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Chapter4Notes

# Chapter4Notes - BACKGROUND INFORMATION For a coupon bond...

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Chapter 04 - Table 4-2 - Notes 1/6 B ACKGROUND I NFORMATION For a coupon bond with face value F , yearly coupon rate C r , the annual coupon payment C is determined by the face value and the yearly coupon rate r C F C , and n years to maturity. The maximum price that investors are willing to pay for this coupon bond at the beginning of the current period is the sum of discounted cash flows in the future, n n i F i C i C i C P ) 1 ( ) 1 ( ... ) 1 ( ) 1 ( 2 (Equation 1). There are two components embedded in the price of the coupon bond. First, it is the discounted future coupon payments from the current period until the bond matures in n years, n i C i C i C ) 1 ( ... ) 1 ( ) 1 ( 2 , note that even the coupon payment for the current period will be discounted because the value of the bond (price) is evaluated at the beginning of the current period, but the annual coupon payment will only be received in the end of each period. Second, the discounted face value that the bond holder will receive when the bond matures n years from the current period, n i F ) 1 ( . A PPLICATION TO T ABLE 4-2 Applying the above definition to a coupon bond with a face value F of 1000, yearly coupon rate C r of 10%, the term to maturity n of 5 years. The annual coupon payment C is 100, which is determined by the face value and the yearly coupon rate r C F C . The value of the coupon bond evaluated at the beginning of the current period t is the sum of the discounted future coupon payments from year t until the bond matures in year t+5 and the discounted face value that the bond holder will receive when the bond matures in year t+5 (with everything discounted using the current yield i c of 10% because it is the relevant yield that investors expect to earn in the next 5 years when it is assumed to remain unchanged until the bond matures),

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Chapter 04 - Table 4-2 - Notes 2/6 5 5 4 3 2 ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( ) 1 ( c c c c c c t i F i C i C i C i C i C P (Equation 2). That is, 1000 621 62 68 75 83 91 ) 1 . 0 1 ( 1000 ) 1 . 0 1 ( 100 ) 1 . 0 1 ( 100 ) 1 . 0 1 ( 100 ) 1 . 0 1 ( 100 ) 1 . 0 1 ( 100 5 5 4 3 2 t P . The time-line representation of the coupon bond is 1 2 3 4 5 Beginning of the current period t when the coupon bond is evaluated End of each period when the coupon payment is received End of the period t+5 when the face value of the bond is received
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Chapter4Notes - BACKGROUND INFORMATION For a coupon bond...

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