# 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
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
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
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)
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 )
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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