Question

One of three alternatives must be selected for collecting excess storm water runoff in a municipality. The alternatives decrease discharge when storm water exceeds the capacity of the treatment plant and excess water is discharged untreated. The alternatives are a mix of store and process later and treatment capacity increase. Perform a benefit-cost analysis to identify the best economic option. Use an interest rate of 3.00%. The life of all alternatives is 60 years. Currently, the annual "cost" of the excess discharge based on environmental harm and penalties to the state is 390,000. The benefit stated for each is the percent reduction in excess discharge and hence annual cost.

Alternative	Investment/ Install Cost	Annual Operating Cost	Benefit Percent
1	2,200,000	100,000	52%
2	2,700,000	115,000	64%
3	4,300,000	130,000	84%

a. What is the annual worth or present worth benefit of alternative 2? Please state if AW or PW

b. What is the incremental B/C ratio of going from alternative 1 to 2?

c. What is the economic preferred alternative and the justification for it using the B/C method?

Answer 1

Solution

a) Alternative 2 has an investment cost of $270,000 and operating cost per year $105,000.
The benefit is 64% of the annual cost that is $390,000
390,000 * 0.64 = 249600

Total Cost = 105000 + ( 390000 * 0.36 ) = 245400

PW of benefits for 50 years with interest rate of 7%
=PV(7%,50,-249600)
= 3444666.275

PW of Cost
=PV(7%,50,245400)
= 3386703.14

NPW = ( PW of Cost + Investment Cost ) - PW of Benefits
NPW = -2642036.87

2) We will create a table forincremental analysis table

PW of the total cost
=PV(7%,50,-21800)
=300856.27

PW of total benefits
=PV(7%,50,-46800)
=645874.93

BC Ratio = Total Benefits / Total Cost

There is a positive incremental benefit because of higher efficiency
( 300856.27 + 645874.93 ) / 500000 = 1.89

BC ratio is positive and so alternative 2 is preferred over alternative 1.

3) We will create a table for values which include cost and benefits

BC Ratio = ( PW of Benefits ) / ( PW of Annual Cost + Investment Cost )

Alternative 3 should be selected considering that it has the highest BC ratio