Question

The state​ lottery's million-dollar payout provides for ​$33 ​million(s) to be paid over 1919 years in 2020 payments of $ 150 comma 000$150,000. The first $ 150 comma 000$150,000 payment is made​ immediately, and the 1919 remaining $ 150 comma 000$150,000 payments occur at the end of each of the next 1919 years. If 1212 percent is the appropriate discount​ rate, what is the present value of this stream of cash​ flows? If 2424 percent is the appropriate discount​ rate, what is the present value of the cash​ flows?

Answer 1

(1)-The present value of this stream of cash flows if the discount rate is 12%

Year	Annual cash flow ($)	Present Value factor at 12.00%	Present Value of annual cash flow ($)
0	1,50,000	1.0000000	1,50,000.00
1	1,50,000	0.8928571	1,33,928.57
2	1,50,000	0.7971939	1,19,579.08
3	1,50,000	0.7117802	1,06,767.04
4	1,50,000	0.6355181	95,327.71
5	1,50,000	0.5674269	85,114.03
6	1,50,000	0.5066311	75,994.67
7	1,50,000	0.4523492	67,852.38
8	1,50,000	0.4038832	60,582.48
9	1,50,000	0.3606100	54,091.50
10	1,50,000	0.3219732	48,295.99
11	1,50,000	0.2874761	43,121.42
12	1,50,000	0.2566751	38,501.26
13	1,50,000	0.2291742	34,376.13
14	1,50,000	0.2046198	30,692.97
15	1,50,000	0.1826963	27,404.44
16	1,50,000	0.1631217	24,468.25
17	1,50,000	0.1456443	21,846.65
18	1,50,000	0.1300396	19,505.94
19	1,50,000	0.1161068	17,416.02
TOTAL			1,254,866.53

“The Present Value of the cash flows will be $1,254,866.53”

(2)-The present value of this stream of cash flows if the discount rate is 24%

Year	Annual cash flow ($)	Present Value factor at 24.00%	Present Value of annual cash flow ($)
0	1,50,000	1.0000000	1,50,000.00
1	1,50,000	0.8064516	1,20,967.74
2	1,50,000	0.6503642	97,554.63
3	1,50,000	0.5244873	78,673.09
4	1,50,000	0.4229736	63,446.04
5	1,50,000	0.3411077	51,166.16
6	1,50,000	0.2750869	41,263.03
7	1,50,000	0.2218443	33,276.64
8	1,50,000	0.1789067	26,836.00
9	1,50,000	0.1442796	21,641.94
10	1,50,000	0.1163545	17,453.17
11	1,50,000	0.0938343	14,075.14
12	1,50,000	0.0756728	11,350.92
13	1,50,000	0.0610264	9,153.97
14	1,50,000	0.0492149	7,382.23
15	1,50,000	0.0396894	5,953.41
16	1,50,000	0.0320076	4,801.14
17	1,50,000	0.0258126	3,871.89
18	1,50,000	0.0208166	3,122.49
19	1,50,000	0.0167876	2,518.14
TOTAL			764,507.77

“The Present Value of the cash flows will be $764,507.77”

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.