Question #$5$ and #$6$ are an application of the NPV to understand which lottery payout option is better.

You just won a lottery. There are two payout options for you:

Option $1$: a lump$-$sum payment of $$500,000$ today;

Option $2$: a payment of $$20,000$ per year for the next thirty years $($starting from next year until the end of the $30$th year$).$

If the required return is $5\%,$ then what$$s the NPV of choosing the first payout option for winning this lottery?

Hint: the value of the option$2$ is considered as the opportunity costs of choosing the first payout option.

$192,550\mathrm{.}98$

Flag question: Question $6$

Question $61$ pts

Assume the required return is still $5\%.$ How much should the annual payment be if the $2$nd option would break$-$even with the $1$st option?