Stephanie and Greg were the first and second place winners in arecent contest sp

Question

Stephanie and Greg were the first and second place winners in arecent contest sponsored by A Lucky Duck. The first place winner isrequired to represent the company at numerous events for one yearin exchange for receiving a prize of $1,000 a year forever. Thesecond place winner is awarded a prize of $1,000 a year for 100years and has no commitments or future obligations to the firm. Theapplicable interestrate is 8 percent. Assuming these two individuals haveperpetual lives, which person is really the top winner in thiscontest and why?

Explanation / Answer

First prizewinner: He will get $ 1000 a year foreever Interest rate = 8% Present value of perpetuity = Cashflows/ Rate                                       = $1000/0.08                                       = $12500 Second prizewinner: He will get $ 1000 a year for 100years Present value = Cashflow * PVCAF 100years 8%                    = $1000 * [1-(1/ (1+r) n)] / r                    = $1000 * [1-(1/ (1+0.08) 100)] / 0.08                    = $1000*12.49432                    = $12494.32 The first prize winner will get $ 12500for the perpetuity period and he is required torepresent the conpany at numerous events for one year inexchange The secon prize winner will get the $12494.32 with in 100 year and he have no obligation The firset prize winner will have towait for evere for $ 12500 but the second prize winner will get $ 12494.32 with in 100years witch almost equal to first prize and he has noobligation Second prize winner is really the topwinner in this contest according to above calculation

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