CHAPTER 3

METHODOLOGY

This chapter attempts to explain the methods used in carrying out the study. In view of this, the

chapter lays more emphasis on the description of the study are, theoretical framework, sampling

procedures, data collection and method data analysis.

3.1 Theoretical framework

Cost-benefit analysis in the area of economics is the most appropriate and popular method of

appraising project from the national viewpoint.

Cost benefit analysis (CBA), sometimes called benefit–cost analysis (BCA), is a systematic

process for calculating and comparing benefits and costs of a project, decision or government

policy (hereafter, "project"). CBA has two purposes:

1. To determine if it is a sound investment/decision (justification/feasibility),

2. To provide a basis for comparing projects. It involves comparing the total expected cost

of each option against the total expected benefits, to see whether the benefits outweigh

the costs, and by how much.

CBA is related to, but distinct from cost-effectiveness analysis. In CBA, benefits and costs are

expressed in monetary terms, and are adjusted for the time value of money, so that all flows of

benefits and flows of project costs over time (which tend to occur at different points in time) are

expressed on a common basis in terms of their "net present value."

Cost is seen as the value of the inputs needed to produce any good or service. This has to be

measured in some units or numeric usually money. Cost includes the fixed cost or overhead cost

and variable cost. Fixed cost must be incurred if any output is produced. Cost also includes the

social cost, which includes external cost of an enterprise such as the value of smoke, damage,

noise and river pollution. Benefit is seen as an addition to the flow of output accruing to a

project.

The concept of Cost-Benefit analysis dates back to an 1848 article by Jules Dupuit and was

formalized in subsequent works by Alfred Marshall. The Corps of Engineers initiated the use of

Cost-Benefit analysis in the US, after the Federal Navigation Act of 1936 effectively required

cost–benefit analysis for proposed federal waterway infrastructure. The Flood Control Act of

1939 was instrumental in establishing Cost-Benefit analysis as federal policy. It demanded that

"the benefits to whomever they accrue [be] in excess of the estimated costs.

Cost-benefit analysis is the area in economics that attempts to compare the total social costs and

benefits of any activity, usually expressed in money terms. The cost and benefits concerned

includes not only direct pecuniary costs and benefits, but also externalities, that are external

effects, not traded in the, markets. This encompasses external cost such as pollution, noise and

disturbance to wildlife and external benefits such as reduction in traveling time or traffic

accidents (John Black, 2005)

Cost-benefit is also seen as the most scientific and useful criterion for project evaluation. It helps

in making correct investment decision to achieve optimum resource allocation by maximizing

the difference between the present value of benefits and cost of a project. It implies the weighing

of the returns against the cost involved in a project. Cost-benefit analysis purports to describe

and quantify the social advantages and disadvantages of a policy in terms of a common monetary

unit. This is the establishment of net social benefit which can be expressed as NSB= Benefits

minus cost. The benefits and costs are measured in terms of shadow or accounting prices of

inputs and output instead of in actual market prices (Jinghan, 2002)

Todaro and Smith (2005) saw cost benefit analysis as a basic tool of economic analysis in which

the actual and potential private and social cost of various economic decisions are weighed

against actual and potential private and social benefits. Decisions or projects that yield the

highest ratio of benefits to costs are usually thought to be most desirable. Cost-benefits analysis

is seen as the basic tool of project analysis. If the total benefits (which includes social benefits)

of any activity exceeds total cost (including social cost) then the projects involved are profitable.

On the other hand, if total cost exceeds total benefits, these would prevent project from springing

up or discourage investors from investing in such projects. Because non- marketed costs and

benefits are difficult to measure and evaluate, the results of cost-benefit analysis can be highly

controversial. In other words, cost-benefit analysis in agriculture means value of inputs needed to

produce agricultural products and the gains to be expected from the sales of such goods. Costs

incurred include expenditure on the initial processing, handling, reduction in wastage, grading ,

quality control, sales transactions and holding inventory to match concentrated harvest seasons

which the continuing demands of consumers (Ezenwa, 1987).

