This document presents a risk assessment of an investment project to build a financial complex and business center at Tecnológico de Antioquia University. A Monte Carlo simulation was used to model the net present value and internal rate of return based on the variability of estimated cash flows. The simulation found a 44% chance that the NPV is between $0-51,680 and a 51% chance it is below $0, with an IRR between 7.47%-12.22%. While the financial assessment is positive, the project's main benefit is providing students, teachers and entrepreneurs experience with financial transactions, negotiations and simulations.

1. Grupo de Investigación
Facultad de Ciencias Administrativas y Económicas
Tecnológico de Antioquia I.U.
Rector: Lorenzo Portocarrero Sierra
Decana: María Jacinta Montoya
Líder grupo: Jorge A. Restrepo Morales

2. An Empirical Approach to Risk Assessment in
an Investment Project: Case Study "Financial
Complex and Business Center at Tecnológico de
Antioquia"
Jorge Aníbal Restrepo M.
Lorenzo Portocarrero Sierra
Julieth Fernanda Usme

3. Abstract
This paper establishes an investment project's risk by using
estimated net profit variability, determined through the
average net profit dispersion rate. Then, based on net cash
flow variability, NPV variability, the level of risk is
determined. NPV and its explanatory variables are modeled
using the Monte Carlo simulation and a pilot study to
determine the probability distribution to profit, costs and
expenses associated to cash flow. The social discount rate is
used to counterbalance the IRR's fundamental re-investment
case, since all the cash flow generated by a project may
actually be re-invested at a rate adjacent to the capital cost.

4. This paper is divided into four sections. The first one
focuses on reviewing the basic concepts and definitions for
the business center. The second one deals with a few factors
the project's financial evaluation should take into account,
and briefly describes ways to quantify risk. The third one
focuses on defining the model to use, and on analyzing pilot
study's consistency, as well as the data gathered. Finally, the
results are presented, along with some recommendations for
the investment project.

5. Institutional Development Plan.
Financial complex and business center was included in order to support academic
training for students, professors, and the community in general. They will get support
in everything related to stock-market management, understanding and operations;
portfolio valuation, business valuation, risk management, technical and fundamental
studies, accounting for operations in capital markets, and knowledge about operations
in the BVC (Colombia Stock Exchange) stock markets. The complex will have the
following three environments:
A Stock-Exchange Office or Business Room that will work under an arrangement with
Bolsa de Valores de Colombia —BVC—.
Trading Desk that will act as a financial laboratory for portfolio valuation. In addition,
the commodities mercantile exchange will work in this environment.
An Accounting Laboratory suitable for risks, technical analysis, business analysis and
valuation.

6. Net present value
The Net present value (NPV) method is one of the most widely used
economic criteria to assess investment projects. It is based on
determining, at the very beginning of the project, the equivalence of
future cash flows generated by a project, and comparing such
equivalence to the initial investment. The difference shall be the
additional (positive or negative) amount a project will add to (or
subtract from) the company's current value. If the project generates
(positive) value for the company, then the project is approved. If, on
the contrary, the NPV is negative, this means the project would destroy
the company's value, and it must be rejected (Bu, 1981).

7. The general expression to calculate NPV is:
NPV = initial investment +
NCFt
1+Ka t
Equation
Where:
NPV = Net Present Value
NCFt = Net Cash Flow for year t
Ka = Capital Cost
It is important to underline that capital cost used in this project will be the social
discount rate represented by the opportunity cost the country incurs when using its
resources to finance projects (Ministerio de Planificación, 2011). These resources
come from the following sources: lower consumption (more savings), lower private
investment, and the external sector. Therefore, it depends on the inter-temporal
reference rate of consumption, the marginal profitability of the private sector, and the
interest rate of foreign credits. For Colombia, it stands at 12% (Aldunate, 2006).

8. Internal rate of return
Internal Rate of Return (IRR) is defined as the annual percentage return generated by the
resources invested in a project. Formally, IRR can be defined as the rate of return (or
discount) that makes the NPV equal to $0.
The general expression to calculate IRR is:
NPV = I0 +
NCFt
1+Ka t
Equation 8.2
IRR is obtained when NPV = 0. Therefore:
0 = I0 +
NCFt
1+IRR t
Where: I0 = Initial Investment, and IRR = Internal Rate of Return
Both the IRR criterion and the NPV are techniques rooted in cash flows deducted from a
focal date, which is usually the very beginning of the project. Therefore, the results will
depend on a logical and correct application of the elements that make it up. In this
particular case, the most precise and concrete decision is achieved using the NPV, since it
implies no confusion (Restrepo, 2009).

