21 - Lecture 21 Bonds Coupon Paying Bonds Let c by the...

Info icon This preview shows pages 1–4. Sign up to view the full content.

Lecture 21 Bonds Coupon Paying Bonds Let c by the yearly coupon payment and m the face value. Suppose the time to maturity is n years. Then the yield to maturity, y, solves p = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c + m 1 + y ( ) n Note: This follows the standard way of computing an internal rate of return. y is therefore the bond’s internal rate of return. Coupon Paying Bonds Let c by the yearly coupon payment and m the face value. Suppose the time to maturity is n years. Then the yield to maturity, y, solves p = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c + m 1 + y ( ) n We now simplify this expression: Coupon Paying Bonds p = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c + m 1 + y ( ) n We now simplify this expression. Let S = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c 1 + y ( ) n Then S 1 + y = c 1 + y ( ) 2 + c 1 + y ( ) 3 + c 1 + y ( ) 4 + ! + c 1 + y ( ) n + 1 Subtract the second equation from the first..
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Coupon Paying Bonds p = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c + m 1 + y ( ) n We now simplify this expression. Let S = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c 1 + y ( ) n Then S 1 + y = c 1 + y ( ) 2 + c 1 + y ( ) 3 + c 1 + y ( ) 4 + ! + c 1 + y ( ) n + 1 S ! S 1 + y = c 1 + y ! c 1 + y ( ) n + 1 Thus S = ??? Coupon Paying Bonds p = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c + m 1 + y ( ) n We now simplify this expression. Let S = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c 1 + y ( ) n Then S 1 + y = c 1 + y ( ) 2 + c 1 + y ( ) 3 + c 1 + y ( ) 4 + ! + c 1 + y ( ) n + 1 S ! S 1 + y = c 1 + y ! c 1 + y ( ) n + 1 Thus S = c y 1 ! 1 1 + y ( ) n " # $ % & ' Coupon Paying Bonds p = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c + m 1 + y ( ) n We now simplify this expression. Let S = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c 1 + y ( ) n Then p = c y 1 ! 1 1 + y ( ) n " # $ % & ' + m 1 + y ( ) n Thus S = c y 1 ! 1 1 + y ( ) n " # $ % & ' Coupon Paying Bonds p = c 1 + y + c 1 + y ( ) 2 + c 1 + y ( ) 3 + ! + c + m 1 + y ( ) n p = c y 1 ! 1 1 + y ( ) n " # $ % & ' + m 1 + y ( ) n With semiannual coupon payments we get: p = 0.5 c 1 + y ( ) 1/2 + 0.5 c 1 + y + 0.5 c 1 + y ( ) 3/2 + ! + 0.5 c + m 1 + y ( ) n p = 0.5 c 1 + y ( ) 0.5 ! 1 1 ! 1 1 + y ( ) n " # $ % & ' + m 1 + y ( ) n
Image of page 2
Yield to Maturity p = c y 1 ! 1 1 + y ( ) n " # $ % & ' + m 1 + y ( ) n Solve this equation for y (usually, one must do this numerically). Exception p=m, i.e., bond is “sold at par”, then y=m/c.
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 4
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '12
  • Murphy
  • Oct

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern