Q1: Assume that you just won the state lottery. Your prize can be taken either
in the form of $40,000 at the end of each of the next 25 years (i.e., $1,000,000
over 25 years) or as a single amount of $500,000 paid immediately.
a. If you expect to be able to earn 5% annually on your investments over the
next 25 years, ignoring taxes and other considerations, which alternative
should you take? Why?
b. Would your decision in part a change if you could earn 7% rather than 5%
on your investments over the next 25 years? Why?
c. On a strictly economic basis, at approximately what earnings rate would you
be indifferent between the two plans?
Answers
Answer:
Solution: (a) Stream 1: Annual Prize Money = $40000 Period = 2 Years = 25 months Interest Rate = 5% (Annual) Present Value of Annuity = $40000*[1-1/(1+5%)^25]/5% = $563757.78 Stream 2: Single amount of $500,000 paid immediately. Stream 1 amount is more than the stream 2 amount . Therefore, $40000 annually prize money for 25 years option is better than the single amount paid option .
(b) Now Interest Rate = 7% Stream 1: Annual Prize Money = $40000 Period = 2 Years = 25 months Present Value of Annuity = $40000*[1-1/(1+7%)^25]/7% = $466143.33 Stream 2: Single amount of $500,000 paid immediately. Stream 2 amount is more than the stream 1 amount. So, it is viable to take single amount in this case. Therefore, single amount paid option is better than the...