Principles of cost-benefit analysis: the basics Most activities lead to costs and benefits. From an.

Principles of cost-benefit analysis: the basics Most
activities lead to costs and benefits. From an economic perspective, it is
assumed that an activity is only undertaken if the total benefits exceed the
costs.

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We call such activity a ‘project’. When is a project
attractive in economic terms? Cost-benefit analysis is complicated by the time
preference of money. Most people and organisations would rather receive a
certain sum of money now instead of next year. Time preference makes it
impossible to simply add and subtract the money inflows and outflows associated
with a project, when they occur at different points in time. We solve this
problem as follows. If someone does not care whether they receive US$100 now or
US$108 a year from now, it is said that the time preference can be expressed by
a discount rate of 8 per cent. More generally, if someone has a time preference
that can be expressed by a discount rate r, they are indifferent about
receiving an amount of x now or an amount of x (1 + r)n in n years
from now. Expressed similarly, an amount x received n years from now currently
has a so-called present value x/(1 + r)n . Using this indifference we
can now convert all current and future expenditures and receivables to the
present situation and count them together. We call this the net present value
of the project:

where:

NPV = net present value of the project at the beginning
of the first year (t = 0) Bi = benefits of the project in year i Ci
= costs of the project in year i (at the beginning of the project (t = 0) this
could include an initial investment I) r = discount rate n = lifetime of the
project

A project is considered to be attractive if the net
present value is positive. Many activities consist of an initial investment,
followed by a constant annual net benefit. In that case, calculating the net
present value as presented in equation [11.1] is highly simplified, and we can
introduce a capital recovery factor α that is a function of the discount
rate and the lifetime of the project:

where:

I = initial investment

B = annual benefits

C = annual costs (excluding capital costs)

α = capital recovery factor

r = discount rate

n = life time or depreciation period of the equipment

Note that in this representation it is assumed that
annual benefits B and annual costs C are constant throughout the lifetime of
the project. An overview of capital recovery factors is given in Table 11.1.
Note that at high discount rates the length of the project lifetime is less
relevant, and for long lifetimes α approaches the discount rate. A series
of constant future costs C and benefits B can be made present by dividing the
annual values by the capital recovery factor α. In many cases, however, we
are interested in the opposite problem. We want to know how an initial
investment translates to annual costs during a series of years. In that case
the initial investment can be converted to constant annual capital costs by
multiplying it by α. The result α∙I represents the total annual
expenditure needed for interest and depreciation. A well-known application of
cost-benefit analysis in the energy field is the calculation of the levelised
costs-of-energy, LCOE. This concept is widely used, for example, as a tool for
comparing the costs of different electric power generation technologies. The
LCOE is the (cost) price of the energy carrier produced for which the discounted
costs are compensated by the discounted benefits, throughout the lifetime of
the project. It is found by setting NPV to zero in equations [11.1] or [11.2a].
For the simplifed case where all costs and benefits are constant each year the
expression for the levelised cost-of-energy becomes:

where:

LCOE = levelised costs of energy (e.g. euro per kWh or
MWh of electricity produced) α = capital recovery factor I = initial
investment OM = annual costs of operation and maintenance F = annual fuel costs
E = annual energy production (electricity for example).

 

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