Question 10.2: Equivalence of the B−C Ratio Formulations The city of Columb...
Equivalence of the B−C Ratio Formulations
The city of Columbia is considering extending the runways of its municipal airport so that commercial jets can use the facility. The land necessary for the runway extension is currently a farmland that can be purchased for $350,000. Construction costs for the runway extension are projected to be $600,000, and the additional annual maintenance costs for the extension are estimated to be $22,500. If the runways are extended, a small terminal will be constructed at a cost of $250,000. The annual operating and maintenance costs for the terminal are estimated at $75,000 . Finally, the projected increase in flights will require the addition of two air traffic controllers at an annual cost of $100,000. Annual benefits of the runway extension have been estimated as follows:
| $325,000 Rental receipts from airlines leasing space at the facility | |||
| $65,000 Airport tax charged to passengers | |||
| $50,000 Convenience benefit for residents of Columbia | |||
| $50,000 Additional tourism dollars for Columbia |
Apply the B–C ratio method with a study period of 20 years and a MARR of 10% per year to determine whether the runways at Columbia Municipal Airport should be extended.
| Conventional B–C: B–C = PW(B)/[I − PW(MV) + PW(O&M)]
Equation (10-1) B–C = $490,000 (P/A, 10%, 20)/[$1,200,000 + $197,500 (P/A, 10%, 20)] B–C = 1.448 > 1; extend runways. |
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| Modified B–C: B–C = [PW(B) − PW(O&M)]/[I − PW(MV)]
Equation (10-2) B–C = [$490,000 (P/A, 10%, 20) − $197,500 (P/A, 10%, 20)]/$1,200,000 B–C = 2.075 > 1; extend runways. |
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| Conventional B–C: B–C = AW(B)/[CR + AW(O&M)]
Equation (10-3) B–C = $490,000/[$1,200,000 (A/P, 10%, 20) + $197,500] B–C = 1.448 > 1; extend runways. |
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| Modified B–C: B–C = [AW(B) − AW(O&M)]/CR
Equation (10-4) B–C = [$490,000 − $197,500]/[$1,200,000 (A/P, 10%, 20)] B–C = 2.075 > 1; extend runways |