Benefit/Cost Ratio (BCR)
Introduction
The Benefit/Cost Ratio (BCR) is a financial metric used in engineering
economics and project evaluation. It helps determine whether a
project is worth undertaking by comparing its expected benefits to its
costs
If BCR > 1 – Project is financially viable and benefits outweigh the costs
If BCR < 1 – Costs outweigh the benefits and project is not
recommended
If BCR = 1 -Benefits and Costs are equal and project is at breakeven
point
Formulae for Benefit/Cost Ratio
The general formulae is:
If we are talking about Future Worth, BCR is:
BCR and the Present Worth
• In Benefit-Cost Ratio (BCR) analysis, we take all costs and benefits
and discount them to the present value using the Minimum
Acceptable Rate of Return (MARR) or another appropriate discount
rate
• This is because money has a time value—a dollar today is worth more
than a dollar in the future due to interest and opportunity costs.
Why we generally use Present worth in BCR
• It ensures all costs and benefits are compared on the same time
basis.
• It accounts for inflation, interest rates, and opportunity costs
• It helps in evaluating long-term projects where cash flows occur over
multiple years
Adjusted BCR
• This method refines the traditional BCR by including intangible
benefits, externalities, and risk-adjusted costs
Note that:
• Intangible benefits include environmental impact, social benefits, or
indirect economic effects
• Externalities (positive or negative) are included in cost/benefit
adjustments.
Formula for ABCR
Incremental Benefit-Cost Ratio (IBCR) Analysis
• When comparing two or more mutually exclusive projects, the
Incremental BCR method helps choose the best alternative. Instead of
comparing each option to "doing nothing," this method compares
incremental benefits and costs between two competing projects
Sensitivity Analysis on BCR
Instead of using a fixed discount rate and fixed cost/benefit values,
sensitivity analysis evaluates how BCR changes under different
scenarios:
• High vs Low Discount Rate/MARR
• Optimistic vs Pessimistic Benefit Estimates
• Changing Project Lifespan.
Problem Solving
A city is evaluating whether to invest in a highway improvement project
that will reduce travel time and accidents. The project has a lifespan of
10 years, and the MARR is 8%. Solve for the BCR
Solution:
• Construction Cost – Since 40 M is spent at year 0, we do not do any
discounting:
• Maintenance Costs (PW) -
Calculating the Present Worth of the Benefits
Computing for the BCR
With BCR > 1, we can say that the project is viable. Accept.
Problem Solving
A company is evaluating whether to build a solar power plant or a coal
power plant. Both have a lifespan of 20 years and an MARR of 8%.
Which should we take?
Computing the Present Worth of Costs
Computing Present Worth of Benefits
Computing BCR for each option
Seatwork
The Shoprite of Hammonton must seek an alternative of two cooling
towers. The following are the alternatives. Assume both have the same
refrigeration capacity and a MARR of 10%
Using BCR. Select the tower that the Shoprite of Hammonton must
select
Tower 1 (By Shark Ripper
Refrigeration)
Tower 2 (By Geese Refrigeration)
Initial Cost – 30’000
Lifespan – 15 years
Maintenance cost on Year 5 – 10’000
Maintenance cost on Year 10 – 5’000
Maintenance cost on Year 12 – 3’000
Annual Savings – 10’000
Salvage Value – 3’000
Initial Cost – 55’000
Lifespan – 18 years
Maintenance cost on Year 6 – 15’000
Maintenance cost on Year 15 – 10’000
Annual Savings – 15’000
Salvage Value – 5’000