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

# 073 007 pv face value 10001007 3 pv 97376 pv coupon

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## 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.

Ask a homework question - tutors are online