Stephanie and Greg were the first and second place winners in a recent contest s

Question

Stephanie and Greg were the first and second place winners in a recent contest sponsored by A Lucky Duck. The first place winner is required to represent the company at numerous events for one year in exchange for receiving a prize of $1,000 a year forever. The second place winner is awarded a prize of $1,000 a year for 100 years and has no commitments or future obligations to the firm. The applicable interest rate is 8 percent. Assuming these two individuals have perpetual lives, which person is really the top winner in this contest and why?

Explanation / Answer

The present value of a perpetuity is the coupon/discount rate. The discount rate here is the interest rate= 8%. So, the first place winner gets 1000/.08= $12,500 in value, less the obligations. The present value of an annuity is the coupon*((1-(1+i)^-n)/i). The second place winner gets 1000*((1-(1.08)^-100)/.08)= $12,494.32, technically.
However, 1-(1.08^-100)~1 (if you round here), in which case the second place winner gets $12,500.
Since the second place winner has no commitments and the present value of this person's prize is the same as the first place winner's but does not have the first year commitment, the second place winner comes out on top.

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