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Unformatted text preview: WEEK 4 LECTURE SUPPLEMENT Bond valuation represents a straightforward application of the present value principles presented by Lecture 1. With respect to these present value principles, generally speaking there are two major bond categories: zerocoupon bonds and coupon bonds. The price (present value) of a zerocoupon bond is determined by discounting the bonds terminal payout by the bonds yield to maturity. For example, the current price of a zerocoupon bond with a face value of $1,000, a yield to maturity of 10%, and a fiveyear maturity is: $620.92 = $1,000/1.1 5 Zerocoupon bonds are illustrative of why, ceteris paribus (that is, holding all other factors constant), bonds that have longer maturities have greater price risk in relation to otherwise comparable bonds with shorter maturities. This result can be generalized to coupon bonds as well. Suppose a zerocoupon bond has a face value of $1,000, a yield to maturity of 10%, and a six year maturity. The price is: $564.47 = $1,000/1.1 6 Now suppose the yield to maturity on both the fiveyear and sixyear zerocoupon bonds rises to 11%. The two bonds, respectively, will be priced at: $593.45 = $1,000/1.11 5 $534.64 = $1,000/1.11 6 On a percentage basis, the price of the fiveyear bond has changed by: (620.92 + 593.45)/620.92 = 0.04424. On a percentage basis, the price of the sixyear bond has changed by: (564.47 + 534.64)/564.47 = 0.05285. Thus, the sixyear bond has greater price risk. Now, let us assume we wish to determine the price of a 10% annual coupon bond with a face value of $1,000, a yield to maturity of 10%, and a fiveyear maturity. The price is determined as follows: 100/1.1 + 100/1.1 2 + 100/1.1 3 + 100/1.1 4 + 100/1.1 5 + 1,000/1.1 5 = 100[1 1.15 ]/.1 + 1,000/1.1 5 = $1,000.00 If the above bond pays coupons 9% annually, the price is: 90/1.1 + 90/1.1 2 + 90/1.1 5 + 1,000/1.1 5 90[1 1.15 ]/.1 + 1,000/1.1 5 = $962.09 If the above bond pays coupons 9% semiannually, the price is: 45/1.05 45/1....
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This note was uploaded on 05/27/2011 for the course BUSN 380 taught by Professor Bloch during the Fall '10 term at DeVry NY.
 Fall '10
 Bloch
 Valuation

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