Question

3. An engineering company has presented three designs to improve traffic flow at a major intersection in a heavily traveled suburban area. The first alternative involves traffic signaling. The second alternative includes traffic signal improvement and intersection widening for exclusive left turns. The third alternative includes extensive reconstruction, including a grade separation structure. The construction costs, as well as annual maintenance and user costs are listed in the following table for each alternative. Determine which alternative is preferred based on the economic criteria if the analysis period is 20 years and the annual interest rate is 15 percent. Show that the result is the same using the present worth, equivalent annual cost, and the rate of return methods. Annual CapitalMaintenance Annual User Salvage Costs (S) | Costs Value(s), (5) 15,000 10,000 9,000 8,000 Alternative Costs (S) Present condition Traffic signals Intersection widening Grade separation 450,000 890,000 1,350,000 500,000 401,000 15,000 350,000 11,000 301,000

Answer 1

Present Worth Method:-

Traffic Signals: =-$4,50,000-$10,000(20 Years,15%) -$4,01,000(20 Years,15%)+$15,000

                                =-$4,50,000-$62593-$2509991+$917

                                =-$30,21,667

                             

Intersection Widening: =-$8,90,000-$9000(20 Years,15%) -$3,50,000(20 Years,15%)+$10,000

                                =-$8,90,000-$5,6334-$21,90,765+$$611

                                =-$31,36,488

Grade Seperation:

=-$13,50,000-$8000(20 Years,15%) -$3,01,000(20 Years,15%)

                                =-$13,50,000-$50,075-$1884058

                                =-$32,84,133

Equivalent annual cost method:

Traffic Signals:

Particulars	Years	20years	End of the 20th year
Capital cost	-45000
Annual maintenence		-10000
Annual user cost		-401000
Salvage value			15000
Total	-45000	-25,72,585	916

=-$26,16,669

Equivalent annual cost method:

Intersection widening

Particulars	Years	20years	End of the 20th year
Capital cost	-890000
Annual maintenence		-9000
Annual user cost		-350000
Salvage value			11000
Total	-890000	-2247099	672

=$31,36,427

Equivalent annual cost method:

Intersection widening

Particulars	Years	20years	End of the 20th year
Capital cost	-1350000
Annual maintenence		-8000
Annual user cost		-301000
Salvage value
Total	-1350000	-1934132

=$32,84,132

Rate of Return method:

Traffic Signals:

Particulars	Years	20years	End of the 20th year
Capital cost	-45000
Annual maintenence		-10000
Annual user cost		-401000
Salvage value			15000
Total	-45000	-25,72,585	916

=-$26,16,669

Rate of Return method::

Intersection widening

Particulars	Years	20years	End of the 20th year
Capital cost	-890000
Annual maintenence		-9000
Annual user cost		-350000
Salvage value			11000
Total	-890000	-2247099	672

=$31,36,427

Rate of Return method::

Intersection widening

Particulars	Years	20years	End of the 20th year
Capital cost	-1350000
Annual maintenence		-8000
Annual user cost		-301000
Salvage value
Total	-1350000	-1934132

=$32,84,132

Decision: as per the given information Traffic Signals is the best method to choose in that the least investment can be done