Facebook runs many data warehouses full of servers. Assume that each existing server is $3$ years old and was bought for $$1,100.$ It could be sold for $$440$ now or for $$220$ in $2$ years. The annual cost of running the server $($for electricity, cooling and repairs$)$ is $$200.$

A new server costs $$1,000$ today and could be sold for $$125$ in $5$ years. The annual cost of running it is $$100.$

Both types of servers are usable for $5$ years and are linearly depreciated to zero over $5$ years.

Facebook's marginal tax rate is $34\%$ and the appropriate cost of capital for this project is $11\%.$

Your task is to find out if Facebook should replace each server now or in two years.

$1.)$ What is the present value of all cash flows if a new server is bought once right now?

$2.)$What is the present value of all cash flows if the old server is sold now, and the new server is bought now and then replaced every $5$ years at the same terms?

$3.)$What is the present value of all cash flows for the next $2$ years if the old server is kept?

$4.)$What is the present value of all cash flows if the server is first replaced in $2$ years, and then every $5$ years thereafter at the same terms?