Question

Congratulations! You have won a state lottery. The state lottery offers you the following (after-tax) payout options:

Option #1: \(12,000,000 after five years Option #2: \)2,150,000 per year for five years Option #3: $10,000,000 after three years

Assuming you can earn 6% on your funds, which option would you prefer?

Short answer

Option #2 would be preferable.

Step-by-step solution

Meaning of Lottery

A lottery could be a kind of gaming in which members buy numbered tickets. The numbers on tickets are picked, and those with particular numbers on their tickets win a prize.

Analyzing the various option

Option #1

$\begin{array}{rcl}Presentvalue& =& Amountrecceivableattheendof5thyear\times PVF@6\%,5year\\ & =& \$12,000,000\times 0.747\\ & =& \$8,964,000\end{array}$

Option #2

$\begin{array}{rcl}Presentvalue& =& Amountrecceivableattheendof1stto5thyear\times PVF@6\%,5year\\ & =& \$2,150,000\times 4.212\\ & =& \$9,055,800\end{array}$

Option #3

$\begin{array}{rcl}Presentvalue& =& Amountreceivableattheendof3rdyear\times PVF@6\%,3year\\ & =& \$10,000,000\times 0.840\\ & =& \$8,400,000\end{array}$

Option #2 depicts more present value as compared to the other option. So, option #2 will be preferable.