Cost-benefit analysis is a highly dynamic subject in the appraisal of a project. There are several

criteria to analyzing cost- benefit, which is given by Jinghan (2002). They include;

1) B - C Benefit- cost;

2) B – C/I Benefit – cost/ investment

3) ΔB/ΔC ΔBenefit/Δcost

4) B/C Benefit/ Cost

Where:

B: Benefit

C: Cost

I: Investment

Δ: Incremental or Marginal

1. B–C/I is for determining the total annual returns on a particular investment in the

economy as a whole irrespective of whom these accrue. The investment (I) here does not

include the private investment that may be incurred by the beneficiaries of the project

such as the cultivators from an irrigation project. A high value of B–C/I may be less

beneficial to the economy even if the private investment happens to be very large. The

problem with this criterion is that it does not put into consideration the private

investment.

2. ΔB/ΔC. The second criterion of ΔB/ΔC is aimed at

determining the size of a project but can only determine a selected project.

3. B – C: the B – C criterion would favour large projects and

make small and medium size projects less beneficial. This criterion can only help in determining

the scale of the project on the basis of the maximization of the difference between benefit and

cost.

4. B/C: This is the best and most reliable criterion for project

evaluation is. This criterion (benefit to cost ratio) is the measure for the evaluation of a project.

If B/C =1, then the project is marginal, it is just covering its cost.

If B/C>1, then benefits are more than cost and it is beneficial to undertake the project.

If B/C<1, then the benefits are less than cost and the project cannot be undertaken,

The higher the benefit- cost ratio, the higher will be the profit attached to a project.

This criterion does not take into account the time horizon of the project. The fact is that future

benefits and costs cannot be treated at par with present benefits and cost. Therefore, the appraisal

rule for project evaluation requires discounting of future benefits and costs because the society

prefers the present to the future.

Due to the flaws above, new criteria were developed, they include;

a. Net present value (NPV)

b. Internal rate of return criterion (IRR)

3.1.1 Net Present Value (NPV)

The net present value criterion is vital in project evaluation. It is equal to the present value of

benefits minus the present value of operating and maintenance cost minus initial outlay. The

NPV is also expressed as Net Present Value of benefits (NPVB) criterion, which equals: Gross

Present Value of Benefits – Gross Present value of costs.

A project is socially profitable if the NPVB> 0. In a case where there are a number of mutually

exclusive projects and the project with the highest net present value of benefits will be chosen.

This criterion in terms of benefits and costs is not a correct method for project evaluation as it

neglected also the time horizon. Capital investments give benefits over a period of time. Hence,

future benefits and cost cannot be equated with present benefits and costs. Since preference is

+ +

given to the present over the future, then future benefits and costs of projects are to be

discounted.

The discounted factor is expressed as D= 1/ (1+i) t

Where i is the social discount rate

t is the time period

The NPV will therefore be

NPV= B1 B2 ….. Bn C1 C2 ….Cn

(1+i) (1+i)2 (1+i)n (1+i) (1+i)2 (1+i)n

B1, B2…Bn- series of gross present benefit in years 1 ton

C1, C2…Cn- series of gross present cost in years 1 to n

i- Social rate of discount for annual compounding.

When choice is to be made on project, one of these two rules can be followed.

1. B1 B2 ... Bn C1 C2 ….Cn

(1+i) (1+i) 2 (1+i) n (1+i) (1+i)2 2 (1+i)n

Only the projects, which the present value benefits exceeds the present value of cost should be

selected.

2. B1 B2 ... Bn

(1+i) (1+i) 2 (1+i) n

C1 C2 ...Cn

(1+i) (1+i) 2 (1+i) n

++-

++>++

> 1

++

++

All projects where the ratio of the present value of benefits divided by the ratio of the present

value of cost is greater than one.

The NPV criterion is considered as the most appropriate rule for perfect evaluation.

