Problem $42$ Intro Facebook runs many data warehouses full of servers. Assume that each existing server is $3$ years old and was bought for $$1,400.$ It could be sold for $$560$ now or for $$280$ in $2$ years. The annual cost of running the server $($for electricity, cooling and repairs$)$ is $$280.$ A new server costs $$1,400$ today and could be sold for $$162\mathrm{.}5$ in $5$ years. The annual cost of running it is $$140.$ 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 $9\%.$ Your task is to find out if Facebook should replace each server now or in two years. Part $1$ What is the present value of all cash flows if a new server is bought once right now? Part $2$ 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? Part $3$ What is the present value of all cash flows for the next $2$ years if the old server is kept? Part $4$ 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?