Suppose you are a consultant for a firm like Yoo, a company building apartments and condominiums worldwide. You are charged with determining how many floors to build a proposed structure in Quito, Ecuador. Each floor will have 15 separate living spaces. They will be rented as apartments for the first 12 years, after which they will be sold as condominiums so that the firm loses ownership of them. Higher floors are more expensive to build but also bring higher rents and higher prices when sold. Each floor costs 12.5 percent more to build than the floor beneath it and each floor adds 4 percent to the rent and price of the living space directly beneath it.
The ground floor costs $1,250,000 to construct. A living space on the ground floor will yield $1250 per month in rent with operating costs and taxes costing $250 per month each month it is rented. Assume a housing shortage in Quito will ensure these living spaces remain full with a waitlist.
Suppose the firm rents the spaces for 12 years, with the profit being received at the end of each year. After the 12 years, the firm can sell each living space on the ground floor for $150,000.
The discount rate is 10 percent.
a) Find the NPV of the first floor.
b) What is the NPV of floors 2-8?
c) How many floors should the firm build? Why?
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