Question

A company has liabilities of $1800 and $2150 due at the end of years 1 and...

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.

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Answer #1

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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

For any query please ask in comment box. Thanks!

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