Present Worth

In a present worth comparison of alternatives, the costs associated with each alternative investment are all converted to a present sum of money, and the least of these values represents the best alternative. Annual costs, future payments, and gradients must be brought to the present. Converting all cash flows to present worth is of-ten referred to as discounting.

EXAMPLE:

Two alternate plans are available for increasing the ca-pacity of existing water transmission lines between an un-limited source and a reservoir. The unlimited source is at a higher elevation than the reservoir. Plan A calls for the con-struction of a parallel pipeline and for flow by gravity. Plan B specifies construction of a booster pumping station. Esti-mated cost data for the two plans are as follows:

	Plan A	Plan B
	Pipeline	Pumping Station
Construction cost	$1,000,000	$200,000
Life	40 years	40 years (structure)
		20 years (equipment)
Cost of replacing
equipment at the
end of 20 yr	0	$75,000
Operating costs	$1000/yr	$50,000/yr

If money is worth 12 percent, which plan is more eco-nomical? (Assume annual compounding, zero salvage value, and all other costs equal for both plans.)

Present worth (Plan A) = P +A(P/A, 12%, 40)

=  $1,000,000 + $1000(8.24378)

=  $1,008,244

Present worth (Plan B) = P + A(P/A, 12%, 40)

+  F (P/F, 12%, 20)

= $200,000 + $50,000(8.24378)

+  $75,000(0.10367)

=  $619,964

Thus, plan B is the least-cost alternative.

A significant limitation of present worth analysis is that it cannot be used to compare alternatives with un-equal economic lives. That is, a ten-year plan and a twenty-year plan should not be compared by discounting their costs to a present worth. A better method of compar-ison is annual cost.