Econ. 614 B - Cost Benefit Analysis
Semester Paper: Econ. 614 B: Cost Benefit Analysis
BASIC MEASURES OF PROJECT WORTH OF INVESTMENT
Semester Paper Submitted as Requirement for the Internal Examination of the
M. Phil. in Economics
Submitted to:
Tribhuvan University
Central Department of Economics
M. Phil. Programme
Submitted by:
Yogendra Dahal
Roll No.: 14
1. Introduction
A structured methodology of
forecasting and comparing the anticipated costs and benefits of alternative
courses of action in order to identify the most effective manner of achieving a
stated goal or objective.
CBA is a process used to determine the
value of a project in relative terms. Project justification is measured as
economic worth to the community. To evaluate a project’s benefit to the
community, a CBA will compare the benefit with the overall cost, to deliver and
sustain the project. If overall benefits are demonstrated to exceed the
expected costs, a project is considered economically viable.
It is an ex ante
exercise. As a technique, it is used most often at the start of a programme or
project when different options or courses of action are being appraised and
compared, as an option for choosing the best approach. It can also be used,
however, to evaluate the overall impact of a programme in quantifiable and
monetized terms.
Nearly every business decision requires a
cost-benefit analysis. Such an analysis can point out the risks and rewards of
decisions or actions. Without cost-benefit analysis, there may be the risk of
taking unprofitable tasks and wasting valuable time and money because guessing
at the benefits or going by instinct can be a recipe for business failure.
A cost-benefit
analysis is used to evaluate the risks and rewards of projects under
consideration. It can be used to project the potential benefits of investing in
marketing ideas, product development, infrastructure enhancements and
operational changes.
2. Subject Matter
A project is simply accepted or rejected on the basis
of these measures depending on the nature of project. In a word, Net Present
Value (NPV), Benefit Cost Ratio (BCR) and Internal Rate of Return (IRR) with
the discount rate are the measures to compare projects' cost and benefit for
project worth. Descriptions of these instruments of cost benefit analysis are
as follows:
(a) Discount Rate
The
rate, per year at which future values are diminished to make them comparable to
values in the present is discount rate. In other words, looking present from
future or future to present or backward looking is discount rate. The discount
rate is also called the present worth factor.
Once all the relevant costs and benefits are expressed in monetary terms, it is necessary to convert them into a common metric, their present value. This process is called discounting and it is based on the fact that the individuals have time preferences between consumption in different periods. The rate at which an individual is willing to exchange the present consumption for the future consumption is called the discount rate. The higher is the discount rate, the greater preference is given to the present consumption.
Where,
Dt = discount factor
r = rate of interest
t = number of time period
(b) Net Present Value (NPV)
Net Present Value (NPV) is the difference
between the present value of cash inflows (cost) and the present value of cash
outflows (benefit) occurs in the course of project's lifetime. NPV is used in
capital budgeting to analyze the profitability of a projected
investment or project. It tells the magnitude of the project and takes
into account the time value of money.
The following is the formula for calculating
NPV:
Ct = Cost of year t
Bt = Benefit at year t
t = number of time periods (1, 2, ……, t)
r = interest (discount) rate
The net present value criterion is an absolute figure
to decide whether investment in a particular project or a number of alternative
projects should be made or not. If NPV is higher than zero, then investment in
project is worthwhile. In the case of the selection of a project from a number
of alternative projects, the projects would be arranged in descending order of
NPV. Generally, an investment with a positive NPV will be a profitable
one and one with a negative NPV will result in a net loss. This concept is the
basis for the Net Present Value Rule, which dictates that the only investments
that should be made are those with positive NPV values.
(c) Benefit Cost Ratio (BCR)
NPV gives the absolute value only. It does not tell us the rate of return per rupee of investment. For this we need another instrument i.e. Benefit Cost Ratio (BCR). It is the ratio of present worth of benefit stream to present worth of cost stream. Benefit cost ratios are most often used in corporate finance to detail the relationship between possible benefits and costs, both quantitative and qualitative, of undertaking new projects or replacing old ones. Mathematically,
The investment is said to be profitable when the
BCR is one or greater than one. This method is widely used in economic analysis
and not in private investment analysis. BCR is superior measure in the sense
that it measures return in per unit of cost but in the case of large investment
projects BCR measure may not appropriate because the lower investment project
may have higher BCR.
