Unit 3 (cont.):
Economic Analysis—
Cost-Benefit Analysis 2
Some Key Terms
Initial (first) cost
A one-time investment cost incurred at the beginning
of the life of a project (e.g. construction cost of a
new road or school).
Recurring costs
Beyond the initial cost, many projects require the use
of resources on a continual basis during their useful
life time, e.g. annual costs on Operation and
Maintenance (O&M)
Recurring costs can be in the form of Uniform
Series or Non-uniform Series
Some Key Terms
Salvage value
Value of remaining assets of a project at the end of
its useful life
It represents a surplus of resources allocated to the
project
Because it is already included in the cost estimates,
“Salvage value” should always be deducted from
“Costs” during CBA calculations
What is Net Present Value (NPV)?
Formula for Calculating NPV
Generic formula:
NPV = PVB – PVC
Benefits and costs have to be
discounted
Benefits and costs may occur as initial
values, uniform annual values, nonuniform series, end-of-period values or
any combination
Formula for Calculating NPV
Interpretation: Single Alternative
If NPV > 0, the proposed project is
economically viable (efficient);
If NPV = 0, the benefits are just enough
to offset costs; consider other criteria
If NPV < 0, the proposed project does
not make economic sense (inefficient),
reject it
Formula for Calculating NPV
Interpretation: Two or More Alternatives
All alternatives with NPV > 0 are
economically viable (efficient)
Out of these, select alternative with the
highest NPV
Formula for Calculating NPV
Generic formula:
Let Bt = benefit in year t
Ct = cost in year t
r = discount rate;
t = year 0, 1, 3, ….., n
Formula for Calculating NPV
Generic formula:
n
n
NPV   (1 r )t   (1 r )t
Bt
t 0
t 0
OR
n
NPV   (1 r )t
t 0
Bt Ct
Ct
Example 1
As a planner working with a district assembly
(DA) you have been tasked to evaluate the
viability of a proposed economic development
programme. The forecasted social costs and
benefits of the programme for the next 8 years
are shown in the table below.
Year
Cost (in $ million)
Benefits (in $ million)
0
1
2
3
4
5
6
7
8
48.0
-
-
8.5
8.5
12.0
4.5
4.5
4.5
12
12
12
12
20
20
20
20
Example 1 (cont.)
(i) Using a discount rate of 8% calculate the net
present value of the programme and
interpret your result.
(ii) Based on the result you obtain in (i)
determine whether or not the proposed
strategy is viable.
(iii) What should be the decision of the DA
regarding the proposal?
Solution
(i) NPV:
t
0
1
2
3
4
5
6
7
8
Ct (in $ million)
48.0
-
-
8.5
8.5
12.0
4.5
4.5
4.5
Bt (in $ million)
-
12
12
12
12
20
20
20
20
-48.0
12
12
3.5
3.5
8
15.5
15.5
15.5
11.1
10.3
2.8
2.8
5.4
9.8
9.0
8.4
Bt – Ct
Discounted (Bt – Ct) -48.0
8
NPV   (10.08)t  $11.6m il.
t 0
Bt Ct
Solution
Interpretation of result
Discounted value of social benefits of the
proposed programme exceeds discounted value
of its social costs by $11.6 million.
(ii) Viability of proposed progrmme:
The proposed programme is economically
viable because its NPV is greater than zero
Solution
(iii) What the DA should do:
The proposed programme should be
adopted because its NPV shows it is
economically viable
Formula for Calculating NPV
When annual benefits and costs occur as
“uniform series” with or without initial
values:
Let B0 = benefit in year 0
AB = uniform annual benefit
C0 = cost in year 0
AC = uniform annual cost
r = discount rate; t = total number of years
Formula for Calculating NPV
When annual benefits and costs occur as
“uniform series” with or without initial
values:

 1  r t  1  
 1  r t  1 
  C0  AC

NPV   B0  AB
t 
t 


 r 1  r   
 r 1  r  
OR
 1  r t  1 

NPV  B0  C0    AB  AC 
t 
 r 1  r  
Example 2
GoG is considering a proposal to construct a new
bypass around city “A”. The proposal will involve an
initial cost of $60 million (for construction) and
$2.25 million annually for maintenance. The bypass
has an estimated life of 20 years during which it is
expected to yield social benefits of $9.75 million
every year.
(i) Using a discount rate of 8%, calculate the net
present value of the proposed project
(ii) Interpret your answer for (i)
(iii) Based on your results make a recommendation
to GoG
Solution
(i) NPV:
C0 =$60 million; AC = $2.25 million;
B0 = 0; AB = $9.75 million; t = 20; r = 8%
 1  r t  1 

