Question

Reconsider Problem 30. [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.

What is the present worth of each increment?

Increment 1 = $_______? (answer unknown, -353463 is incorrect)
Increment 2 = $_______? (answer -43374)

Answer 1

Annual cost of heat loss without insulation = 1.5 * 250000 = 375000

For 1 inch insulation

First cost = 0.4 * 250000 = 100000

Annual cost = 0.11*375000 = 41250

For 2 inch insulation

First cost = 0.85 * 250000 = 212500

Annual cost = 0.08*375000 = 30000

For PW analysis First increment

Incremental first cost = 100000 - 0 = 100000

Incremental annual cost = 41250 - 375000 = -333750 (Annual savings in cost)

NPW of first increment = -100000 + 333750*(P/A,10%,10)

= -100000 + 333750*6.144567

= 1950749.24 ~ 1950749

For PW analysis second increment

Incremental first cost = 212500 - 100000 = 112500

Incremental annual cost = 30000 - 41250 = -11250 (Annual savings in cost)

NPW of first increment = -112500 + 11250*(P/A,10%,10)

= -112500 + 11250*6.144567

= -43373.62 ~ -43374

Based on incremental PW analysis, 1 inch insulation should be selected