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BUSN380 Week 4 TCO 5 Bond Valuation Notes - Lecture Supplement

# BUSN380 Week 4 TCO 5 Bond Valuation Notes - Lecture Supplement

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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: zero-coupon bonds and coupon bonds. The price (present value) of a zero-coupon bond is determined by discounting the bond’s terminal payout by the bond’s yield to maturity. For example, the current price of a zero-coupon bond with a face value of \$1,000, a yield to maturity of 10%, and a five-year maturity is: \$620.92 = \$1,000/1.1 5 Zero-coupon 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 zero-coupon 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 five-year and six-year zero-coupon 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 five-year bond has changed by: (-620.92 + 593.45)/620.92 = -0.04424. On a percentage basis, the price of the six-year bond has changed by: (-564.47 + 534.64)/564.47 = -0.05285. Thus, the six-year 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 five-year 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- 1.1 -5 ]/.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- 1.1 -5 ]/.1 + 1,000/1.1 5 = \$962.09 If the above bond pays coupons 9% semi-annually, the price is:

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45/1.05 + 45/1.05 2 + 45/1.05 3 … + 45/1.05 10 + 1,000/1.05 10 45[1- 1.05
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