"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 four$-$year period. The general manager has forecast that Trips Logistics will need to handle a demand of $300,000$ units for each of the next five years. Historically, Trips Logistics has required $2,000$ 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. The general manager must decide whether to sign a four$-$year rent or obtain warehousing space on the spot market each year. The four$-$year rent will cost $$1$ per square foot per year, and the spot market rate is expected to be $$1\mathrm{.}30$ per square foot per year for each of the four years. While the whole cost of four$-$year rental option must be paid currently, the cost of spot market option would need to be paid annually at the beginning of each year. The discount rate is $10\%$ per year.

a$.$ Create the cash flow for each alternative.

b$.$ Determine the NPV of each alternative.

c$.$ Which alternative is better?

d$.$ Given the uncertain nature of demand, create a graph comparing the two alternatives across demand scenarios from $50,000$ to $400,000$ units per year?

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