Chapter 7 Interest Rates and Bond valuation 0
0 Chapter 7 Interest Rates and Bond Valuation
Chapter Outline Bonds and Bond valuation ■More on Bond Features o Bond Ratings ■、 Some Different Types of Bonds ■Bond Markets -Inflation and Interest Rates Determinants of Bond Yields
1 Chapter Outline n Bonds and Bond Valuation n More on Bond Features n Bond Ratings n Some Different Types of Bonds n Bond Markets n Inflation and Interest Rates n Determinants of Bond Yields
Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate Understand bond ratings and what they mean Understand the impact of inflation on interest rates Understand the term structure of interest rates and the determinants of bond yields
2 Key Concepts and Skills n Know the important bond features and bond types n Understand bond values and why they fluctuate n Understand bond ratings and what they mean n Understand the impact of inflation on interest rates n Understand the term structure of interest rates and the determinants of bond yields
Bond Definitions Bond Par value (face value) ■Coupon rate ■Coupon payment Maturity date Yield or Yield to maturity 3
3 Bond Definitions n Bond n Par value (face value) n Coupon rate n Coupon payment n Maturity date n Yield or Yield to maturity
PV of Cash Flows as rates change Bond Value PV of coupons PV of par Bond Value PV annuity PV of lump sum Remember,as interest rates increase,the PVs decrease So,as interest rates increase,bond prices decrease and vice versa 4
4 PV of Cash Flows as Rates Change n Bond Value = PV of coupons + PV of par n Bond Value = PV annuity + PV of lump sum n Remember, as interest rates increase, the PVs decrease n So, as interest rates increase, bond prices decrease and vice versa
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