Question

A​ state-sponsored Forest Management Bureau is evaluating alternative routes for a new road into a formerly inaccessible region. Three mutually exclusive plans for routing the road provide different​ benefits, as indicated in table below. The roads are assumed to have an economic life of 50 years, and MARR is 6​% per year. Which route should be selected according to the​ B-C ratio​ method? Assume that a roadway must be constructed.

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Route	Construction Costs		Annual Maintenance Cost		Annual Savings in Fire Damage		Annual Recreational Benefit		Annual Timber Access Benefit
A	​350000		4300		​11000		5500​		2500​
B	230000		3000		8000		6500		1400
C	180000		1600		5000		2500		500

Click the icon to view the interest and annuity table for discrete compounding when the MARR is 6​% per year.

Perform the incremental​ B-C Analysis.​ Fill-in the table below. ​(Round to four decimal​ places.)

Answer 1

B/C ratio = present value of benefits / present value of costs

The present value factor for 60 years and 6% rate with discrete compounding is 16.1614

Route A:

present value of benefits = (11000 + 5500 + 2500) * 16.1614 = 307,067

present value of costs = (4300 * 16.1614) + 350,000 = 419,494

B/C ratio = 307,067 / 419,494 = 0.7320

Route B:

present value of benefits = (8000 + 6500 + 1400) * 16.1614 = 256,966

present value of costs = (3000 * 16.1614) + 230,000 = 278,484

B/C ratio = 307,067 / 419,494 = 0.9227

Route C:

present value of benefits = (5000 + 2500 + 500) * 16.1614 = 129,291

present value of costs = (1600 * 16.1614) + 180,000 = 205,858

B/C ratio = 307,067 / 419,494 = 0.6281

The B/C ratio of all the routes is less than 1. This means that the present value of the benefits is less than the present value of costs. However, the road must be constructed. Hence, the route with the highest B/C ratio should be chosen.