Question

1. Conduct a Benefits-Cost Analysis on the following Highway Project using:

Initial Costs of Tunnel. = $5,000,000
Annual costs for operating/maintenance = 150,000

Annual savings and benefits to travelers = 250,000

Residual value of benefits after horizon = 350,000

Useful life of investment = 30 years
Interest Rate = 6%

a. Find B-C Ratio of Annual Worth

b.Find B-C Ratio of Future Worth

c.Find B-C Ratio of Present Worth

Answer 1

ANSWER:

I = 6% AND N = 30

A) B/C RATIO OF ANNUAL WORTH:

Annual worth of benefits = Annual savings and benefits + Residual value(a/f,i,n) = 250,000 + 350,000(a/f,6%,30) = 250,000 + 350,000 * 0.0126 = 250,000 + 4,410 = 254,410

Annual worth of costs = Annual worth of initial cost(a/p,i,n) + Annual costs = 5,000,000(a/p,6%,30) + 150,000 = 5,000,000 * 0.0726 + 150,000 = 363,000 + 150,000 = 513,000

B/C ratio = aw of benefits / aw of costs = 254,410 / 513,000 = 0.4959

B) B/C RATIO OF FUTURE WORTH:

Future worth of benefits = Annual worth of benefits(f/a,i,n) = 254,410(f/a,6%,30) = 254,410 * 79.058 = 20,113,145.78

Future worth of costs = Annual worth of costs(f/a,i,n) = 513,000(f/a,6%,30) = 513,000 * 79.058 = 40,556,754

B/C ratio = fw of benefits / fw of costs = 20,113,145.78 / 40,556,754 = 0.4959

C) B/C RATIO OF PRESENT WORTH:

Present worth of benefits = Annual worth of benefits(f/a,i,n) = 254,410(p/a,6%,30) = 254,410 * 13.765 = 3,501,953.65

Present worth of costs = Annual worth of costs(f/a,i,n) = 513,000(p/a,6%,30) = 513,000 * 13.765 = 7,061,445

B/C ratio = fw of benefits / fw of costs = 3,501,953.65 / 7,061,445 = 0.4959