Class 10 Completed

# N here we will focus on level coupon bonds ie coupon

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N Here we will focus on level coupon bonds, i.e. coupon-paying bonds with constant coupon payments. N A coupon bond is an interest-only loan, i.e. it pays interest (called coupon payments) each period and the entire principal is repaid at maturity. N A typical coupon-paying bond promises to make semi-annual payments to the bondholder for the life of the bond (until maturity) These payments are called coupon payments .

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8 Level Coupon Bond Characteristics Continued N The number of years (or periods) until the bond holder receives the face value of the bond from the issuer is called the bond s time to maturity . N At maturity, the issuer repays the debt by paying the bondholder the face value F (also called principal or par value) of the bond, plus one last coupon payment. N The periodic interest payments (cash flows) of a bond are determined by the coupon rate c. N The annual coupon payment is given by the coupon rate times the bond s par value c*F When coupon payments are semi-annual, the coupon payments are equal to the coupon rate times face value divided by two. N The contract between the issuer and the bondholder is called the bond indenture. The bond s coupon rate, par value, and maturity date are all part of its indenture.
9 Level Coupon Bonds N Cash flows associated with a level coupon bond: N 0 1 2 3 n-1 n Periods N ---|------|------|------|-----------------------|------|--- N C C C ………… . C C Cash F Flows N Where: C is the \$ amount of each coupon payment N Interest payment/cash flow associated with the bond n is the number of periods until maturity F is the face value of the bond N All these cash flows are known when the bond is issued. The cash flows are not affected by changes in market interest rates!

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10 Bonds are Easy! N A coupon paying bond s payments consist of two parts: 1. An annuity of n cash flows of C 2. Payment of the bond s face value F at maturity n periods from now. N Given an appropriate interest (discount) rate r, the price of the bond at time 0 is equal to the present value of its cash flows: n n B n n B r F r r C PV P r F r C r C r C r C PV P ) 1 ( ) 1 ( 1 ) 1 ( ) 1 ( ......... ) 1 ( ) 1 ( ) 1 ( 0 3 2 0 + + ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = = + + + + + + + + + + = =
11 Bond Pricing N Given the cash flows associated with a bond, what do we need to value (price) the bond? Need to compute the present value of these cash flows. Need a periodic interest rate (or discount rate) r to compute the present value of these cash flows. N What is r? Effective periodic market interest rate. Also called the yield-to-maturity (ytm) or bond-equivalent yield. N Expected rate of return investors demand per period on similar securities. N When coupons are paid semi-annually, you compute the effective semi- annual rate by dividing the YTM by two.

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