Chapter 5 - 156 Introduction to the Valuation of Debt...

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156 Introduction to the Valuation of Debt Securities c. The dealer will buy a package of Treasury strips such that the cash flow from the package will replicate the ::: flow of a 4% 8-year Treasury issue and sell the overvalued Treasury issue. The cost of buying the package Treasury strips is \$89.3155. The value of selling the Treasury issue or, if reconstituted, the value of the synrl:l coupon Treasury created is \$89.4971. The arbitrage profit is therefore \$0.1816 (\$89.4971 - \$89.3155). d. The process of dealers selling the Treasury issue will drive down its prices until the market price is closa the arbitrage-free value of \$89.3154. Period~ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Years 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 C-ash flow 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 102 Total Present value 2.825% 1.9451 1.8916 1.8396 1.7891 1.7399 1.6921 1.6457 1.6004 1.5565 1.5137 1.4721 1.4317 1.3923 1.3541 1.3169 65.3162 89.4971 SOLUTIONS TO PRACTICE QUESTIONS 1. a. The cash flow per \$100 of par value for this security is: X~. ~aslt.fio;w 1 \$7 2 7 3 7 4 7 5 107 Year 1: present value 1 = The present value for each cash flow assuming a discount rate of 5% is: \$7 (l.05)1 \$7 Year 2: present value , = = \$6.3492 ( l.05)2 Year 3: present value 3 = \$7 = \$6.0469 ( l.05)3 \$7 Year 4: present value, = = \$5.7589 (l.05)4 Year 5: present value, = \$lO7 = \$83.8373 ( l.05)5 The present value is the sum of the five present values above, \$108.6590 . ••••••• = \$6.6667 -

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~ cash flow for this security is \$2,309.75 for each year. The present value of each cash flow assuming a discount 6% is: Year 1: present value) \$2,309.75 = \$2,179.0094 (1.06)1 Year 2: present value , \$2,309.75 = \$2,055.6693 ( 1.06)2 Year 3: present value 3 = \$2,309.75 = \$1,939.3106 (1.06)3 Year 4: present value, = \$2,309.75
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Chapter 5 - 156 Introduction to the Valuation of Debt...

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