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Bond Pricing and Yield-to-maturity
Lecture 3 Bond Pricing and Yield-to-maturity
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2 parts to this tutorial Part I: Bond Pricing Part II: Yield-to-maturity (YTM)
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Part I: Bond Pricing PV(Bond) = PV(Coupon payments) + PV(Face value or principal) = PMT[(1 – (1/(1+r)^N))/r] + [FV/(1+r)^N] where PMT = Coupon payment per coupon period r = discount rate on bond cash flows N = total number of coupon payments remaining FV = fair value or principal or par value of the bond
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Cash flows from coupon bond
A coupon bond has fair value of $1,000, coupon rate of 8%, and coupon payments made semiannually. The bond has a maturity of 9 years and a required return of 10%. Draw a timeline of the cash flow stream from this coupon bond.
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Timeline of cash flows
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What is the value of this coupon bond?
Discounting cash flows one-by-one:
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Separation of the cash flow stream
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Numerical Example Using the financial calculator:
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Bond valuation using financial calculator
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Part II: YTM calculation
YTM is the discount rate that makes the PV of the bond’s future cash flows equal to the bond price.
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Information needed to calculate YTM
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Numerical Example Information given: Bond price = $950 Coupon rate = 8% Coupon paid semiannually Time to maturity = 9 years Fair value = $1,000
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Three ways to calculate YTM
Trial and error Financial calculator Spreadsheet
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YTM calculation with financial calculator
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Practice, practice, practice
Given a bond with a current price of $1020, fair value of $1000, coupon rate of 10%, semiannual coupon payments, and 13 years to maturity. Calculate the yield-to-maturity of this bond. Check answer: %
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Practice makes comfort
Given a bond with a current price of $1020, fair value of $1000, coupon rate of 10%, quarterly coupon payments, and 13 years to maturity. Calculate the yield-to-maturity of this bond. Check answer: %
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Practice makes everything easy
Given a zero-coupon bond (does not make any coupon payment) with a current market price of $550, face value of $1,000 and 13 years to maturity. What is the yield to maturity if the interest on this bond is compounded semiannually? Check answer: %
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