Benefit Cost Ratio
Fanny Widadie
What is a Benefit-Cost Ratio?
• A benefit-cost ratio (BCR) is an indicator, used
in the formal discipline of Cost-Benefit Analysis,,
that attempts to summarize the overall value of
money of a project or proposal.
• A BCR is the ratio of the benefits of a project or
proposal, expressed in monetary terms, relative to
its costs, also expressed in monetary terms.
• All benefits and costs should be expressed in
discounted present values.
2
• In the absence of funding constraints, the best value for money
projects are those with the highest net present value. Where there
is a budget constraint, the ratio of NPV to the expenditure falling
within the constraint should be used.
• In practice, the ratio of NPV to expenditure is expressed as a
BCR.
• BCRs have been used most extensively in the field of transport
cost-benefit appraisals.
• The NPV should be evaluated over the service life of the project.
• A major shortcoming of BCRs is that, by definition, they ignore
non-monetized impacts. Attempts have been made to overcome
this limitation by combining BCRs with information about those
impacts that cannot be expressed in monetary terms
• A further complication with BCRs concerns the precise
definitions of benefits and costs. These can vary depending on
the funding agency.
EGR 403 - Cal Poly Pomona - SA12
3
Cost-benefit analysis
• Cost-benefit analysis is a term that refers both to:
– helping to appraise, or assess, the case for a project or proposal, which
itself is a process known as project appraisal; and
– an informal approach to making decisions of any kind.
• Under both definitions the process involves, whether explicitly
or implicitly, weighing the total expected costs against the total
expected benefits of one or more actions in order to choose the
best or most profitable option.
• The formal process is often referred to as either CBA
(Cost-Benefit Analysis) or BCA(Benefit-Cost Analysis).
• The cost-benefit analysis is explicitly designed to inform the
practical decision-making of enterprise managers and investors
focusing on optimizing their social and environmental impacts.
EGR 403 - Cal Poly Pomona - SA12
4
• Cost–benefit analysis is typically used by
governments to evaluate the desirability of a given
intervention.
– It is an analysis of the cost effectiveness of different
alternatives in order to see whether the benefits outweigh
the costs.
– The costs and benefits of the impacts of an intervention
are evaluated in terms of the public's willingness to pay
for them (benefits) or willingness to pay to avoid them
(costs).
– Inputs are typically measured in terms of opportunity
costs - the value in their best alternative use.
– The guiding principle is to list all parties affected by an
intervention and place a monetary value of the effect it
has on their welfare as it would be valued by them.
EGR 403 - Cal Poly Pomona - SA12
5
• The process involves monetary value of initial and ongoing
expenses vs. expected return.
– Constructing plausible measures of the costs and benefits of
specific actions is often very difficult.
– In practice, analysts try to estimate costs and benefits either by
using survey methods or by drawing inferences from market
behavior.
• For example, a product manager may compare manufacturing and marketing
expenses with projected sales for a proposed product and decide to produce
it only if he expects the revenues to eventually recoup the costs.
– Cost–benefit analysis attempts to put all relevant costs and benefits
on a common temporal footing.
– A discount rate is chosen, which is then used to compute all
relevant future costs and benefits in present-value terms.
– Most commonly, the discount rate used for present-value
calculations is an interest rate taken from financial markets.
EGR 403 - Cal Poly Pomona - SA12
6
Benefit-Cost Ratio Analysis
• If the PW of benefits PW of costs 0.
The alternative is
considered acceptable.
• Restated:
Benefit-cost ratio B/C =.
PW of benefit/PW of cost  1.
• Fixed input, maximize B/C.
Example 9-3
Year
0
1
2
3
4
5
PW of:
Cost
Benefit
$
$
$
$
$
$
MARR =
7.00%
Alternative
A
B
(1,000.00) $ (1,000.00)
300.00 $
400.00
300.00 $
350.00
300.00 $
300.00
300.00 $
250.00
300.00 $
200.00
($1,000.00)
($1,000.00)
$ 1,230.06 $
1,257.75
B/C =
1.23
1.26
Select:
B
Other alternatives for comparison:
PW $
230.06 $
257.75
EUAC
$56.11
$62.86
FW
$322.67
$361.50
IRR
15.24%
17.47%
EGR 403 - Cal Poly Pomona - SA12
7
Benefit-Cost Ratio Analysis
• If the EUAB - EUAC 0.
The alternative is considered acceptable.
• Restated:
Benefit-cost ratio: B/C = EUAB/EUAC  1
Or, using PW: B/C = PWB/PWC 
• Neither input or output fixed - use incremental
B/C.
• Note: Salvage Value is considered a “negative
cost”, not a benefit
• B/C Ratio Analysis is popular in government
• Very easy to use with databases and spreadsheets
EGR 403 - Cal Poly Pomona - SA12
8
Benefit Cost Ratio Analysis Example
Reject increment if incremental B/C Ratio is < 1
Cost
PWB
B/C
Increment
incr Cost
incr PWB
incr B/C
Keep
D
1000
1340
1.34
B
2000
4700
2.35
A
4000
7330
1.83
C
6000
8730
1.46
E
9000
9000
1
B-D
1000
3360
3.36
B
A-B
2000
2630
1.36
A
C-A
2000
1400
0.70
A
E-A
5000
1670
0.33
A
EGR 403 - Cal Poly Pomona - SA12
9
Benefit Cost Ratio Analysis Example
First Increment is B-D. Incremental B/C > 1, so choose
higher cost alternative
Cost
PWB
B/C
Increment
incr Cost
incr PWB
incr B/C
Keep
D
1000
1340
1.34
B
2000
4700
2.35
A
4000
7330
1.83
C
6000
8730
1.46
E
9000
9000
1
B-D
1000
3360
3.36
B
A-B
2000
2630
1.36
A
C-A
2000
1400
0.70
A
E-A
5000
1670
0.33
A
EGR 403 - Cal Poly Pomona - SA12
10
Benefit Cost Ratio Analysis Example
Reject increment if incremental B/C Ratio is < 1
Cost
PWB
B/C
Increment
incr Cost
incr PWB
incr B/C
Keep
D
1000
1340
1.34
B
2000
4700
2.35
A
4000
7330
1.83
C
6000
8730
1.46
E
9000
9000
1
B-D
1000
3360
3.36
B
A-B
2000
2630
1.36
A
C-A
2000
1400
0.70
A
E-A
5000
1670
0.33
A
EGR 403 - Cal Poly Pomona - SA12
11