$($Please Show Step by Step Calculations$)$ You own a cab company and are evaluating two options to replace your fleet. Either you can take out a five$-$year lease on the replacement cabs for $$461$ per month per cab, or you can purchase the cabs outright for $$31,000,$ in which case the cabs will last eight years. You must return the cabs to the leasing company at the end of the lease. The leasing company is responsible for all maintenance costs, but if you purchase the cabs, you will buy a maintenance contract that will cost $$107$ per month for the life of each cab. Each cab will generate revenues of $$1,093$ per month. Assume the cost of capital is fixed at $12\mathrm{.}9\%.($Hint: Make sure to round all intermediate calculations to at least four decimal places.$)$

A$.$ Calculate the NPV per cab of both possibilities: purchasing the cabs or leasing them.

B$.$ Calculate the equivalent monthly benefit of both opportunities.

C$.$ If you are leasing a cab, you have the opportunity to buy the used cab after five years. Assume that in five years a five$-$year$-$old cab will cost either $$10,400$ or $$15,700,$ with equal likelihood; will have maintenance costs of $$500$ per month; and will last three more years. Which option should you take?