1) Projects implemented in multiple stages must decide whether to anticipate infrastructure for future stages. Anticipating can reduce total capital expenditures (CapEx) but increases upfront costs. 2) A general rule was deduced to evaluate the decision: compare the present value (PV) of the integrated infrastructure option versus the non-integrated option. 3) The rule shows the PV comparison depends on how much capital is anticipated (β), the total CapEx savings from integrating (α), and the time between stages (N). If N is less than the break-even period, anticipating infrastructure maximizes NPV and IRR.

1. Decision criterion for anticipation of the infrastructure in staged projects
Tito Livio M. Cardoso
São Paulo, Brazil, 24-Oct-2018
Projects that will be deployed in multiple stages always go through an important discussion to define the scope of
implementation of the first stage: anticipate or not, the investment in infrastructure for the following stages?
In general, the option to anticipate results in a total CapEx, of the two stages, smaller, for example, deploying in the first
stage all the earthworks and civil works for pump station, water treatment, drainage and secondary substations, leaving
to the next stage only the equipment and distribution lines. The same case occurs in the anticipation of the civilian base
of transporters, or construction of the mill building that will house the mills of the 2 stages, for example. In this option
the infra will be integrated, that is, 100% shared between the production lines at the end of the 2nd stage.
The alternative of not anticipating anything produces a non-integrated infra-scope, where each deployment stage
includes a complete infrastructure, with a smaller size that corresponds only to the need associated with the productive
capacity of a stage. This approach, while not minimizing and CapEx below the two stages, should produce a smaller
CapEx for the 1st stage and present greater layout flexibility since the non-shared structures need not be adjacent.
This decision on the option to adopt is decisive for the engineering project and different managers stand in a
controversial way on the subject. In recent work, a manager has asserted himself on the integrated infrastructure
option: "If it is known to have expansion, it is absurd to make a 'cast' project that makes the company spend more if it
wants to expand." Another manager has already achieved a significant CapEx reduction by eliminating all anticipation of
infra for the 2nd stage and argues that this decision maximizes the NPV of the project. Who's right?
Answer: It depends...
It depends on:
 Additional investment in Stage 1 to advance in integrated infrastructure option
 "Saving", i.e. the total cost reduction (along of the all stages) on the integrated infrastructure option
 When will be the construction of stage 2
t = 0 t = 6 years
CapEx in infra
= US$ 200 M
CapEx in infra
= US$ 200 M
Stage 1
Cap. Total:
15 MTPY
Stage 2
Cap. Total:
30 MTPY
t = 40 years
A) Example, without infrastructure
anticipation.
t = 0 t = 6 years
CapEx in infra
= US$ 240 M
CapEx in infra
= US$ 120 M
Stage 1
Cap. Total:
15 MTPY
Stage 2
Cap. Total:
30 MTPY
t = 40 years
B) Example, with infrastructure
anticipation.

2. The company can always carry out another investment with the capital that would be immobilized in the integrated
infra-option. This alternative investment may monetize more than the larger CapEx total difference in the non-
integrated option if sufficient time is given. That is, for the same project, the integrated option can add or disaggregate
value depending on the time interval between the implementation of each stage. Like any decision-making process in
industrial projects, we need to calculate the present value of each option to identify the one that maximizes value to our
particular case.
Next we will deduce a general rule that supports the decision between anticipating or not the investment in an
integrated infrastructure for projects implemented in two stages. Let's assume that the total OpEx will be approximately
the same, with or without integrated infrastructure.
1) Option model without integration, i.e., identical and individual infrastructures for each stage:
The total investment without integration, ITSI, is the investment bro to implement the individual infra of each stage, ITSI
= 2 x ISI. That is, we invested ISI in year zero (today) and asaving ISI in year N. If the 2nd stage will be implemented in
year N, the Present Value of this investment will be:
1
1
(1 )
SI N
VPI ISI
i
 
    
Where i is the annual interest rate that discounts the capital invested in year N.
2) Model integrated option, i.e., common infrastructure in anticipation of Stage 1:
The total investment with integration, ITCI, presents the saving  in relation to the non-integrated option:
ITCI = (1-) ITSI = 2 (1-) ISI
In practice  is between 20% and 40%. Investments in the infra stage 1 and 2 will no longer be the same. Integration
investment, ICI, in stage 1 is greater. Be  (0.5 to 1.0) as the ratio of the total integration with infrastructure
investment, ITCI is disbursed in the 1st stage, ie as is "d anticipates the" capex below common to both stages. What
remains for the stage 2 is the residual investment (1-) of the total with integration:
ICI (t=0) = . ITCI = 2 (1-) ISI  Integrated infrastructure investment in stage 1
ICI (t=N) = (1-) ITCI = 2 (1-) (1-) ISI  Integrated infrastructure investment in stage 2
The Present Value of this investment, VPICI, will be:

3.  
 
ISI
i
VPI
i
ICI
ICIVPI
NCI
N
Nt
tCI










 

1
)1(
)1(2
1
)(
)0(


3) Decision criterion on anticipation in integrated infra:
Whenever the present value of the integrated option is greater than the present value of the option without
anticipation, anticipating the infra destroys project value (reduces NPV and IRR).
since ISI is common to both sides of the inequality, it disappears, leaving only the three variables we cited before
deducing the criterion for decision making: the anticipated capital in the integrated option (), the saving in CapEx total
in the integrated option () and the time interval between the two stages (N).
An important, and somewhat obscure, conclusion of this deduction is that the decision criterion is independent of the
size of the investment or plant capacity, and is applicable to mega-projects for billions or small projects.
Example:
As a quick example of applying this criterion, suppose a project for plant deployment in 2 stages of the same capacity.
CapEx design is US$ 800 million being US$ 160 million on the shared infrastructure to be deployed in the 1st stage,
leaving only US$ 8 million in the 2nd stage deployment. The option without anticipation would result in the
implementation of independent infrastructure at an estimated cost of US$ 13 million in each stage. So, the option of
anticipating the infrastructure presents savings of US$ 20 million in total CapEx. The anticipation without option reduces
US$ 30 million of CapEx for Stage 1 but increases by US$ 5 million in Stage 2.
Applying the criterion presented for = 0.077 and = 0.667, calculated by the reported values, and adopting an
opportunity cost i = 10% per year (typical), we find that N = 4 years is the interval between the implementation of 2
stages that equals the present values of the two options. Conclusion:
 If N < 4 years, the option to anticipate the infra common to both stages is the one that reduces the VPI,
therefore, maximizes the NPV and IRR.
   
valoragreganãoAntecipar
1
)1(
)1(2
1
1
1 
















NN
CISI
ii
VPIVPI

 Anticipate does not add value

4.  If N> 4 years, it is best left to expand the infra at the time of the implementation of stage 2, because the
profitability of the capital not immobilized in the anticipation of the infra surpasses the economy that would be
obtained with the anticipation of the infra.
i = 10%
ALPHA = 0.077
BETA = 0.667
N
Without
Integration With integration
1+1/(1+i)N 2(1-)[+(1-)/(1+i)N
]
1 1,91 1,79
2 1,83 1,74
3 1,75 1,69
4 1,68 1,65
5 1,62 1,61
6 1,56 1,58
7 1,51 1,55
8 1,47 1,52
9 1,42 1,49
10 1,39 1,47
It is important to note that the time to when the best decision is by anticipating the scope of the next stage is very
sensitive to the relationship between the volume of capital anticipated and the savings that will be obtained with it.