Wayne County will build an aqueduct to bring water in from the upper part of the state. It can be built at a reduced size now for $300 million and be enlarged in 25 years for an additional $350 million. An alternative is to construct the full-sized aqueduct now for $400 million.

Both alternatives would provide the needed capacity for the 50-year analysis period. Maintenance costs are small and may be ignored. At 6% interest, which alternative should be selected?

Question

Wayne County will build an aqueduct to bring water in from the upper part of the state. It can be built at a reduced size now for $300 million and be enlarged in 25 years for an additional $350 million. An alternative is to construct the full-sized aqueduct now for $400 million.

Both alternatives would provide the needed capacity for the 50-year analysis period. Maintenance costs are small and may be ignored. At 6% interest, which alternative should be selected?

Accepted Answer

TABLE SOLUTION

This problem illustrates staged construction. The aqueduct may be built in a single stage, or in a smaller first stage followed many years later by a second stage to provide the additional capacity when needed.

For the Two-Stage Construction

PW of cost=$300 million + 350 million (P/F,6%,25)

=$300 million + 81.6 million

=$381.6 million

For the Single-Stage Construction

PW of cost=$400 million

The two-stage construction has a smaller present worth of cost and is the preferred construction plan.

5-BUTTON SOLUTION

H	G	F	E	D	C	B	A
Answer	Solve for	FV	PV	PMT	n	i	Problem	1
$81.55	PV	-350		0	25	6%	Two-Stage	2
$300.00	year 0							3
$381.55	total							4

This is less than the $400M for the one-stage construction, so the two-stage is preferred.

Question 5.2: Wayne County will build an aqueduct to bring water in from t...

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