Question

3. An engineer wants to run a sanitary sewer either through a deep cut or a lift station. The costs are estimated as follows. Which design should she select using least cost analysis? The interest rate is 7 % . ( 5 points ) Deep Cut Lift Station Cost of pipe $50,000 Cost of lift station $25,000 $500/year $2,000/year Annual 0&M Expected life 40 years 20 years

Answer 1

As per the information provided in the question the engineer want to make a choice between two alternatives as deep cut or lift station to run sanitary sewer

Deep Cut Alternative

Cost of pipe (I) = $50000

Annual Operation and maintenance cost (A) =$ 500 per year

Useful life (N) = 40 years

Interest rate (i) = 7%

Present worth (PW) of cost = 50000 + 500(P/A,7%,40) =50000 + 500(13.3317) = 50000 + 6665.85

Present worth (PW) of cost =$56665.85 (Lowest Cost)

Lift station Alternative

Cost of lift station (I) = $25000

Annual Operation and maintenance cost (A) =$ 2000 per year

Useful life (N) = 20 years

Interest rate (i) = 7%

Though the lifecycle of both the alternative (deep cut or lift station) are not equal, we need to use lowest common multiple (LCM) method of lifecycle of alternative, to convert the unequal lifecycle to equal lifecycle.   Accordingly to estimate the present worth (PW) of cost the effective Life cycle of Lift station Alternative has to repeat 2 times

Present worth (PW) of cost = 25000 + 25000(P/F,7%,20) + 2000(P/A,7%,40)

Present worth (PW) of cost = 25000 + 25000(0.2584) + 2000(13.3317)

Present worth (PW) of cost = 25000 + 6460 + 26663.4

Present worth (PW) of cost = $58123.4

Among two alternatives, the engineer should select Deep Cut Alternative to run sanitary sewer for its least cost or cost effectiveness.