Chap007s - Interest Rates and Bond Valuation Chapter Seven...

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Interest Rates and Bond Valuation Chapter Seven
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Bond Definitions Par value (face value, it’s also the future value of the bond) Coupon rate (use it to find coupon payment) Coupon payment (equal to coupon rate times the par value for annual bonds) Maturity date (will give you the number of periods) Yield or Yield to maturity (interest rate)
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Present Value of Cash Flows as Rates Change Bond Value = PV of coupons + PV of par Bond Value = PV annuity + PV of lump sum
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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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Valuing a Discount Bond with Annual Coupons Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 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 + 1000 / (1.11) 5 B = 369.59 + 593.45 = 963.04 Using the calculator: N = 5; I/Y = 11; PMT = 100; FV = 1000 CPT PV = -963.04
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Valuing a Premium Bond with Annual Coupons Suppose you are looking at 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 = -1196.36
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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 Selling at a discount, called a discount bond If YTM < coupon rate, then par value < bond price Selling at a premium, called a premium bond
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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 Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be reinvested Short-term bonds have more reinvestment rate risk than long-term bonds
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Computing Yield-to-maturity YTM is simply another name for interest rate (not to be confused with coupon rate) Yield-to-maturity is the rate implied by the current bond price Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity
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YTM with Annual Coupons Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928.09.
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