Chap007

# Chap007 - Chapter 7 I nterest Rates and Bond Valuation Key...

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Chapter 7 Interest Rates and Bond Valuation

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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 7-2
Chapter Outline Bonds and Bond Valuation More about Bond Features Bond Ratings Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields 7-3

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Bond Definitions Bond Par value (face value) Coupon rate Coupon payment Maturity date Yield or Yield to maturity 7-4
Present Value of Cash Flows as Rates Change Bond Value = PV of coupons + PV of par Bond Value = PV of annuity + PV of lump sum As interest rates increase, present values decrease So, as interest rates increase, bond prices decrease and vice versa 7-5

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Valuing a Discount Bond with Annual Coupons Consider a bond with a coupon rate of 10% and annual coupons. 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) 5 ] / .11 + 1,000 / (1.11) 5 B = 369.59 + 593.45 = 963.04 Using the calculator: N = 5; I/Y = 11; PMT = 100; FV = 1,000 CPT PV = -963.04 7-6
Valuing a Premium Bond with Annual Coupons Suppose you are reviewing a bond that has a 10% annual coupon and a face value of \$1000. 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 + 1000 / (1.08) 20 B = 981.81 + 214.55 = 1196.36 Using the calculator: N = 20; I/Y = 8; PMT = 100; FV = 1000 CPT PV = -1,196.36 7-7

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Graphical Relationship Between Price and Yield-to-maturity (YTM) 600 700 800 900 1000 1100 1200 1300 1400 1500 0% 2% 4% 6% 8% 10% 12% 14% Bond Price Yield-to-maturity (YTM) 7-8
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 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 7-9

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The Bond Pricing Equation t t r) (1 FV r r) (1 1 - 1 C Value Bond + + + = 7-10
Example 7.1 Find present values based on the payment period How many coupon payments are there? What is the semiannual coupon payment? What is the semiannual yield? B = 70[1 – 1/(1.08) 14 ] / .08 + 1,000 / (1.08) 14 = 917.56 Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT PV = -917.56 7-11

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Interest Rate Risk Price Risk Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon rate bonds Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested
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