A company must make yearly payments starting at $100,000 and increasing by 6% ev

Question

A company must make yearly payments starting at $100,000 and increasing by 6% every year for 10 years. Payments are due at the end of each year. They can invest in a portfolio of coupon-paying bonds that vary in term from 1 to 10 years (a total of 10 unique bonds). Each bond has a coupon rate equal to the term of the bond (i.e. the 10-year bond has a coupon rate of 10%, the 8-year bond has a coupon rate of 8%). They decide to do an absolute matching strategy to back the liability. At a yield rate of 5% how much would the company need to have available to purchase bonds for this absolute matching strategy?

Explanation / Answer

SOLUTION:

If $100,000 increases at 6%, after 10 years it would be,

$106,000 for one year.

At the rate of 5% yield rate, assume that the coupon rate for 5% is for 5 years.

The 10-year yield is 5%, so

= $106,000 / ( 1 + 0.05)^5

The company need to pay $83.053.77

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