Notesale: Turn your study into money

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BENEFIT-COST ANALYSIS
(Review)
Social benefit-cost analysis is a process of identifying, measuring and comparing the social
benefits and costs of an investment project or program
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For example, a private
project may pay taxes, provide employment for the otherwise unemployed, and generate
pollution
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Social benefit-cost analysis is used to appraise private
projects from a social viewpoint as well as to appraise public projects
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The benefit of the project is measured as the value of the extra electricity produced by the dam
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(We use the word “appraise” in a
prospective sense, referring to the process of actually deciding whether resources are to be
allocated to the project or not
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The benefit of the project is the value of this increase in the future supply
of electricity over and above what it would have been in the absence of the project
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We assume
that these factors of production could have produced output (not necessarily food) valued at $Y
in some alternative and unspecified uses, but in a competitive and undistorted market the value
of additional inputs will be bid up to the level of the value of the additional output they can
produce
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F igu re 1
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In other words, a project does not have to constitute what is termed a
Pareto improvement (a situation in which at least some people are better off and no one is
worse off as a result of undertaking the project) to add to economic welfare, but merely a
potential Pareto improvement
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The problem with this view
is that transfers are normally accomplished by means of taxes or charges which distort economic
behavior and impose costs on the economy
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When we compute present values for use in a social benefit-cost analysis we need to make a
decision about the appropriate rate of discount
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In other words, in using a market rate of interest as the discount rate, the current generation is
making decisions about the distribution of consumption flows over time without necessarily
consulting the interests of future generations
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In summary, the hypothetical project (or any other project) can be appraised from four different
points of view:
(i) the project benefit-cost analysis: this is represented by Area A+B and is obtained by valuing
all project inputs and outputs at private market prices;
(ii) the private benefit-cost analysis: this is obtained by netting out tax and interest and debt
flows from the project appraisal, and, if the firm’s equity holders are not part of the referent
group as in our example illustrated in Figure 1
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In our example, the
non-referent group net benefits are summarized by the private appraisal (Area B), although in
other cases the private project owners may be part of the referent group
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1
...
1
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The spreadsheet is developed in five parts in the following order:
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(i) a data section containing all relevant information about the project – costs, outputs, prices, tax
rates etc
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All the entries in the remaining four parts of the spreadsheet consist of references to the
data in this first section;
(ii) a section containing the project benefit-cost analysis;
(iii) a section containing the private benefit-cost analysis;
(iv) a section containing the efficiency benefit-cost analysis;
(v) a section containing the referent group benefit-cost analysis
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The economy would be working efficiently in the sense that no reallocation of scarce
resources could make anyone better off without making someone else worse off to a greater
degree
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Identifying winners and losers, cost benefits for both parties, here is the example:
A proposed new airport will benefit air travelers but will inflict costs on residents in the
vicinity of the proposed site
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The role of the decision-maker is then to determine whether X dollars worth of gain for one
group justifies Y dollars worth of pain for another
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We would like you to do a benefit-cost analysis
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In the process of this meeting it may emerge that all
these questions have been carefully considered and that in fact the proposed project design is the
best option
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Benefit-cost analysis is a tool to support current decisions rather than for assessing their
performance in implementing past decisions
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Investment Appraisals: Principles
Investment Appraisals from a personal Point of View
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Saving- refraining from consumption so that scarce resources are freed up for a use other
than producing goods for current consumption;
Investing – the process of using scarce resources to produce goods for future
consumption
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“Time value of money “– dollars at different times cannot be directly compared
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Internal rate of return- (BC-AC)/AC, is the marginal productivity less 1, which we denote as
rp
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Present Value- BC/(1+r) , AC is the opportunity cost , r – discount rate
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*If NPV is positive we take the project, otherwise we don’t
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Inter-temporal Production Possibilities curve ( IPPC) - starts at the consumption combination
which would occur if no investment were undertaken in the current year
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[(1+r)n – 1]/[(1+r)n
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+ B/(1+r)n,
Annuity due- has the same net of streams but the costs are accrued in the beginning of the years
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+ B/(1+r)n–1
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If we take the limit of PV(A) as n goes to infinity
we get PV(P) = B/r
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When we include the initial capital cost of the project in the net benefit stream and use a discount
rate reflecting the opportunity cost of capital we are taking full account of the cost of capital
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The existence of inflation raises the question of whether project inputs and outputs should be
measured at the prices in force at the time of the appraisal– constant prices – or at the prices in
force when the project input or output occurs – current prices
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Real rate of interest = Money rate- inflation rate
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CH #3- INVESTMENT APPRAISAL: DECISION-RULES
Discounted Cash Flow Analysis in Practice
Mechanical calculations can now be performed at will, which has theenormous advantage
of allowing more project options and alternative scenarios to be consideredthan ever before
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Common to all DCF analysis is the conceptualization of an investment project as a net
benefit stream as measured by a “cash flow”
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When resources (funds) are given up now, as investment
outlays, the “cash flow” negative indicates that there is a net outflow of funds
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The process of project appraisal and evaluation can be considered in terms of three aspects of
cash flow analysis:
1
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Valuation of costs and benefits
3
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Discounting and the Time Value of Money
There is a need for discounting when comparing any flow of funds (costs and revenues or
benefits) over time
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The net cash flows of these projects are given as:
Year