(d) Internal Rate of Return (IRR)
BCR does not tell us what benefits of project
can generate during its lifetime. For this we need another instrument i.e.
Internal Rate of Return (IRR). The internal rate of return (IRR) represents the
interest rate in which the net present value (NPV) of a project's expected total
cash flows, both positive and negative, sum to zero.
It represents the average earning power of the money used in the project over the project life. It is also sometime called yield of the investment. IRR is the discount rate that sets NPV = 0 and BCR = 1. It is the interest rate that makes the total value of present benefit equal to present value of total cost.
Symbolically,
Rate of interest, which if used as
the discount rate for a project, would yield a NPV of zero. It is the discount
rate at which it would be just worthwhile doing project. So the IRR is the
discount rate, r*, at which:
Where,
r* = Internal rate of return
3. Analysis
On the basis of subject matter of the study, the
instruments of cost benefit analysis further explained with the help of
illustration.
(a) Calculation of
Discount Rate
An individual is not necessarily indifferent between
receiving Rs 100 today and receiving the same Rs. 100 in ten years time. This
is true even if there is no inflation, because Rs 100 today can be used
productively in the consequent ten years, producing a value greater than the
initial Rs 100. The rate at which an individual is willing to exchange the
present consumption for the future consumption is called the discount rate.
The present value of a cost or a benefit X received
in time t given the discount rate r is calculated as follows:
For example, if the discount rate is 10%, a benefit
of Rs 1000 received in 8 years is:
Similarly, if the discount rate is 15%, a benefit of
Rs. 1000 received in 8 years is:
(b)
Calculation of Net Present Value
When discount rate is used in cost benefit analysis, computation of
NPV of investment is possible for different years. For example,
|
Year |
Project
Cost |
Project
benefits |
Net
cash flow |
Discount
factor (10%) |
Present
value of benefit and cost |
Discount
Factor (15%) |
Present
Value of Benefit and cost |
|
1 |
5200 |
1000 |
-4200 |
0.9091 |
-3818.18 |
0.8696 |
-3652.17 |
|
2 |
100 |
1000 |
900 |
0.8264 |
743.8017 |
0.7561 |
680.5293 |
|
3 |
100 |
1000 |
900 |
0.7513 |
676.1833 |
0.6575 |
591.7646 |
|
4 |
100 |
1000 |
900 |
0.6830 |
614.7121 |
0.5718 |
514.5779 |
|
5 |
100 |
1000 |
900 |
0.6209 |
558.8292 |
0.4972 |
447.4591 |
|
6 |
100 |
1000 |
900 |
0.5645 |
508.0265 |
0.4323 |
389.0948 |
|
7 |
100 |
1000 |
900 |
0.5132 |
461.8423 |
0.3759 |
338.3433 |
|
8 |
150 |
1000 |
850 |
0.4665 |
396.5313 |
0.3269 |
277.8665 |
|
|
|
|
2050 |
|
141.745 |
|
-412.538 |
The net present value (NPV) is the sum of the
discounted annual cash flows (Present value of benefit), taking an interest of
10% and 15%
NPV = Present worth of Benefit stream – Present worth
of Cost Stream
The net present value represents the net benefit over
and above the compensation for time and risk. NPV is higher than zero (141.745)
at 10% discount rate, the investment in the project is worthwhile. Project,
which have negative NPV (-412.538) at 15% discount rate is rejected.
c) Calculation of
Benefit Cost Ratio
For return per unit of investment, we use benefit
cost ration (BCR). Calculation of benefit cost ration is the same as that of NPV.
But, we have to divide the present value of benefit by present value of cost.
For correct result, NPV is not enough, we have to calculate BCR
It means for every rupees investment, projects will get
Rs. 1.037 return from 10 percent discount rate and Rs. 0.887 from 15% discount
rate.
