-term bonds
The sensitivity of bond prices to changes in yie...

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