Chapter 7 - Interest Rates and Bond Valuation Chapter Seven...

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Interest Rates and Bond Valuation Chapter Seven
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Chapter Outline Bonds and Bond Valuation More on Bond Features Bond Ratings Some Different Types of Bonds Bond Markets Inflation and Interest Rates Determinants of Bond Yields
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Bond Definitions Bond Par value (face value) Coupon rate Coupon payment = coupon rate * face value Maturity date Yield or Yield to maturity (YTM) Market interest rate for bonds with similar features
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Present Value of Cash Flows as Rates Change Bond Value = PV of coupons + PV of par Bond = PV annuity + PV of lump sum As interest rates increase the PV’s decrease As interest rates increase, bond prices decrease and vice versa
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The Bond-Pricing Equation t t r) (1 F r r) (1 1 - 1 C Value Bond + + + =
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Relationship Between Price and Yield-to-maturity 600 700 800 900 1000 1100 1200 1300 1400 1500 0% 2% 4% 6% 8% 10% 12% 14% Coupon rate = 8% with annual coupons; Par value = $1000; Maturity = 10 years
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Valuing a Bond Example 1 Suppose you are looking at a bond that has a 10% coupon rate, annual coupons, and a face value of $1000. There are 5 years to maturity and the YTM is 11%. What is the price of this bond? Value = PV of annuity + PV of lump sum Value = 100[1 – 1/(1.11) 5 ] / .11 + 1000 / (1.11) 5 Value = 369.59 + 593.45 = 963.04 (bond sells for less than its face value - discount bond)
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Interest rate change (Example 1) Suppose a year has gone by. The bond now has 4 years to maturity. If the interest rate in the market has risen to 12%, what will the bond worth? Value = PV of annuity + PV of lump sum Value = 100[1 – 1/(1.12) 4 ] / .12 + 1000 / (1.12) 4 Value =303.73+635.52=939.25 (bond with its 10% coupon is priced to yield 12% at $939.25)
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Valuing a Bond Example 2 Suppose you are looking at a bond that has a 9% coupon rate, semi-annual coupons, and a face value of $1000. There are 20 years to maturity and the YTM is 9%. What is the price of this bond? Value = PV of annuity + PV of lump sum Value = 45[1 – 1/(1.045) 40 ] / .045 + 1000 / (1.045) 40 Value = 828.07 + 171.93 = 1000.00
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Valuing a Bond Example 3 Suppose you are looking at a bond that has a 10% coupon rate, semi-annual coupons, and a face value of $1000. There are 20 years to maturity and the YTM is 8%. What is the price of this bond? Value = PV of annuity + PV of lump sum Value = 50[1 – 1/(1.04) 40 ] / .04 + 1000 / (1.04) 40 Value = 989.64 + 208.29 = 1197.93 ( premium bond )
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Bond Prices: Relationship Between Coupon Rate and Yield to Maturity 1. If YTM = coupon rate, par value = bond price 2. If YTM > coupon rate, par value > bond price Selling at a discount, called a discount bond 3. If YTM < coupon rate, par value < bond price Selling at a premium, called a premium bond
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Interest Rate Risk The risk that arises for bond owners from changes in interest rates change in price due to interest rate fluctuations
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