(d) Calculation of
Internal Rate of Return
The process of determining IRR is trial and error. If
the result is positive a higher rate is used, if negative a lower rate is used
and process is repeated until NPV is reduced to zero. Thus, the discount rate
that yields a zero NPV and BCR equal to one is the IRR. If the discount rate
used in NPV is less than the social discount rate i.e. the value of IRR, the
project under consideration is worthwhile. IRR tells maximum returns that a
project generates maximum during its life time. We need at least two discount
rate to calculate IRR. Suppose 10% and 15% are two discount rates.
It is computed through the following method
If we plot this discount rate (IRR=11.1251)
on the below formula we will get NPV exactly equal to zero, it means BCR equals
to one.
IRR is always compare with a market rate of interest
for validate to use. In this case, IRR is 11.1251% and if market rate of
Interest is 12%, than project rejected. So, if IRR > rate of interest than
project is accepted otherwise rejected.
(e) Relationship
between NPV and IRR
To see the link between them, we put the values of
NPV for different discount rates on the vertical axis and the discount rate on
the horizontal axis.
The above figure shows when the interest increases from 10% to 15% NPV declines from 141.745 to -412.538 and When IRR equal to 11.1251 then NPV becomes zero.The IRR is the point at which the NPV profile crosses the x-axis. The slope of the NPV profile reflects how sensitive the project is to the changes in discount rate.
4. Findings
·
Looking present from future or future to
present or backward looking is discount rate. The discount rate is also called
the present worth factor where all the relevant costs and benefits are
expressed in monetary terms to convert them into a common metric.
·
NPV
is used in capital budgeting to analyze the profitability of a
projected investment or project. It tells the magnitude of the
project and takes into account the time value of money.The above results shows
that, the project with 10% discount rate is accepted because NPV (141.745) is
positive and profitable but we can't accept the project of 15% discount rate
due to the negativity of the NPV(-412.538).
·
BCR
is superior measure in the sense that it measures return in per unit of cost
but in the case of large investment projects BCR measure may not appropriate
because the lower investment project may have higher BCR. BCR is greater than
one (1.037) at 10% discount rate; the discounted benefits outweigh the
discounted costs, means the project results in net gains for the society. But due
to BCR less than one (0.887) from 15% discount rate is not acceptable.
·
IRR represents the average earning power
of the money used in the project over the project life. It is also sometime
called yield of the investment. IRR is the discount rate that sets NPV = 0 and
BCR = 1. From the computation of the above given cost and benefit stream with
10% and 15% discount rate we get IRR equal to 11.1251. If we plot
this discount rate (IRR=11.1251) on the below formula we will get BCR exactly
equal to zero, it means BCR equals to one. IRR is always compare with a market rate of interest
for validate to use. In this case, IRR is 11.1251% and if market rate of
Interest is 12%, than project rejected. So, if IRR > rate of Interest than
project is accepted otherwise rejected.
5. Conclusion
NPV is a measure of the absolute welfare
gain over the whole life of the project. The key determinants of the
NPV calculation are the appraisal horizon, the discount rate and the accuracy
of estimates for costs and benefits.
Relative measure of benefit which
indicates the capacity of the project to generate the benefit is BCR. The
choice of an appropriate discount rate is a main limitation of BCR. Once an
appropriate discount rate is provided, the BCR is a better guide for investment
decision compared to the NPV criterion.
IRR approach
is mostly used by financial managers as it is expressed in percentage form and
excellent guidance on a project’s value and associated risk with an advantage of knowing the actual
returns of the money which you invested today. If discount rate for the project
changes every year then, it is difficult to make such comparison.
Economies of scale, reinvestment rate, dependent or contingent project, mutually exclusive projects, different duration of the project, a mix of positive and negative future cash flows etc. are the basic limitations of the NPV, BCR and IRR calculation method. From the careful observation over these limitations provide guidelines for the valuation of costs and benefits by using different several criteria for project evaluation.
References
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09, 2016.
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S. (1998). "Public Investment: Some Measuring Instruments".
Tribhuvan University Journal. Vol XXI-2. pg 35-46. Central Department of
Economics, TU, Kirtipur
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