The state lottery\'s million dollar payout provides for $1 million to be paid in

Question

The state lottery's million dollar payout provides for $1 million to be paid in 20 installments of $50,000 per payment. The first $50,000 payment is made immediately and the 19 remaining $50,000 payments occur at the end of each of the next 19 years. If 12 percent is the discount rate, what is the present value of this stream of cash flows? If 24 percent is the discount rate, what is the present value of the cash flows? If 12 percent is the discount rate, the present value of the annuity due is $.

Explanation / Answer

If Discount Rate is 12% :

Present Value = 50,000 + 50,000/1.12 + 50,000/1.12^2 + 50,000/1.12^3 + ... + 50,000/1.12^19

Present Value = 50,000*(1-(1/1.12)^20)/(1-1/1.12)

Present value = $418,288.84

If Discount Rate is 24% :

Present Value = 50,000 + 50,000/1.24 + 50,000/1.24^2 + 50,000/1.24^3 + ... + 50,000/1.24^19

Present Value = 50,000*(1-(1/1.24)^20)/(1-1/1.24)

Present value = $254,835.92

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