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You have a cash obligation of \$132,240 to be made at the end of year 5. Show how youcan use coupon bonds with a coupon rate of 8%, a face value of \$1,000, a maturitydate at the end of year 6, and a yield to maturity of 8% to ensure that you can meetyour cash obligation at the end of year 5. Suppose that you purchase the bonds at thebeginning of year 1 and that the market interest rate changes only once right afteryou have purchased the bonds. There are three possible interest rates, 7.9%, 8%, and8.1%, each of which occurs with probability 1/3.
\$132,240/(1.08)^5=\$90,000 Duration of the bond=5years Thus, I need to buy 90 units of the bond to immunize against the invest rate risk. 1/3*\$80(1.079)^4+\$80(1.079)^3+\$80(1.079)^2+\$80(1.079)+\$80+\$1080/1.079*90 +…

0(1.08)^2+\$80(1.08)+\$80+\$1080/1.08*90 + 1/3*\$80(1.081)^4+\$80(1.081)^3+\$80(1.081)^2+\$80(1.081)+\$80+\$1080/1.081*90 =1/3*(\$132,240+\$132,240+\$132,240) =\$132,240

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