Question

A toll bridge across the Mississippi River is being considered as a replacement for the current 1-40 bridge linking Tennessee to Arkansas. Because this bridge, if approved, will become a part of the U.S. Interstate Highway system, the B-C ratio method must be applied in the evaluation. Investment costs of the structure are estimated to be $17,300,000, and $310,000 per year in operating and maintenance costs are anticipated. In addition, the bridge must be resurfaced every sixth year of its 30-year projected life at a cost of $1,150,000 per occurrence (no resurfacing cost in year 30). Revenues generated from the toll are anticipated to be $2,000,000 in its first year of operation, with a projected annual rate of increase of 2.75% per year due to the anticipated annual increase in traffic across the bridge. Assuming zero market salvage value for the bridge at the end of 30 years and a MARR of 7% per year, should the toll bridge be constructed? Also, assume that the initial surfacing of the bridge is included in the initial investment costs of the structure Click the icon to view the interest and annuity table for discrete compounding when the MARR is 7% per year The benefit-cost ratio of the project with PW is 1.38 (Round to two decimal places.)

Answer 1

We have the following information

Cost
Initial Cost ($)	17,300,000
Annual Operating and Maintenance Cost ($)	310,000
Resurfacing Cost every 6th year	1,150,000

Revenue
Year 1	2,000,000
Year 2	2,055,000
Year 3	2,111,513
Year 4	2,169,579
Year 5	2,229,243
Year 6	2,290,547
Year 7	2,353,537
Year 8	2,418,259
Year 9	2,484,761
Year 10	2,553,092
Year 11	2,623,302
Year 12	2,695,443
Year 13	2,769,568
Year 14	2,845,731
Year 15	2,923,988
Year 16	3,004,398
Year 17	3,087,019
Year 18	3,171,912
Year 19	3,259,139
Year 20	3,348,766
Year 21	3,440,857
Year 22	3,535,480
Year 23	3,632,706
Year 24	3,732,606
Year 25	3,835,252
Year 26	3,940,722
Year 27	4,049,091
Year 28	4,160,442
Year 29	4,274,854
Year 30	4,392,412

Life = 30 years

Minimum Acceptable Rate of Return (MARR) = 7% per year

Present Worth (PW) of Cost = PW(C)

PW(C) = 17,300,000 + 310,000(P/A, 7%, 30) + 1,150,000(P/F, 7%, 6) + 1,150,000(P/F, 7%, 12) + 1,150,000(P/F, 7%, 18) + 1,150,000(P/F, 7%, 24)

PW(C) = 17,300,000 + 310,000[((1 + 0.07)³⁰ – 1)/0.07(1 + 0.07)³⁰] + 1,150,000/(1 + 0.07)⁶ + 1,150,000/(1 + 0.07)¹² + 1,150,000/(1 + 0.07)¹⁸ + 1,150,000/(1 + 0.07)²⁴

PW(C) = 17,300,000 + (310,000 × 12.409) + (1,150,000 × 0.6663) + (1,150,000 × 0.444) + (1,150,000 × 0.2959) + (1,150,000 × 0.1971)

PW(C) = 22,990,585

Present Worth (PW) of Benefit = PW(B)

PW(B) = [Annual Benefit × (P/F, 7%, n)]

(P/F, i, n) = Single payment present worth factor

Where n is the year 1 to 30

The objective is to find the present worth amount (P) of a single future sum (F) which will be received after n periods at an interest rate of i compounded at the end of every interest period.

Year	Revenue	P/F Factor	Present Worth
Year 1	2,000,000	0.9346	1,869,200.00
Year 2	2,055,000	0.8734	1,794,837.00
Year 3	2,111,513	0.8163	1,723,627.65
Year 4	2,169,579	0.7629	1,655,171.89
Year 5	2,229,243	0.713	1,589,449.92
Year 6	2,290,547	0.6663	1,526,191.26
Year 7	2,353,537	0.6227	1,465,547.32
Year 8	2,418,259	0.582	1,407,426.73
Year 9	2,484,761	0.5439	1,351,461.56
Year 10	2,553,092	0.5083	1,297,736.68
Year 11	2,623,302	0.4751	1,246,330.81
Year 12	2,695,443	0.444	1,196,776.64
Year 13	2,769,568	0.415	1,149,370.53
Year 14	2,845,731	0.3878	1,103,574.35
Year 15	2,923,988	0.3624	1,059,653.34
Year 16	3,004,398	0.3387	1,017,589.58
Year 17	3,087,019	0.3166	977,350.17
Year 18	3,171,912	0.2959	938,568.73
Year 19	3,259,139	0.2765	901,152.06
Year 20	3,348,766	0.2584	865,321.08
Year 21	3,440,857	0.2415	830,966.93
Year 22	3,535,480	0.2257	797,957.93
Year 23	3,632,706	0.2109	766,137.72
Year 24	3,732,606	0.1971	735,696.56
Year 25	3,835,252	0.1842	706,453.46
Year 26	3,940,722	0.1722	678,592.27
Year 27	4,049,091	0.1609	651,498.82
Year 28	4,160,442	0.1504	625,730.40
Year 29	4,274,854	0.1406	601,044.42
Year 30	4,392,412	0.1314	577,162.95
Total Present Worth			33,107,578.78

PW(B) = 33,107,578.78

The Benefit-Cost (B/C) ratio = 33,107,578.78/22,990,585

The Benefit-Cost (B/C) ratio = 1.4