Benefit-Cost Ratio
Lecture No. 66
Chapter 16
Contemporary Engineering Economics
Copyright © 2006
Contemporary Engineering Economics, 4th
edition, © 2007
Benefit-Cost Analysis



The Benefit-cost analysis is commonly used to
evaluate public projects.
Benefits of a nonmonetary nature need to be
quantified in dollar terms as much as possible and
factored into the analysis.
A broad range of project users distinct from the
sponsor can and should be considered—benefits
and disbenefits to all these users can and should
be taken into account.
Contemporary Engineering Economics, 4th
edition, © 2007
Framework of Benefit-Cost
Analysis
1)
2)
3)
4)
Identifying all the users and sponsors of the
project.
Identifying all the benefits and disbenefits of the
project.
Quantifying all benefits and disbenefits in dollars
or some other unit of measure.
Selecting an appropriate interest rate at which to
discount benefits and costs in future to a present
value.
Contemporary Engineering Economics, 4th
edition, © 2007
Benefit-Cost Ratio Criterion
Benefit - C ost R atio =
Equivalent U sers' N et Benefits
Equivalent Sponsor' s N et C ost
If this BC ratio exceeds 1, the project can be justified.
Contemporary Engineering Economics, 4th
edition, © 2007
Definition of Benefit-Cost Ratio
N
B 

b n (1  i )
n
c n (1  i )
n
n0
N
C 

n0
bn=Benefit at the end of period n, bn  0
cn=Expense at the end of period n, c n  0
An= bn – cn
N = Project life
i =Sponsor’s interest rate (discount rate)
Contemporary Engineering Economics, 4th
edition, © 2007
Breakdown of the Sponsor’s Cost
K
I 

c n (1  i )
n
Equivalent capital investment
at n = 0
n0
N
C' 
c
n
(1  i )
n
n  K 1
B C (i) 
B
C

B
I  C'
Equivalent O&M costs
at n = 0
, I  C'  0
Contemporary Engineering Economics, 4th
edition, © 2007
Example 16.1 Benefit-Cost ratio
K=1
N=5
Contemporary Engineering Economics, 4th
edition, © 2007
Solution:
B = $20( P / F , 10% , 2 ) + $30( P / F , 1% , 3 )
+$30( P / F , 10% , 4 ) + $20( P / F , 10% , 5 )
= $71.98
C = $10 + $10( P / F , 10% , 1) + $5( P / F , 10% , 2 ) + $5( P / F , 10% , 3 )
+ $8( P / F , 10% , 4 ) + $8( P / F , 10% , 5 )
= $37.41
I = $10 + $10( P / F , 10% , 1)
= $19.09
C’ = C – I
= $18.3
B C (10% ) 
71.98
$19. 09  $18.32
 1.92  1, A ccept the project.
Contemporary Engineering Economics, 4th
edition, © 2007
Relationship between B/C Ratio and
NPW
B
I  C'
1
B > (I + C’)
B – (I+ C’) > 0
PW(i) = B – C > 0
Contemporary Engineering Economics, 4th
edition, © 2007
Incremental Analysis Based on BC(i)



If BC(i)k-j > 1, select
alternative j.
If ΔI + ΔC’ = 0, we cannot
use the benefit-cost ratio.
When this happens, just
select the project with the
largest B value.
In situations where public
projects with unequal
service lives are to be
compared , compute all
component values (B, I, and
C’) on an annual basis.
 B  Bk  B j
I  Ik  I J
 C'  C' k  C'
BC ( i ) k  j 
Contemporary Engineering Economics, 4th
edition, © 2007
j
B
I  C '
Example 16.2 Incremental Benefit-Cost
Ratios – Three Alternatives
A1
A2
A3
I
$5,000
$20,000
$14,000
B
12,000
35,000
21,000
C’
4,000
8,000
1,000
PW(i)
$3,000
$7,000
$6,000
Contemporary Engineering Economics, 4th
edition, © 2007
Solution
A1
A2
A3
BC(i)
1.33
1.25
1.40
Ranking Base
A1
A3
A2
I +C’
$9,000
$15,000
$28,000
B C ( i ) 2 1 
$ 2 1, 0 0 0  $ 1 2, 0 0 0
($ 1 4, 0 0 0  $ 5, 0 0 0 )  ($ 1, 0 0 0  $ 4, 0 0 0 )
 1.5  1, select A 2 .
B C (i) 2  3 
$ 3 5, 0 0 0  $ 2 1, 0 0 0
($20, 0 0 0  $ 1 4, 0 0 0 )  ($8, 0 0 0  $ 1, 0 0 0 )
 1. 0 8  1, select A 2 .
Contemporary Engineering Economics, 4th
edition, © 2007
Summary


1)
2)
3)
4)
A benefit-cost analysis is commonly used to evaluate
public projects:
Difficulties involved in public project analysis include the
following:
Identifying all the users who can benefit from the
project.
Identifying all the benefits and disbenefits of the
project.
Quantifying all benefits and disbenefits in dollars or
some other unit of measure.
Selecting an appropriate interest rate at which to
discount benefits and costs to a present value.
Contemporary Engineering Economics, 4th
edition, © 2007

The B/C ratio is defined as:
B C (i ) 
B
C

B
I  C'
, I  C' 0
The decision rule is if BC(i) > 1, the project is acceptable.
 The net B/C ratio is defined as
B / C (i ) 
B  C'
I

B'
,I  0
I'
The net B/C ratio expresses the net benefit expected per
dollar invested. The same decision rule applies as for the
B/C ratio.
Contemporary Engineering Economics, 4th
edition, © 2007