Question

In: Finance

Jack and Diane are lottery winners. They hold the ticket to the Grand Prize in the...

Jack and Diane are lottery winners. They hold the ticket to the Grand Prize in the “Set for Life” Prize that makes 20 consecutive annual payments of $50,000 starting immediately. There is one hitch: the eleventh payment (to be received at the end of year 10) is not $50,000 but only $20,000 (that is, this payment is $30,000 LESS than the other 20). Which of the following comes closest to the present value of the prize if interest rates are 5%?

a.

$ 635,849

b.

$ 686,430

c.

$ 743,867

d.

$ 591,154

e.

$ 551,529

Solutions

Expert Solution

a.
$ 635,849
Statement showing Cash flows
Particulars Time PVF 5% Amount PV
Cash Inflows                                            -                      1.0000                 50,000.00              50,000.00
Cash Inflows                                        1.00                    0.9524                 50,000.00              47,619.05
Cash Inflows                                        2.00                    0.9070                 50,000.00              45,351.47
Cash Inflows                                        3.00                    0.8638                 50,000.00              43,191.88
Cash Inflows                                        4.00                    0.8227                 50,000.00              41,135.12
Cash Inflows                                        5.00                    0.7835                 50,000.00              39,176.31
Cash Inflows                                        6.00                    0.7462                 50,000.00              37,310.77
Cash Inflows                                        7.00                    0.7107                 50,000.00              35,534.07
Cash Inflows                                        8.00                    0.6768                 50,000.00              33,841.97
Cash Inflows                                        9.00                    0.6446                 50,000.00              32,230.45
Cash Inflows                                     10.00                    0.6139                 20,000.00              12,278.27
Cash Inflows                                     11.00                    0.5847                 50,000.00              29,233.96
Cash Inflows                                     12.00                    0.5568                 50,000.00              27,841.87
Cash Inflows                                     13.00                    0.5303                 50,000.00              26,516.07
Cash Inflows                                     14.00                    0.5051                 50,000.00              25,253.40
Cash Inflows                                     15.00                    0.4810                 50,000.00              24,050.85
Cash Inflows                                     16.00                    0.4581                 50,000.00              22,905.58
Cash Inflows                                     17.00                    0.4363                 50,000.00              21,814.83
Cash Inflows                                     18.00                    0.4155                 50,000.00              20,776.03
Cash Inflows                                     19.00                    0.3957                 50,000.00              19,786.70
Present value of prize            635,848.65

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