The town of Springfield, current population 2000, recently suffered a fire that destroyed its Civic
Center Building, a facility that provided all sorts of services to the community. The question is
whether, and on what terms, to rebuild it. The real interest rate is 3%, and it is known that the
average citizen derives benefits from the civic center that are worth $150 a year to each of them.
Architects have provided plans for two versions of a rebuilt Civic Center, each of which will yield
these same benefits over its lifespan, but with different lifespans and different costs, which are
shown in the table below:
Version A Version B
Time for construction 1 year 2 years
Cost of construction $4000 $8000
Cost of operation $1000/year $2000/year
Expected lifespan 12 years 18 years
As you can see, Version A is cheaper to build and to operate, but it falls apart 10 years after
construction is completed. Version B takes longer to build, costs more, and lasts more.
a. Write the formulas for, and then calculate, the present values of the benefits and operating costs for both versions.
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