NPV  B0  C0    AB  AC 
t 
 r 1  r  
 1  0.0820  1 
  $13.64m il
NPV  $0  $60m il  $9.75  $2.25
20 
 0.081  0.08 
Solution
(ii) Interpretation:
Discounted (present) value of the social
benefits of proposed project exceeds
discounted (present) value of its social costs by
$13.64 million
(iii) Recommendation:
Since NPV > 0, the proposal is economically
viable (efficient) and is recommended for
approval by GoG.
Trial Question 1
 A proposal for providing electricity to a small remote town for
40 years is being considered by government. The investment
costs, operation and maintenance (O&M) costs, benefits and
disbenefits of the proposal are as summarized in the table
below. Using a discount rate of 6%, calculate the net present
value of the proposal and determine whether it is
economically justifiable
Description
Estimates
Annual benefits, $/year
72,500,000
Present value of all disbenefits, $
76,600,000
Investment (initial) costs, $
O&M costs, $/year
Project life, years
300,500,000
49,000,000
40
Trial Question 2
GoG is considering two alternative proposals to improve road safety
and reduce traffic congestion in city “A”: (a) constructing a new bypass
or (b) upgrading existing roadways. The Bypass Proposal will have an
initial cost of GHC60 million and annual maintenance costs of GHC2.25
million. It is expected to yield benefits of GHC9.75 million per year.
The Upgrading Proposal has an initial cost of GHC7 million, annual
maintenance costs of GHC262,500 and annual social benefits of
GHC1.14 million. Each project has a life of 30 years. The Bypass
Proposal, which would have donor funding component, involves a
discount rate of 8% while the Upgrading Proposal, to be funded wholly
by government, has a discount rate of 4%.
i. Calculate the net present value of each proposal and determine
if it is economically viable
ii. Which of the two proposals is more economically justifiable.
Benefit-Cost Ratio (BCR)
Defined simply as:
Discounted Benefits
BCR =
Discounted Costs
Benefit-Cost Ratio (BCR)
It gives indication of how much benefit will be
produced for every GHC1 of cost incurred on a
programme or project
E.g.
BCR of 1.5 means for every GHC1 of cost
incurred, $1.5 worth of benefits will be produced
BCR of 0.7 means for every GHC1 of cost
incurred, GHC0.7 worth of benefits will be
produced
What about: BCR of 2.0? BCR of 1.0?
Benefit-Cost Ratio (BCR)
Rules:
If CBR > 1, the project is economically viable
(efficient) because its social benefits exceed its social
costs; accept it on the basis of the efficiency
If CBR = 1, the social benefits of the project are just
enough to offset its social costs; other criteria need
to be considered in making a decision
If CBR < 1, the project does not make economic
sense (inefficient) because its social costs exceed its
social benefits; reject it on the basis of efficiency
Formula for Calculating BCR
Generic formula:
n
BCR 

t 0
n

t 0
Bt
(1 r ) t
Ct
(1 r )
t
Example 3
As a planner working with a district assembly
(DA) you have been tasked to evaluate the
viability of a proposed economic development
programme. The forecasted social costs and
benefits of the programme for the next 8 years
are shown in the table below.
Year
Cost (in $ million)
Benefits (in $ million)
0
1
2
3
4
5
6
7
8
48.0
-
-
8.5
8.5
12.0
4.5
4.5
4.5
12
12
12
12
20
20
20
20
Example 3 (cont.)
(i) Using a discount rate of 8% calculate the BCR
of the programme and interpret your result.
(ii) Based on the result you obtain in (i)
determine whether or not the proposed
strategy is viable.
(iii) What should be the decision of the DA
regarding the proposal?
Solution
(i) BCR:
t
0
1
2
3
4
5
6
7
8
Ct (in $ million)
48.0
-
-
8.5
8.5
12.0
4.5
4.5
4.5
Discounted Ct
48.0
-
-
12
12
12
12
20
20
20
20
Bt (in $ million) Discounted Bt
0
n
BCR 

t 0
n

t 0
Bt
(1 r ) t
Ct
(1 r ) t
∑
Solution
Formula for Calculating BCR
When annual benefits and costs occur as
“uniform series” with or without initial
values:

 (1  r ) t  1 

BCR   B0  AB
t 
 r (1  r ) 


 (1  r ) t  1 

C0  AC
t 
 r (1  r ) 

Example 4
GoG is considering a proposal to construct a new
bypass around city “A”. The proposal will involve an
initial cost of $60 million (for construction) and
$2.25 million annually for maintenance. The bypass
has an estimated life of 20 years during which it is
expected to yield social benefits of $9.75 million
every year.
(i) Using a discount rate of 8%, calculate the BCR
of the proposed project
(ii) Interpret your answer for (i)
(iii) Based on your results make a recommendation
to GoG
Solution