Fin 390 Chapter7

# Fin 390 Chapter7 - Chapter 7 Interest Rates and Bond...

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7-1 Chapter 7 Interest Rates and Bond Valuation

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Chapter Outline Bonds and Bond Valuation Bond feature Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields 7-2
Key Concepts and Skills Know the important bond features and bond types Understand bond values and why they fluctuate and the determinants of bond yields Understand bond ratings and what they mean Understand the impact of inflation on interest rates Understand the term structure of interest rates 7-3

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Bond Definitions Bond – a debt security issued by a company for borrowing money with the following features: Par value (face value) Coupon rate Coupon payment Maturity of time period Yield or Yield to maturity 7-4
The Bond Pricing Equation A.2 Table r) (1 1 A.3 Table r r) (1 1 - 1 C Value Bond t t + + + = FV 7-5 FV - Par value (face value) C - Coupon payment = FV * coupon rate t - Maturity (or number of periods) r - Yield to maturity Bond Value = PV ( Coupon Annuity) + PV (Par Value)

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The Bond Pricing Equation A.2 Table r) (1 1 Value Bond t + = FV 7-6 FV - Par value (face value) t - Maturity (or number of periods) r - Yield to maturity Current yield = Coupon / Price Zero Coupon Bound: C=0
Premium Bound (Coupon rate > yield to maturity) A bond has a 10% annual coupon and a face value of \$1000, 20 years to maturity, and the yield to maturity is 8%. What is the price of this bond? FV = 1000 , t=20 r=8% coupon rate = 10% Coupon payment = 1000*10% =100 Annuity discount factor (t=20, r=8%) = 9.8181 (Table A.3,pA-6) PV (C annuity) = 100 * 9.8181 = 981.81 Discount factor (t=20, r=8%) = 0.2145 (Table A.2, pA-4) PV (Par value) = 1000 * 0.2145 = 214.5 Bound value = 981.81 + 214.5 = 1196.31 Key point : Premium bound: Price (or PV) > Par or Face Value 7-7

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Discount Bond (coupon rate < yield to maturity) A bond with an annual coupon rate of 8%. The par value is \$1,000, and the bond has 5 years to maturity. The yield to maturity is 10%. What is the value of the bond? FV =1000, coupon rate = 8%, r=10%, t=5 Coupon payment = 1000*8% = 80 Annuity discount factor (10%, t=5)=3.7908 (Table A.3, pA-6) PV (C Annuity) = 80 * 3.7908 = 303.26 Discount factor (10%, t=5) = 0.6209 (Table A.2, p A-4) PV (Par Value) = 1000 * 0.6209= 620.9 Bound value = 303.26 + 620.9 = 924.16 Key point : Price (or PV) < Par or Face Value 7-8
Bond Prices Relationship Between Coupon and Yield If YTM > coupon rate, then par value > bond price Why? The discount provides yield above coupon rate Price below par value, called a discount bond If YTM < coupon rate, then par value < bond price Why? Higher coupon rate causes value above par Price above par value, called a premium bond If YTM = coupon rate, then par value = bond price 7-9

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Summary Table 7-10
Bond Prices with a Spreadsheet There is a specific formula for finding bond prices on a spreadsheet PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis) YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis) Settlement and maturity need to be actual dates The redemption and Pr need to be input as % of par value Click on the Excel icon for an example 7-11

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YTM with Annual Coupons
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