A company has liabilities of $1800 and $2150 due at the end of years 1 and 2 respectively. The only investments available are 1-year 5% annual coupon bonds and 2-year 6% annual coupon bonds and both redeemable at par. How much of each bond (in terms of maturity values) should the company buy in order to exactly (absolutely) match the assets and liabilities.
Ans:
Ans:
Liability after 1 year : $1,800
Investment in 1 year bond @ : 5%
Investment to be done today @5% to earn $1,800 after 1 year.
= Amount required * present value factor
Present value factor: 1/(1.05)^1 = 0.95238
Value of asset company should buy : 1,800*0.95238
= $1,714.29
Liability after 2 year: $2,150
Investment in 1 year bond @ : 6%
Investment to be done today @6% to earn $2,150 after 2 year.
= Amount required * present value factor
Present value factor: 1/(1.06)^2 = 0.8900
Value of asset company should buy : 2,150*0.8900
= $1,913.50
So investment should be done in 1 year bond : 1714.29 and $ 1913.50 in 2 years bond.
Total investment : $1714.29+$1913.50 = $3627.79
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