$4.$ Trips Logistics, a third$-$party logistics firm that provides warehousing and other logistics services, is facing a decision regarding the amount of space to rent for the upcoming three$-$year period. The general manager has forecast that Trips Logistics will need to handle a demand of $100,000$ units for each of the next three years. Historically, Trips Logistics has required $1,000$ sq$.$ ft$.$ of warehouse space for every $1,000$ units of demand. For the purposes of this discussion, the only cost Trips Logistics faces is the cost for the warehouse. Trips Logistics receives revenue of $$1\mathrm{.}22$ for each unit of demand. The general manager must decide whether to sign a three$-$year rent or obtain warehousing space on the spot market each year. The three$-$year rent will cost $$1$ per square foot per year, and the spot market rate is expected to be $$1\mathrm{.}20$ per square foot per year for each of the three years. The discount rate is $10\%$ per year.

a$)$ Determine the NPV of each alternative using Excel.

b$)$ Copy the Excel cells and embed it in this Word file.

c$)$ Which alternative is better?

d$)$ Given the uncertain nature of spot market rates in reality, create a graph comparing the two alternatives across various spot market rate scenarios? Copy the graph and embed it in this Word file.

e$)$ At what specific spot market rate value do the two alternatives converge, indicating a break$-$even point?