Question

The gaming commission is introducing a new lottery game called Infinite Progresso. The winner of the Infinite Progresso jackpot will receive $900 at the end of January, $2,100 at the end of February, $3,300 at the end of March, and so on up to $14,100 at the end of December. At the beginning of the next year, the sequence repeats starting at $900 in January and ending at $14,100 in December. This annual sequence of payments repeats indefinitely. If the gaming commission expects to sell a minimum of 1,000,000 tickets, what is the minimum price they can charge for the tickets to break even, assuming the commission earns 3.00 %/year/month on its investments and there is exactly one winning ticket?

Please use Excel Functions to answer

Answer 1

First we will need to find the annual net value of the cashflows. The cashflows are shown below.

Since the yearly rate is 3%, it means monthly rate is .25%. Using the formula =NPV(rate,cashflow), we get that yearly value of the cashflow is 88132.83.

Now, since this will go on till infinity, that means the NPV of this is

=88132.83/.03

= 2937761

Lets say the price that they charge is x, then to break even, the price must be

1000000x=2937761

=2937761/1000000

=2.94 should be the minimum price to break even.