You have a cash obligation of $132 240 to be made at the end of year 5. Show how youcan use

QUESTION

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

ANSWER:

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