Your firm is considering developing an apartment complex. The firm owns land that could be used for the project; it was bought last year for $500,000. Real estate has gone up sharply in the last year: the land could be sold today for $625,000. Real estate values are expected to increase at 5 percent per year going forward from today. The permitting fees and sewage infrastructure development required for development cost $250,000 (the bill is due now and the project could not have proceeded without this work). This expense will be depreciated over the 30-year life of the project.

The apartment buildings will be four-plex townhouses (i.e. buildings that have four apartments each). Each apartment will rent for $1,000 per month. Initially, your firm will build 20 townhouses.

Each townhouse will cost $120,000 and will be depreciated straight-line to zero over the 30-year life of the project. In addition, the project will require a net working capital investment of $20,000 today—this amount will be recovered at the end of the project. At the end of the project, the townhouses will be completely trashed—the plan is to demolish them and sell the land. Demolition costs will be $150,000 before tax. Your variable cost is $1,250 per year per townhouse. Fixed costs are $130,000 per year. Your firm’s tax rate is 34% and the cost of capital is 10% .

Find the NPV

{Hint:   In year 30 the land will be unencumbered.

With increases of 5 percent per year, the land will be worth $2,701,213.98 After tax, our after-tax opportunity benefit is

$2,701,213.98 – (2,701,213.98 -500,000) ×.34 = $1,952,801.23.The demolition cost is$150,000×(1 –.34)}