Valuing a Discount Bond with Annual Coupons Consider a bond with a coupon rate of 10%and coupons paid annually.The par value is $1,000 and the bond has 5 years to maturity.The yield to maturity is 11%.What is the value of the bond? Using the formula: ■ B=PV of annuity PV of lump sum ■B=$100[1-1/(1.11)]/.11+$1,000/(1.11)5 ■B=$369.59+593.45=$963.04 0 Using the calculator: ■ N=5;I/Y=11;PMT=100;FV=1,000 ■CPT PV=-963.04
5 Valuing a Discount Bond with Annual Coupons n Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1,000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond? q Using the formula: n B = PV of annuity + PV of lump sum n B = $100[1 – 1/(1.11)5] / .11 + $1,000 / (1.11)5 n B = $369.59 + 593.45 = $963.04 q Using the calculator: n N = 5; I/Y = 11; PMT = 100; FV = 1,000 n CPT PV = -963.04
Valuing a Premium Bond with Annual Coupons Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1,000.There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond? Using the formula: B=PV of annuity PV of lump sum ■B=$100[1-1/(1.08)20]/.08+$1,000/(1.08)20 ■B=$981.81+214.55=$1,196.36 Using the calculator: N=20;IY=8;PMT=100;FV=1,000 CPT PV=-1,196.36 6
6 Valuing a Premium Bond with Annual Coupons n Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1,000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond? q Using the formula: n B = PV of annuity + PV of lump sum n B = $100[1 – 1/(1.08)20] / .08 + $1,000 / (1.08)20 n B = $981.81 + 214.55 = $1,196.36 q Using the calculator: n N = 20; I/Y = 8; PMT = 100; FV = 1,000 n CPT PV = -1,196.36
Graphical Relationship Between Price and YTM 1500 1400 1300 1200 1100 1000 900 800 700 600 0% 2% 4% 6% 8% 10% 12% 14% YTM 7
7 Graphical Relationship Between Price and YTM
Bond Prices:Relationship Between Coupon and Yield If YTM coupon rate,then par value bond price If YTM>coupon rate,then par value bond price a Why? Price below par=“discount'”bond If YTM coupon rate,then par value bond price a Why? ▣Price above par=“premium”bond 8
8 Bond Prices: Relationship Between Coupon and Yield n If YTM = coupon rate, then par value = bond price n If YTM > coupon rate, then par value > bond price q Why? q Price below par = “discount” bond n If YTM < coupon rate, then par value < bond price q Why? q Price above par = “premium” bond
The Bond-Pricing Equation F Bond Value =C 十 r (1+r)t 9
9 The Bond-Pricing Equation t (1 r) F r t (1 r) 1 1- Bond Value C