Your dreams of becoming rich have just come true. You have won the State of Tranquility’s Lottery. The State offers you two payment plans for the $5,000,000 advertised jackpot.

Part A: Given the following cash inflow at the end of each year, what is the future value of this cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year?

Year 1 $15,000

Year 2 $20,000

Year 3 $30,000

Years 4 through 6 $0

Year 7 $150,000

Part B: County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for 25 years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume that it is an ordinary annuity and that the price is the same as present value.

Part C: A local government is about to run a lottery but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next 25 years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?

Part D: Your dreams of becoming rich have just come true. You have won the State of Tranquility’s Lottery. The State offers you two payment plans for the $5,000,000 advertised jackpot. You can take annual payments of $250,000 for the next 20 years or $2,867,480 today.

a. If your investment rate over the next 20 years is 8%, which payoff will you choose?

b. If your investment rate over the next 20 years is 5%, which payoff will you choose?

c. At what investment rate will the annuity stream of $250,000 be the same as the lump sum payment of $2,867,480?

 

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