The state lottery\'s million-dollar payout provides for $1.4 million to be paid
ID: 2810312 • Letter: T
Question
The state lottery's million-dollar payout provides for $1.4 million to be paid in 25 installments of $56 comma 000 per payment. The first $56 comma 000 payment is made immediately, and the 24 remaining $56 comma 000 payments occur at the end of each of the next 24 years. If 9 percent is the discount rate, what is the present value of this stream of cash flows? If 18 percent is the discount rate, what is the present value of the cash flows?
a. If 9 percent is the discount rate, the present value of the annuity due is $
nothing. (Round to the nearest cent.)
Explanation / Answer
Years Cash flow Discount factor @ 18% Present value 0 56000 1 56000 1 56000 0.847458 47457.63 2 56000 0.718184 40218.33 3 56000 0.608631 34083.33 4 56000 0.515789 28884.18 5 56000 0.437109 24478.12 6 56000 0.370432 20744.17 7 56000 0.313925 17579.8 8 56000 0.266038 14898.14 9 56000 0.225456 12625.54 10 56000 0.191064 10699.61 11 56000 0.161919 9067.466 12 56000 0.13722 7684.293 13 56000 0.116288 6512.113 14 56000 0.098549 5518.74 15 56000 0.083516 4676.898 16 56000 0.070776 3963.473 17 56000 0.05998 3358.875 18 56000 0.05083 2846.505 19 56000 0.043077 2412.292 20 56000 0.036506 2044.315 21 56000 0.030937 1732.471 22 56000 0.026218 1468.195 23 56000 0.022218 1244.233 24 56000 0.018829 1054.435 361253.14 If discount rate is 18%, present value of cash flows is $ 361253 If interest rate is 9%, present value of the cashflows Years Cash flow Discount factor @ 9% Present value 0 56000 1 56000 1 56000 0.917431 51376.15 2 56000 0.84168 47134.08 3 56000 0.772183 43242.27 4 56000 0.708425 39671.81 5 56000 0.649931 36396.16 6 56000 0.596267 33390.97 7 56000 0.547034 30633.92 8 56000 0.501866 28104.51 9 56000 0.460428 25783.96 10 56000 0.422411 23655.01 11 56000 0.387533 21701.84 12 56000 0.355535 19909.94 13 56000 0.326179 18266 14 56000 0.299246 16757.8 15 56000 0.274538 15374.13 16 56000 0.25187 14104.71 17 56000 0.231073 12940.1 18 56000 0.211994 11871.65 19 56000 0.19449 10891.42 20 56000 0.178431 9992.13 21 56000 0.163698 9167.092 22 56000 0.150182 8410.176 23 56000 0.137781 7715.758 24 56000 0.126405 7078.677 599570.26 If discount rate is 18%, present value of cash flows is $ 599570
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