A refining company entered into a contract for raw materials with an agreement to pay $600,000 now and $150,000 per year beginning at the end of the fifth year. The contract was made for 10 years. At the end of the third year, because of unexpected profits, the company requested that it be allowed to make a lump-sum payment in advance for the rest of the contract. Both parties agreed that 7 percent compounded annually was a fair interest rate, What was the amount of the lump sum?
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I don't have my Eng Econ book, so I don't have the equations or charts. Buy, here is how:
1) Forget the $600K, that is spent money
2) End of year 5 is January 1, year 6, so you are going to make 5 payments of $150K each for 5 years ( Years 6, 7, 8, 9, 10) ===> you need the Present Value of a 5 Year Annuity that pays $150K for 5 years at 7%. That gives you the Present Value of the contract at the end of year 5
3) start of Year 4, what is the Present Value at 7% for 2 years (Years 4 & 5) of that Future Value you need for the Annuity at the start of Year 6. That is the value to buy the contract
1) Forget the $600K, that is spent money
2) End of year 5 is January 1, year 6, so you are going to make 5 payments of $150K each for 5 years ( Years 6, 7, 8, 9, 10) ===> you need the Present Value of a 5 Year Annuity that pays $150K for 5 years at 7%. That gives you the Present Value of the contract at the end of year 5
3) start of Year 4, what is the Present Value at 7% for 2 years (Years 4 & 5) of that Future Value you need for the Annuity at the start of Year 6. That is the value to buy the contract