3.1.2 The Internal Rate of Return criterion

The criterion refers to the percentage rate of return of implicit in the flows of benefit and cost of

projects

The internal rate of returns (IRR) is the discount rate at which the present value of returns minus

cost is zero. The formula for the calculation of IRR is

B1-C1 B2-C2 …Bn-…..Cn

(1+i) (( (1+i)2 (1+i)n ` `

Where ‘r’ is the internal rate of returns

3.2. Study area

This research would be carried out in Akure metropolis, Ondo state Nigeria so as to make the

results useful for farmers and intending fish farmers in the state. The farms to be studied include:

3.3 Sampling Procedure.

The sampling procedure used in this study is called the purposive sampling where the study was

aimed at gathering information from particular farms as a representative of similar sized farms.

The reason for this is due to little or no record keeping by other fish farmers. Hence, a farm with

considerable record of expenditure and income within the year was chosen.

= 0++

3.4 Data collection

As a result of the kind of study that was researched, the data collection instrument that was used

to gather information was the primary source, this was done by the use of personal interview.

The interview was designed to reflect the general information, construction information, and

production information. The fish farmer was able to relate directly with the researcher and gave

some vital information that were not even in the records in the farm. The researcher was able to

get direct answers from the farm owner as questions were flexible enough and were poised to

elicit direct answers.

3.5 Method of data analysis

In order to achieve our stated objectives of the study, the following tools for analyzing the data

collected were employed:

3.5.1 Benefit-cost ratio (b-c ratio):

This is the ratio obtained when the present worth of the benefit stream is divided by the present

worth of the cost stream. It is used to directly note how much cost could rise without making the

project economically unattractive. Cost- benefit ratio is usually computed by using gross cost and

gross benefit.

More specifically, using the present worth of the gross benefit less the associated cost and then

comparing it with the present worth of the project is mathematically computed as:

B-C RATIO = Benefit

Cost

If B/C =1, then the project is marginal, it is just covering its cost.

If B/C>1, then benefits are more than cost and it is beneficial to undertake the project.

If B/C<1, then the benefits are less than cost and the project cannot be undertaken,

3.5.2 Net benefit-investment ratio (NBI ratio):

This is the present worth of the net benefit divided by the present worth of the investment. It is a

form of the benefit-cost ratio and has been infrequently used in project analysis. Net benefit-

investment ratio is used to determine an incremental net benefit or cash flow calculation for a

project. The net benefit-investment ratio is calculated by:

NBI RATIO = Present worth of net benefit

Present worth of investment

3.5.3 Net Present Worth (NPW):

It is the most straightforward discounted cash flow measure of project worth. It is the present

worth of incremental cash flow stream.

Calculation of the NPW requires the determination of the appropriate discount rate, which is also

used in the calculation of B-C ratio and the NBI. :

NPW = Discounted Benefit –Discounted Cost.

3.5.4 Internal Rate of Returns (IRR)

In computing the internal rate of returns, the following rules are needed

1. Two discount rates are involved in the calculation

2. The net present value of the higher discount rate must give a negative figure

The calculation of the IRR is given as

LDR + DIFFERENCE IN 2DR (NPV AT LDR/ SUM OF NPV OF THE 2DR)

Where

NPV: NET PRESENT VALUE

LDR: LOWER DISCOUNT RATE

2DR: TWO DISCOUNT RATES

3.5.5 The Decision Rule:

If the project has an IRR that is equal to or greater than the lending rate, then the project should

be accepted. Hence accept the project if it is greater than the cut off rate or that is higher than the

cost of borrowing

3.5.6 Sensitivity analysis

Sensitivity analysis is a measure used to determine the how viable a project can be when some

variables are changed. This means that it is a method that is used to know how profitable it is to

embark on a project when there are changes in some factors that enhances the viability of the

project. In most cases, these factors could either be change in cost of production, revenue or

both. This is usually calculated using percentage. In this study, a 20percent provision was made

with respect to cost over-run or fall in revenue.