Question

A toll bridge across the Ohio River is being considered as a replacement for the current John F. Kennedy I-65 bridge linking Indiana to Kentucky at Louisville. Because this bridge, if approved, would become a part of the United States interstate highway system, benefit-cost analysis must be applied in the evaluation. Initial investment costs of the structure are estimated to be $18,000,000, and $475,000 per year in operating and maintenance costs are anticipated over its 30-year projected lifetime. In addition, the bridge must be completely resurfaced every fifth year at a cost of $1,500,000 per occurrence; in other words, consider the first resurfacing to occur at t=5, the second at t=10, and so forth, but with no resurfacing cost in year 30 (because the bridge will be replaced at that time). Revenues generated from the tolls are anticipated to be $3,500,000 in its first year of operation (i.e., at t=1), with a projected annual rate of increase of 2% per year due to an anticipated annual increase in traffic across the bridge. Assuming zero salvage value for the bridge at the end of 30 years and a MARR of 10% per year, what is the benefit-cost ratio of the project? Report your answer to the nearest hundredth (e.g., two decimal points).

Answer 1

i = 10%

Present value of geometric series = C *[(1+g)^n/(1+i)^n - 1]/(g-i)

Present value of toll charges = 3500000 * [(1+0.02)^30/(1+0.10)^30 - 1]/(0.02-0.10)

= 3500000 * [(1.02)^30/(1.10)^30 - 1]/(-0.08)

= 3500000 * 11.2024186

= 39208465.10

Present value of all cost = 18000000 + 475000*(P/A,10%,30) + 1500000*[(P/F,10%,5) + (P/F,10%,10) + (P/F,10%,15) + (P/F,10%,20) + (P/F,10%,25)]

= 18000000 + 475000*9.426914 + 1500000*[0.620921 + 0.385543 + 0.239392 + 0.148643 + 0.092295]

= 24707975.37

B/C ratio = 39208465.10 / 24707975.37 = 1.587 = 1.59 (two decimal places)