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Problem #1

The document presents 5 problems involving calculating benefit-cost ratios for infrastructure projects. Problem 1 involves a proposed $2 million bridge that would last 20 years with annual maintenance costs of $180,000 and public benefits of $900,000 but costs of $250,000 to the public. Problem 2 involves a proposed parking lot costing $175,000 to build with annual costs of $17,500 and increasing annual benefits from $18,000 to $21,500 over 12 years. Problem 3 involves tire balancing equipment costing $12,699 with annual savings of $1,500 and salvage value of $250 over 12 years. Problem 4 involves a $14 million bypass road with annual resurfacing costs of $

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1K views3 pages

Problem #1

The document presents 5 problems involving calculating benefit-cost ratios for infrastructure projects. Problem 1 involves a proposed $2 million bridge that would last 20 years with annual maintenance costs of $180,000 and public benefits of $900,000 but costs of $250,000 to the public. Problem 2 involves a proposed parking lot costing $175,000 to build with annual costs of $17,500 and increasing annual benefits from $18,000 to $21,500 over 12 years. Problem 3 involves tire balancing equipment costing $12,699 with annual savings of $1,500 and salvage value of $250 over 12 years. Problem 4 involves a $14 million bypass road with annual resurfacing costs of $

Uploaded by

Dianne Villanueva
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Problem #1

A proposed bridge on the interstate highway system is being considered at the cost of
$2 million. It is expected that the bridge will last 20 years. The federal and state
governments will pay these construction costs. Operation and maintenance costs are
estimated to be $180,000 per year. Benefits to the public are estimated to be $900,000
per year. The building of the bridge will result in an estimated cost of $250,000 per year
to the general public. The project requires a 10% return. Determine the B/C ratio for the
project. State any assumption made about benefits or costs.
Solution:
• $250,000 cost to general public is disbenefit
AWBENEFITS = 900,000 - 250,000 = $650,000
AWCOSTS = 2,000,000(A/P, 10%, 20) + 180,000 = $415,000
B/C = $650,000/$415,000
B/C= 1.57

Problem #2
The town of Podunk is considering building a new downtown parking lot. The land will
cost $25,000 and the construction cost of the lot is estimated to be $150,000. Each year
costs associated with the lot are estimated to be $17,500. The income from the lot is
estimated to be $18,000 the first year and increase by $3,500 each year for the twelve
year expected life of the lot. Determine the B/C ratio if Podunk uses a cost of money of
4%.
Solution:
PWBENEFITS = 18,000(P/A, 4%, 12) + 3,500(P/G, 4%, 12) = $334,298
PWCOSTS = 175,000 + 17,500(P/A, 4%, 12) = $339,238
B/C = $334,298 / $339,238
B/C= 0.99

Problem #3
Tires-R-Us is considering the purchase of new tire balancing equipment. The machine
will cost $12,699 and have an annual savings of $1,500 with a salvage value at the end
of 12 years of $250. If the MARR is 6%, use B/C analysis to determine whether or not the
equipment should be purchased.
Solution:
PWBENEFITS = $1,500(P/A, 6%, 12) + $250(P/F, 6%, 12) = $12,700.25
PWCOSTS = $12,699
B/C = 12,700/12,699
B/C = 1.00
Conclusion: Yes, the machine should be purchased
Problem #4
Dunkin City wants to build a new bypass between two major roads that will cut travel time
for commuters. The road will cost $14,000,000 and save 17,500 people $100/yr in gas.
The road will need to be resurfaced every year at a cost of $7,500. The road is expected
to be used for 20 years. Determine if Dunkin City should build the road using B/C analysis.
The cost of money is 8%.
Solution:
PW of Costs = 14,000,000 + 250,000(P/A, 8%, 20) = $16,454,500
PW of Benefits = (17,500)(100)(P/A, 8%, 20) = $17,181,500
B/C = 17,181,500/16,454,500
B/C = 1.04
Conclusion: Yes, Dunkin City should build the bypass.

Problem #5
Rash, Riley, Reed, and Rogers Consulting has a contract to design a major highway
project that will provide service from Memphis to Tunica, Mississippi. R4 has been
requested to provide an estimated B/C ratio for the project.
Relevant data are:
Initial cost $20,750,000
Right of way maintenance 550,000
Resurfacing (every 8 years) 10% of first cost
Shoulder grading and re-work (every 6 years) 750,000
Average number of road users per year 2,950,000
Average time savings value per road user $2

Determine the B/C ratio if i = 8%.

Solution:
AWBENEFITS = 2,950,000 × $2 = $5,840,000
AWCOSTS = 20,750,000(A/P, 8%, ∞) + 550,000 + .10(20,750,000)(A/F, 8%, 8) +
750,000(A/F, 8%, 6) = $2,507,275
B/C = $5,840,000 / $2,507,275
B/C= 2.33

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