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Chapter 10

# Chapter 10 - Learning Objectives In this chapter you will...

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Learning Objectives In this chapter, you will learn: 1. How to calculate bond prices and yields. 2. The importance of yield to maturity. 3. Interest rate risk. 4. How to measure the impact of interest rate changes on bond prices. 10-1

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10-2 Bond Prices and Yields Our goal in this chapter is to understand the relationship between bond prices and yields. In addition, we will examine some fundamental tools that fixed-income portfolio managers use when they assess bond risk.
10-3 Bond Basics, I. A Straight bond is an IOU that obligates the issuer of the bond to pay the holder of the bond: A fixed sum of money (called the principal, par value, or face value) at the bond’s maturity, and sometimes Constant, periodic interest payments (called coupons) during the life of the bond U.S. Treasury bonds are straight bonds .

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10-4 Bond Basics, II. Two basic yield measures for a bond are its coupon rate and its current yield . value Par coupon Annual rate Coupon = price Bond coupon Annual yield Current =
10-5 Straight Bond Prices and Yield to Maturity The price of a bond is found by adding together the present value of the bond’s coupon payments and the present value of the bond’s face value. The Yield to maturity (YTM) of a bond is the discount rate that equates the today’s bond price with the present value of the future cash flows of the bond.

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10-6 The Bond Pricing Formula In the formula, C represents the annual coupon payments (in \$), FV is the face value of the bond (in \$), and M is the maturity of the bond, measured in years. ( 29 ( 29 2M 2M 2 YTM 1 FV 2 YTM 1 1 1 YTM C Price Bond + + + - = PV of (coupons) PV of ( principal)
10-7 Example: Using the Bond Pricing Formula What is the price of a straight bond with: \$1,000 face value, coupon rate of 8%, YTM of 9%, and a maturity of 20 years? ( 29 ( 29 ( 29 ( 29 \$907.99. 171.93 0.82807) (888.89 2 0.09 1 1000 2 0.09 1 1 1 0.09 80 Price Bond 2 YTM 1 FV 2 YTM 1 1 1 YTM C Price Bond 0 2 2 0 2 2 2M 2M = + × = + + + - = + + + - = × × Financial Calculator: FV=\$1,000, N=40, Pmt= \$40, i=4.5 PV=\$907.99

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10-8 Premium and Discount Bonds, I. Bonds are given names according to the relationship between the bond’s selling price and its par value. Premium bonds : price > par value YTM < coupon rate Discount bonds : price < par value YTM > coupon rate Par bonds : price = par value YTM = coupon rate
10-9 Premium and Discount Bonds, II.

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10-10 Premium and Discount Bonds, III. In general, when the coupon rate and YTM are held constant: for premium bonds : the longer the term to maturity, the greater the premium over par value. for discount bonds : the longer the term to maturity, the greater the discount from par value.
10-11 Premium and Discount Bonds, IV. Consider two bonds, both with a 9 percent coupon rate and the same yield to maturity of 7 percent, but with different maturities of 5 and 10 years. Which has the higher price?

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