A company must pay liabilities of $1000 due one year from now and another $2000

Question

A company must pay liabilities of $1000 due one year from now and another $2000 due two years from now. There are two available investments, a one-year zero coupon bond and two- year bonds with 10% annual coupons maturing at Par. The one-year spot rate is 8% and the 4. forward rate for year 2 is 9%. If the liabilities are matched exactly, with bonds (assets), what is the Par value of each bond (the one-year zero coupon bond and the two-year bond with annual 10% coupons)? What is the total cost for the bonds from part a?" a. b.

Explanation / Answer

a. Computation of the par value of each bond:
PV of the bond = 1000/1.08 + 2000/(1.08)(1.09)
= 925.93 + 1,698.95
= 2624.87 = 2625

Here, it was given that liabilities are matched exactly, that means we need to use matching method
To pay $2000 in year two, we require a two year bond =$2,000/ 1.10 = $1818.18
and this will pay a coupon payment of = 2,000 - 1,818.18 = 181.82 coupon payment in year one.
Therefore, $1,818.18 is the face value of the two year bond.
Now, let us calculate face value for one year bond:
face value for one year bond = $1,000 - coupon payment in one year
= $1,000-181.82 = 818.18.

b. Total cost of the bonds:

We buy 2000/1.1 = 1818.18 in face value
Thus, the purchase price = (181.82 / 1.08) + [2000 / (1.08)(1.09)] = 1867.30
and for one year bond it costs =818.18 / 1.08 = 757.57
Therefore, the total cost is 1,867.30 + 757.57 = 2624.87.

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