Question

You work for Pinstripe Partners LLC, a Cayman Islands based hedge fund founded by one of your fellow students. Your company can both invest and borrow cash at an annual rate of 2% compounded continuously.
You own a derivative contract that will pay out $150 million in 5 years (this
will be the only payment). Your boss instructs you to sell this contract and replace it
with another one which will already pay out in 3 years and which has the same present
value as the existing contract. What will be the sum paid out by the replacement
contract after 3 years?

Answer 1

You work for Pinstripe Partners LLC, a Cayman Islands based hedge fund founded by one of your fellow students. Your company can both invest and borrow cash at an annual rate of 2% compounded continuously.

(a) You own a derivative contract that will pay out $150 million in 5 years (this
will be the only payment). Your boss instructs you to sell this contract and replace it
with another one which will already pay out in 3 years and which has the same present
value as the existing contract. What will be the sum paid out by the replacement
contract after 3 years?

(b) You have invested $100 million in the company Advantage Electronics Inc.
The value of this investment grows at a rate of 6% per year compounded continuously.
At the same time, you have also invested $80 million in West End Property, growing
at a rate of 8% compounded continuously. After how many years will both investments
have the same value?