COST-BENEFIT ANALYSIS NPV 1 Flashcards
is the most important criterion for the financial and the economic evaluation
project’s net present value (NPV)
If incremental NPV is positive.
then this project at scale 2 is preferable to scale 1
This procedure (scale increase) is repeated until a scale is reached where the NPV of the
incremental benefits and costs associated with a change in scale are negative.
If the initial scale of the project had a negative NPV, but all the subsequent incremental net present values for changes of scale were positive,
It still would be possible for the overall project to have a negative NPV.
assuming that each successive increment of investment has a unique IRR. If this condition is met, then the optimum scale for the facility will be the one at which the IRR
for the incremental benefits and costs equal to the discount rate used to calculate the net present value of the project
the scale at which the IRR is always maximized
The scale where the IRR=MIRR
maximum net present value
where IRR is equal to the discount rate called MIRR
becomes particularly difficult for large indivisible projects such as infrastructure investments in roads, water systems, and electric generation facilities.
The decision about an appropriate time to start
If these projects are built too soon, a
a large amount of idle capacity will exist
a large amount of idle capacity will exist
In such cases, the foregone return (that would have been realized if these funds had been invested elsewhere) might be larger in value than the benefits gained in the first few years of the project’s life
Whenever the project is undertaken too early or too late
The NPV of such projects may still be positive but it will not be at its maximum
The determination of the correct timing of investment projects will be a function of
how future benefits and costs are anticipated to move in relation to their present values.
In Case A, the project should be postponed
If the present value of the benefits that are lost by postponing the start of the project from time period t to t+1 is less than the opportunity cost of capital multiplied by the present value of capital costs as of period t.
because the funds would earn more in the capital market than if they were used to start the
project.
then the project should proceed.
if the foregone benefits are greater than the opportunity cost of the investment.
Case A: Potential Benefits are a Rising Function of Calendar Time
rKt > Bt+1 ⇒ Postpone
rKt < Bt+1 ⇒ Start
Case B: Both Investment Costs and Benefits are a Function of Calendar Time
rKt > Bt+1 + (Kt+1 – Kt) ⇒ Postpone
rKt < Bt+1 + (Kt+1 – Kt) ⇒ Start
The term, (K1-K0), represents the
savings of the increase in capital costs by commencing the project in t0 instead of t1
could be abandoned at some point in time with the result that a
the one-time benefit is generated, equal to its scrap value,
five special cases regarding scrap value and change in scrap value of a project
SV > 0 and ∆SV < 0 SV > 0 but ∆SV > 0 SV < 0 but ∆SV = 0 SV < 0 but ∆SV > 0 SV < 0 and ∆SV < 0
SV > 0 and ∆SV < 0
SV > 0 but ∆SV > 0
machinery;
Land
SV < 0 but ∆SV = 0
SV < 0 but ∆SV > 0
SV < 0 and ∆SV < 0
a nuclear plant;
severance pay for workers
Clean-up costs
Case C: Potential Benefits Rise and Decline According to Calendar Time
Stop if rSVtn – Btn+1 – ∆SVtn+1 > 0
Start if rKt < Bt
it is necessary to consider the length of life of the two
or more projects.
If the mutually exclusive projects are expected to have
continuous high returns over time
The reason for wanting to ensure that mutually exclusive projects are compared over the same span of time is to
give them the same opportunity to accumulate
value over time,
Economic rent that give fixed factor of production
The reason for wanting to ensure that mutually exclusive projects are compared over the same span of time is to
give them the same opportunity to accumulate
value over time,
Economic rent that earned by fixed factor of production
An increase in the scale of a project will
require additional expenditures and will
likely generate additional expected benefits
when the project is viable?
present value of (B1 - C1) is positive
The NPV is the maximum because the
incremental NPV for any addition to the scale of the project would be negative
Therefore, in order to pick the optimum scale for a project, first, we must make sure that the NPV of the overall project is X and then the NPV of the last addition to the investment to increase
project’s scale must also be
positive
non-negative
the MIRR from incremental investments will initially rise as the scale is increased,
but will soon begin to fall with further expansions.
This path of the MIRR will also cause
the IRR to rise for the initial ranges of scale and then to fall.
At some point, the IRR and the MIRR must be
equal and then change their relationship to each other
at the scale that MIRR is less than IRR: in this range,
expansions of scale will cause the overall IRR to FALL
The scale where the IRR=MIRR is
always the scale at which the IRR is maximized
Optimum scale
when the relevant discount rate is precisely equal to the maximum IRR (NPV) is maximum
if a project is delayed too long, then
shortages of goods or services will persist and the output foregone will be greater than the alternative yield of the funds involved.
The situations where timing of investment projects becomes an important issue
a) The benefits of the project are a continuously rising function of calendar time, but investment costs are independent of calendar time.
b) The benefits and investment costs of the project are rising with calendar time.
c) The benefits are rising and then declining with calendar time while the investment costs are a function of calendar time.
d) The benefits and investment do not change systematically with calendar time
The benefits of the project are a continuously rising function of calendar time, but investment costs are independent of calendar time.
benefits net of operating costs are continuously rising through time and costs do not depend on calendar time.
Ex: the benefits of a road improvement
The benefits of the project are a continuously rising function of calendar time, but investment costs are independent of calendar time. If project POSTPONE then
lost benefits but the same capital in alternative uses yields rK, where K denotes the initial capital expenditure and r denotes the opportunity cost of capital for one period.
NET gain or benefits
net gain of AIDC
net benefit of CDE
