Question

The county fire department is considering two options (A and B) for upgrading its aging physical facility. Assume an interest rate of 6% per year and 50-year time period.

Option A: Involves remodeling the existing fire station by spending $2,252,000 now. In addition, the cost for personnel and equipment will be $126,000 per year.

Option B: Calls for buying 5 acres of land for building a new fire station. The cost of the land in that area is estimated to be $366,000 per acre. The size of the new fire station would be 9,000 square feet with a construction cost of $151.18 per square foot. Contractor fees are expected to be $421,500(Assume all of the costs for plan B occur at time 0). In addition, the sale of the old site is to anticipated to net a positive $500,000 five years in the future from today.

Q1: Determine the Present Worth of Plan A and Pan B.

Q2: Which plan is better on the basis of present worth analysis?

Answer 1

Here, we have

Rate of interest,i = 6% per year = 0.06

Time period,n = 50 years = 50

1. PRESENT WORTH

• OPTION A:

Cost of remodeling ,C= $2,252,000

Cost of personnel and equipment cost,E = $126,000 per year

Present worth ,PW​​​​​A= Cost of remodeling + Present value of personnel and equipment cost for the given time period,i.e. 50 years.

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• OPTION B

Cost of land = $366,000 × 5 = $1,830,000

Cost of construction = $151.18 × 9000 = 1,360,620

Total cost,C = $ 3,190,620

Amount incurred on selling the old site after five years,S = $500,000

Present worth,PW​​​​​B​​​ = Total cost of construction + Present value of amount incurred on selling of old site.

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1. Option A is better plan then that of option B because option A has less present worth then option B.