Question

[Parker County Community College (PCCC) is trying to determine whether to use no insulation or to use insulation that is either 1 inch thick or 2 inches thick on its steam pipes. The heat loss from the pipes without insulation is expected to cost $1.50 per year per foot of pipe. A 1-inch thick insulated covering will eliminate 89 percent of the loss and will cost $0.40 per foot.A 2-inch thick insulated covering will eliminate 92 percent of the loss and will cost $0.85 per foot. PCCC Physical Plant Services estimates that there are 250,000 feet of steam pipe on campus. The PCCC Accounting Office requires a 10 percent/year return to justify capital expenditures. The insulation has a life expectancy of 10 years.

Determine which insulation (if any) should be purchased based on an incremental present worth analysis.

Answer 1

Answer:
Considering capital cost:
A1 Capital cost = Per foot cost × given Pipe feet
= $0.40 × 250,000
= $100,000

A2 Capital cost= Per foot cost × given Pipe feet
= $0.85 × 250000
= $212500

Considering Benefits:
A1 Benefit = (Percentage of loss elimination × Heat loss) × given Pipe feet
= (89% × $1.50) × 250000
= $333750

A2 Benefit = (Percentage of loss elimination × Heat loss) × gven Pipe feet
= (92% × $1.50) × 250000
= $345000

Given,
Interest rate (i) = 10% = 0.10
The number of years (n) = 10
Annual benefit (A) = $333750 for A1, and $345000 for A2.

Now considering future worth of A1 and A2, we have
Future worth of A1 is given by

=> A1 = 333750(1+0.10^10 -1) / 0.10
          = 5318973.7

Future worth of A2 is given by

=> A2 = 345000((1+0.10)^10 -1)/0.10
           = 5498265

From above its clear that based on future worth A2 would be purchased over A1 based on higher future worth.

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