FIN-2Lecture 9-The Term Structure of Interest Rates and Yield Derivation

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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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This note was uploaded on 05/03/2013 for the course FIN 101 taught by Professor Mugabi during the Spring '13 term at De Haagse Hogeschool.

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