Question

28. Recently, in an ad on television, the announcer declared that the Indiana State Lottery was currently worth $30,000,000. Starting one year from today, the lucky winner would receive $1,000,000 at the end of each of the next 30 years. At 6% interest rate and assuming there are no taxes on the winnings, what is the actual present value of this lottery for the winner? a. b. If gamblers bought a total of S30,000,000 in tickets and one person won, what is the present value of the state's profit after providing for payment to the winner? Suppose you win the lottery just described and you are given your choice of taking the annuity or getting one payment, today, of $15,000,000. Which choice has the highest present value if the interest rate is expected to remain at 600 for 30 years? c. d. What would you choose if you believed that the interest rate was going to fall to 5% one year from today and remain at 5% for the following 29 years? What is the present value of your choice in 15d? e.

Answer 1

28.

A.

Actual present value = 1000000*(1-1/1.06^30)/.06

Actual present value = $13764831

B.

Present value of the state's profit = 30000000 - 1000000*(1-1/1.06^30)/.06

Present value of the state's profit = $16235169

C.

Highest present value is of choice of $15000000. because it is higher than PV of the annuity that is $13764831.

D.

In the changed scenario,

PV of annuity = (1000000*(1-1/1.05^29)/.05)*(1/1.06) + 1000000/1.06

PV of annuity =$15227488

Now, I will choose this annuity payment when interest rate for the next 29 years is 5%.

E.

Present value of choice in 15d = (1000000*(1-1/1.05^29)/.05)*(1/1.06) + 1000000/1.06

Present value of choice in 15d =$15227488