0

1

2

3

Project A

–100

+50

+40

+30

Project B

–100

+30

+45

+50

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If project years are also calendar years, then all costs and benefits accruing during that year are
assumed to accrue on 31 December of that year
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e
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Similarly, “year 2” refers to two years from year 0, and so on
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It could be a quarter, month, week
or day – the same principles hold whatever the time period used, but then of course the (annual)
discount rate would have to be adjusted accordingly
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Which would you prefer? A and B both havetotal costs
of $100, but A’s benefits total $120 while B’s benefits total $125
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We need to discount all future
values to derive their equivalent present values
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What is the present value (PV) of $100 a year from now assuming a
discount rate of 10% per annum?
PV = $100 × 1/1
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909) = $90
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909” in this example is the discount factor
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Using Annuity Tables
When an investment project produces a cash flow with a regular or constant amount in each year
it is possible to calculate the present value of this stream more easily using an Annuity Table
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Annuity Tables can be used to calculate the PV of a stream of equal annual net benefits
occurring over a subset of consecutive years during a project’s life
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In this case
Annuity Tables can be used for years 5 to 10 and Discount Tables for other years
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A positive NPV value for a given project tells us that the project benefits are greater than its
costs, and vice versa
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The implicit assumption is that there is no budget constraint
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#4 PRIVATE BENEFIT COST ANALYSIS – FINANCIAL ANALYSIS
When a project is being evaluated by a private or public enterprise from a purely commercial or
‘private’ perspective, account is taken only of the benefits and costs of the project that accrue to
the enterprise itself and that affect its profitability
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Cash flows play a central role in the appraisal of any investment project, they are a summary of
various costs and benefits expected to accrue over the project’s life
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The length of the years is also called lifetime, planning horizon or time horizon
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Investments costs are: cost of construction and installation of physical assets, cost of building
up
stock
and
cost
of
training
the
staff
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Project benefits consist mainly of the value of the output produced by the project
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We assume that there is no inflation; we
estimate all costs and benefits throughout the project’s life at the price level obtaining at the time
of appraisal
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Then w compare
the project IRR with real cost of capital
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Changes in relative prices should not be ignored in the project appraisal and therefore should be
incorporated into our cash flow estimates
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Generally defined it is the difference between the net benefit flow with the new investment
and the net benefit flow without this investment
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page 67-69)
There are usually two forms of investment or capital cost: fixed investment and working
capital
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These costs appear as negative items in the cash flow
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A ‘golden rule’ in discounted cash flow analysis is that all investment costs should be recorded
in the cash flow only in the year in which the investment cost was actually incurred
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One method of calculating the annual depreciation is the straight line
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page 70)
When a project is first established and the stocks of working capital are first set up, the full
amount of the initial working capital will be recorded as an investment cost
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page 71)
All cash inflows and outflows relating to the debt financing of the project including the
disbursement and repayment of the loan itself, need to be incorporated into the cash flow
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*An example of calculating the return on total investment, cost of debt finance and return equity
can be found on page 75 of the book
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From a private investor’s standpoint, taxes paid to government are like any other
costs, to be deducted in deriving a net cash flow
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But as both of them appear in the accountant’s profit and loss
statement for the project, and therefore affect the project’s declared or taxable profits, we need to
perform a “side” calculation of the project’s taxable profits, applying the same conventions used
by the accountant
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The private analysis will be used to assess whether the project is attractive from a private point
of view and this will be determined by comparing the private IRR with the required rate of
return
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A range of discount rates is used for several reasons: first, in the private analysis, the firm’s
required rate of return on equity capital may not be known; second, there may be valid reasons
why the market rate of interest should be replaced by a shadow (or social) discount rate in the
efficiency or referent group analysis, and we don’t know what the rate should be; third, we want
to see how sensitive the NPV is to the choice of discount rate

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