Exercise $1(30$ points: $10$ points per question$)$

You are offered an investment with the following conditions:

$$ The cost of the investment is $1,000$ in the beginning $($year $0)$ and $300$ one year after $($end of the first year$).$

$$ The discount rate is $15\%.$

$$ The resale value of the investment is $200($after $5$ years$).$

$1.$ The investment pays out a sum Y at the end of the first year. This payout is constant during $5$ years. Calculate the smallest Y which would entice you to accept the investment.

$2.$ We suppose that Y$=200,$ compute the NPV and the IRR of the project. Should the project be accepted?

$3.$ We suppose that Y$=250$ and this payout grows at the rate of $20\%$ per year. Compute the NPV and the IRR of the project. Should the project be accepted?