Question

(Present value) The state lottery's million-dollar payout provides for $2 million(s) to be paid over 24 years in 25 payments of $80,000. The first $80,000 payment is made immediately, and the 24 remaining $80,000 payments occur at the end of each of the next 24 years. If 11 percent is the appropriate discount rate, what is the present value of this stream of cash flows? If 22 percent is the appropriate discount rate, what is the present value of the cash flows? a. If 11 percent is the appropriate discount rate, what is the present value of this stream of cash flows? $ (Round to the nearest cent.)

Answer 1

The present value of the stream of cash flows at an 11 percent discount rate is approximately $919,076.52. To calculate the present value of the stream of cash flows, we need to discount each payment back to its present value using the appropriate discount rate. In this case, we have 25 payments of $80,000.

To find the present value at an 11 percent discount rate, we can use the formula for the present value of an annuity: PV = PMT * (1 - (1 + r)^-n) / r. Where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods. Using this formula, we can substitute the given values into the equation: PV = $80,000 * (1 - (1 + 0.11)^-25) / 0.11.

Simplifying the equation, we find that the present value at an 11 percent discount rate is approximately $919,076.52. If the appropriate discount rate is 22 percent, we can follow the same steps to find the present value at this rate: PV = $80,000 * (1 - (1 + 0.22)^-25) / 0.22. Calculating this equation, we find that the present value at a 22 percent discount rate is approximately $489,545.60.

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