Lecture 3 Bond Pricing and Yieldtomaturity 2 parts

Lecture 3 Bond Pricing and Yield-to-maturity

2 parts to this tutorial Part I: Bond Pricing Part II: Yield-to-maturity (YTM)

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

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.

Timeline of cash flows

What is the value of this coupon bond? Discounting cash flows one-by-one:

Separation of the cash flow stream

Numerical Example Using the financial calculator:

Bond valuation using financial calculator

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.

Information needed to calculate YTM

Numerical Example Information given: Bond price = $950 Coupon rate = 8% Coupon paid semiannually Time to maturity = 9 years Fair value = $1, 000

Three ways to calculate YTM 1. Trial and error 2. Financial calculator 3. Spreadsheet

YTM calculation with financial calculator

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: 9. 725665243%

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: 9. 727270497%

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: 4. 652024901%