Question

1. Recently, a lucky person won the lottery. The lottery winnings were reported to be $85.5 million. In reality, the winner got a choice of $2.85 million per year for 30 years or $46 million today.

1. a) Explain briefly why winning $2.85 million per year for 30 years is not equivalent to winning $85.5 million. You may use simple calculations (with assumptions such as an interest rate of 3% p.a.) to explain your answer.

2. b) The evening news interviewed a group of people the day after the winner was announced. When asked, most of them responded that, if they were the lucky winner, they would take the $46 million up-front payment. Suppose you were that lucky winner, how would you decide between the annual installments or the up-front payment?

Answer 1

Ans a.
We need to find the PV of the Annuity of $2.85 Million
per year .
Formula for present value of an anuuity = PV= A [ {(1+k)n-1}/k(1+k)n]
PV = Present value of Annuity
A = periodical investment=$2.85 Million
K=interest rate=3% pa
N=periods=30 years
PV =2.85*[(1.03^30-1)/(3%*1.03^30)
PV =$55.86M
So PV of $2.85 per year annuity for 30 years @3% rate is	$55.86 Million.
So the PV of the annuity is not the same as $85 Million upfront payment.
Ans b.
As the PV of the $2.85 M annuity for 30 years is $55.86 Million, the
upfront payment of $46 Million as asked by respondents is lower
than that.
So it is advisable to get the Annuity than the upfront payment.