Question

​(Present value​) The state​ lottery's million-dollar payout provides for ​$1 ​million(s) to be paid over 24 years in 25 payments of $ 40 comma 000. The first $ 40 comma 000 payment is made​ immediately, and the 24 remaining $ 40 comma 000 payments occur at the end of each of the next 24 years. If 8 percent is the appropriate discount​ rate, what is the present value of this stream of cash​ flows? If 16 percent is the appropriate discount​ rate, what is the present value of the cash​ flows? a. If 8 percent is the appropriate discount​ rate, what is the present value of this stream of cash​ flows?

Answer 1

Present Value No Present Value $ 40,000 37,037 1.0000 40,000 0.8621 34,483 29,727 0.7432 0.6407 25,626 22,092 0.5523 Computation of Present value at 8% and 16% :- Payment Cash Year PVF @8% flows $ 40,000 1.0000 40,000 0.9259 40,000 0.8573 40,000 0.7938 40,000 0.7350 40,000 0.6806 40,000 0.6302 40,000 0.5835 40,000 0.5403 40,000 0.5002 40,000 0.4632 40,000 0.4289 40,000 0.3971 34,294 31,753 29,401 27,223 25,207 23,340 21,611 19,045 16,418 0.4761 0.4104 0.3538 0.3050 14,153 12,201 20,010 0.2630 10,518 0.2267 9,067 7,817 0.1954 0.1685 6,739 40,000 0.3677 0.1452 5,809 40,000 0.1252 5,008 0.3405 0.3152 0.1079 4,317 0.2919 3,722 40,000 40,000 40,000 40,000 40,000 0.2703 18,528 17,155 15,885 14,708 13,618 12,610 11,676 10,811 10,010 9,268 8,582 7,946 7,358 6,813 6,308 3,208 2,766 0.2502 0.2317 0.2145 2,384 40,000 0.0930 0.0802 0.0691 0.0596 0.0514 0.0443 0.0382 0.0329 0.0284 2,055 1,772 0.1987 1,528 40,000 40,000 40,000 40,000 0.1839 0.1703 0.1577 1,317 24 1,135 10,00,000 4,61,150 2,82,905 Present value of cashflows at 8% is $461,150/. Present value of cashflows at 16% is $282,905/.