Question

Answer is in bold. Need to know how to work the problem. Thanks!

Problem 3 A city is evaluating a proposal to erect and operate a parking facility in its downtown area. Three designs on available sites have been identified. The costs and benefits are indicated below, where all dollars are in thousands. If the city's discount rate is 10 %, which design (if any) should be selected on the basis of a B/C analysis? Choose 1 Design 3 $200 Design 2 $180 Design 1 $240 Cost of site 1,400 20 700 2,200 Cost of building 360 310 410 Annual maintenance cost Ener 80 600 620 830 Annual fee collection 30 years 30 years 30 Service life years

Answer 1

B/C Ratio = PV of annual fee / (Cost of site + Cost of building + PV of annual maintenance cost)

Therefore,

B/C Ratio for Design 1 = [830 x P/A(10%, 30)] / [240 + 2,200 + 410 x P/A(10%, 30)]

= (830 x 9.4269) / [2,440 + (410 x 9.4269)]

= 7,824 / (2,440 + 3,865)

= 7,824 / 6,305

= 1.24

B/C Ratio for Design 2 = [600 x P/A(10%, 30)] / [180 + 700 + 360 x P/A(10%, 30)]

= (600 x 9.4269) / [880 + (360 x 9.4269)]

= 5,656 / (880 + 3,394)

= 5,656 / 4,274

= 1.32

B/C Ratio for Design 3 = [620 x P/A(10%, 30)] / [200 + 1,400 + 310 x P/A(10%, 30)]

= (620 x 9.4269) / [1,600 + (310 x 9.4269)]

= 5,845 / (1,600 + 2,922)

= 5,845 / 4,522

= 1.29

Since Design 2 has highest B/C Ratio, this is the best alternative.

NOTE: "Choose 1" is not the answer that's written - it means question is asking you to choose 1 option out of the given 3.