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**Unformatted text preview: **Interest Rates and Bond Valuation Chapter Seven 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) Present Value of Cash Flows as Rates Change • Bond Value = PV of coupons + PV of par Bond Value = PV annuity + PV of lump sum The Bond-Pricing Equation t t r) (1 F r r) (1 1- 1 C Value Bond + + + = 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 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 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 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 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 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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