Assume that you just won the state lottery. Your prize can be taken either in th
ID: 2744471 • Letter: A
Question
Assume that you just won the state lottery. Your prize can be taken either in the form of $20,000 at the end of each year over the next 25 years or as a lump sum of $250,000 paid immediately. (A) If you expect to be able to earn 9% annually on your investments over the next 25 years, which alternative should you take? Why? (B) Would your decision in part (A) be altered if you could earn 7% rather than 9% on your investment? Why? (C) At approximately what interest rate would you be indifferent between the two plans? Show relevant computations leading to all your answers.
Explanation / Answer
Answer A.
Present Value Option 1 = 20,000*(1-(1/1.09)^25)/0.09
Present Value Option 1 = $196,451.59
Present Value Option 2 = $250,000
Since, present value of option 2 is more than option 1. We will select option 2.
Answer B.
Present Value Option 1 = 20,000*(1-(1/1.07)^25)/0.07
Present Value Option 1 = $233,071.66
Present Value Option 2 = $250,000
Since, present value of option 2 is more than option 1. We will select option 2.
Answer C.
Let i% be the interest rate at which both option will be indifferent.
250,000 = 20,000*(1-(1/(1+i))^25)/ i
i = 6.24%