Unit 3 (cont.): Economic Analysis—

Cost-Benefit Analysis 2

Some Key TermsInitial (first) costA 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 costsBeyond 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 TermsSalvage valueValue of remaining assets of a project at the end of its useful lifeIt represents a surplus of resources allocated to the projectBecause 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, non-uniform series, end-of-period values or any combination

Formula for Calculating NPV

Interpretation: Single AlternativeIf NPV > 0, the proposed project is economically viable (efficient); If NPV = 0, the benefits are just enough to offset costs; consider other criteriaIf NPV < 0, the proposed project does not make economic sense (inefficient), reject it

Formula for Calculating NPV

Interpretation: Two or More AlternativesAll 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:

OR

n

t

n

tr

C

r

Bt

tt

tNPV0 0

)1()1(

n

tr

CBtttNPV

0)1(

Example 1As 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 0 1 2 3 4 5 6 7 8

Cost (in $ million) 48.0 - - 8.5 8.5 12.0 4.5 4.5 4.5

Benefits (in $ million) 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

Bt – Ct -48.0 12 12 3.5 3.5 8 15.5 15.5 15.5

Discounted (Bt – Ct) -48.0 11.1 10.3 2.8 2.8 5.4 9.8 9.0 8.4

.6.11$8

0)08.01(

milNPVt

CBt

tt

Solution

Interpretation of resultDiscounted 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 benefitC0 = cost in year 0AC = 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:

OR

t

t

t

t

rr

rACC

rr

rABBNPV

1

11

1

1100

t

t

rr

rACABCBNPV

1

1100

Example 2GoG 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%

t

t

rr

rACABCBNPV

1

1100

milmilNPV 64.13$08.0108.0

108.0125.2$75.9$60$0$ 20

20

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 justifiableDescription Estimates

Annual benefits, $/year 72,500,000

Present value of all disbenefits, $ 76,600,000

Investment (initial) costs, $ 300,500,000

O&M costs, $/year 49,000,000

Project life, years 40

Trial Question 2GoG 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%.

Calculate the net present value of each proposal and determine if it is economically viable

Which of the two proposals is more economically justifiable.

Benefit-Cost Ratio (BCR)Defined simply as:

BCR =Discounted Benefits

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 efficiencyIf 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 decisionIf 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

tr

C

n

tr

B

tt

tt

BCR

0)1(

0)1(

Example 3As 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 0 1 2 3 4 5 6 7 8

Cost (in $ million) 48.0 - - 8.5 8.5 12.0 4.5 4.5 4.5

Benefits (in $ million) 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 - -

Bt (in $ million) - 12 12 12 12 20 20 20 20

Discounted Bt 0

n

tr

C

n

tr

B

tt

tt

BCR

0)1(

0)1(

Solution

Formula for Calculating BCR

When annual benefits and costs occur as “uniform series” with or without initial values:

t

t

t

t

rrr

ACCrr

rABBBCR

)1(1)1(

)1(1)1(

00

Example 4GoG 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