LN_7_PPT - Bond Valuation Interest Rates Bond Bond...

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1 Bond Valuation & Interest Rates ± Bond ² Bond valuation ² Bond features and types Prof. Q. Ma HADM 2222: Bond Valuation 1 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 2 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 ± Par value or face value (F) ± Coupon rate Prof. Q. Ma HADM 2222: Bond Valuation 3 ² Coupon payment (C) ± Maturity (T) ± Yield to maturity (r) Bond Pricing Equation Bond Value = PV of coupons + PV of par 1 Prof. Q. Ma HADM 2222: Bond Valuation 4 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 5 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 6 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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2 Properties of Bond Price ± Price & yield relationship ² Everything else the same, higher yield leads to lower bond price. ± Coupon rate & yield relationship ² If coupon rate = YTM, then bond price = par value Prof. Q. Ma HADM 2222: Bond Valuation 7 ² 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 8 850.61 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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LN_7_PPT - Bond Valuation Interest Rates Bond Bond...

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