Required information In order to provide drinking water as p

Required information In order to provide drinking water as part of its 50- year plan, a west coast city is considering constructing a pipeline for importing water from a nearby community that has a plentiful supply of brackish ground water. A full-sized pipeline can be constructed at a cost of $125 million now Alternatively, a smaller pipeline can be constructed now for $65 million and enlarged 16 years from now for another $115 million. The pumping cost will be $25,000 per year higher for the smaller pipeline during the first 16 years, but it will be approximately the same thereafter. Both pipelines are expected to have the same useful life with no salvage value At an interest rate of 6% per year, which alternative is more economical? The present worth of the full-sized pipeline is determined to be $ The sma and that of the small-sized pipeline is $ 7 pipeline is the most economical pipeline.

Solution

Full Size

Small size

Investment (Cost in $)

125Mil

65 Mil

Annual Expenditure ($ per year)

$c

$(c+25000) for first 16 years and $c thereafter

Enlargement Cost

-

$115 Mil in year 16

Salvage Value ($)

-

-

Useful life (years)

50

50

Let the pumping cost of water per year be $c for both the pipelines from years 1 to 50 and small sized pipeline has $25000 extra per year for pumping for the first 16 years.

PW of cost of full size = 125,000,000 + c(P/A, 6%,50)

PW of small size = 65,000,000 + 115,000,000(P/F, 6%, 16) + 25000 (P/A, 6%, 16) + c(P/A,6%.50)

The P/A factor is a uniform series present worth factor which is used to calculate the present value of annual costs, incurred every year. E.g., for both the pipelines, the annual cost of pumping is c per year, for 50 years. Alternatively for the small pipeline, there is an extra cost of $25000 per year for 16 years at 6%.

The P/F factor is the present to future worth factor when other charges which do not occur annually, are calculated for their present value. E.g., For small sized pipeline, the pipe is enlarged in year 16 for $115,000,000 at 6%. This expense occurs only once.

The formulae for P/A and P/F are:

Therefore, PW of full size = 125,000,000 + c[{((1+0.06)^50)- 1}/ 0.06* (1+0.06)^50

= $125,000,000+ 15.8c

Similarly PW of small pipeline = 65000000+ 115,000,000*(1/(1+0.06)^16) + 25000*(1/(1+0.06)^16) + c[{((1+0.06)^50)- 1}/ 0.06* (1+0.06)^50

9841.157+45269322.63+15.8c+65000000

= $110,279,163.8 + 15.8c

Since 15.8c is common to both , the present worth of cost for smaller pipeline is less than that of the bigger pipeline. This is the cost that is being compared, so the smaller present worth of cost is better as an investment.

The present worth of the full sized pipeline is $125,000,000+ 15.8c and that of the small sized pipeline is $110,279,163.8 + 15.8c.

The small pipeline is the most economical pipeline.

	Full Size	Small size
Investment (Cost in $)	125Mil	65 Mil
Annual Expenditure ($ per year)	$c	$(c+25000) for first 16 years and $c thereafter
Enlargement Cost	-	$115 Mil in year 16
Salvage Value ($)	-	-
Useful life (years)	50	50