9. For some analysts and executives, the IRR criterion is better than the NPV method, which
contests the assumption that the latter is easier to understand. They argue that a profitability
rate is an indicator that entails less complexity and greater understanding than a net amount
of money expressed in updated terms. However, because of the conflicts that arise as
compared to the NPV criterion, the IRR is not the most highly recommended criterion
when assessing a decision. The reason is, among other things, the possibility of multiple
rates, and the implicit assumption that profits are re-invested at the same internal rate of
return as the project has. These are the significant flaws of the method. Inexperienced
users, especially, may be thus misled in their decisions to invest (Bolten & Pérez, 1981).
In this paper, a Modified Internal Rate of Return (MIRR) is obtained. Thus, the IRR flaws
can be overcome. The method used for calculation solves the problem of multiple rates, as
well as the problem of having no solutions because there will always be an MIRR. The
MIRR method may be used for making financial economic decisions because it is a
universal method in its conception.

10. Applying Monte Carlo Simulation to the Assessment of Projects Using @Risk
Risk analysis may be defined as the systematic use of available information to establish how
frequently some events may take place, and the scale of consequences (Medina, S. &
Restrepo, J., 2013). It is normal to associate risk with negative events like losing money in
an investment. However, opportunities can be found in the risk analysis process because it
requires that all the possible results of a given situation be explored.
Risk Analysis with Monte Carlo Simulation (SM)
The restrictions posed by single point estimates are corrected by using a more robust and
refined quantitative risk analysis with Monte Carlo simulations (SM). The variables that are
random, or have a degree of uncertainty are incorporated into the model using their
probability distribution. It represents the values that the variables are likely to take. By using
probability distributions, the SM approaches reality to describe the uncertainty of the
variables in a risk analysis.

11. Probability distributions In business phenomena analyses, a wide variety of probability
distributions can be found. Below are described the distributions used in this study.Normal
distribution: it is one of the most thoroughly studied and widely used theoretical distributions in
practice. When the data are not normal, it is possible to transform them, or use other statistical
methods that do not require this kind of restrictions, such as the so-called non-parametric
methods (Pértegas Díaz & Pita Fernández, 2001). Uniform distribution: it is very versatile
because the analyst only needs to define the minimum and maximum values. Production costs,
revenue from the sales of a new product, inventory loss, among others, can be placed in this
category. Triangular distribution: it is very useful as an initial approach when the information
available is not reliable, or there is little information. This distribution is used in economics
when the subject under study involves analyzing the length of private projects using optimistic,
pessimistic, and most likely estimates (Olivares et al., 2009). The analyst defines the minimum,
maximum, and most likely values. PERT distribution: It is similar to triangular distribution.
Minimum, maximum, and most likely values are defined. In practice, the PERT method requires
that the analyst allocate three different values (time for tasks, cash flow for investors, etc.) to
optimistic, pessimistic and most likely scenarios (Pérez, 1998).

12. Project Risk It has been established that there is a risk factor when evaluating a project.
Therefore, one of the purposes when measuring risks is maximizing NPV or IRR expectation
(Tufféry, 1972). Below, an explanatory model is developed to calculate NPV and IRR
expectation. Since several risk sources co-exist in a project, for this paper's purposes, estimated
cash flow variability will be considered the most relevant risk. This implies that the rest of the
variables are considered risk-free: capital cost, service life, investment, etc.
NPV and IRR Probability Distribution NPV Distribution
For risk analysis, cash flows in a project feature a random behavior. This means that for a
thorough analysis, it is essential to know NVP’s probabilistic behavior. According to the Central
Limit Theorem (CLT), a linear combination of random variables has a normal distribution when
the number of variables tends to infinity. In general, a large number of events is needed for the
theorem to apply: a sample with n >=30 elements is considered large. For the NPV random
variable, the CLT can be applied because this variable is the result of adding random cash flows
updated to the current value.

13. Cash Flow Structure
Method of Calculation
𝑛
(𝑑𝐻 ∗ 𝑑𝑎𝑦𝑠 ∗ 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟)/(1 + 𝑡𝑑) 𝑖
𝐼𝑛𝑐𝑜𝑚𝑒 =
Income from Services
𝑖=1
𝑛
(𝑑𝐻 ∗ 𝑑𝑎𝑦𝑠 ∗ 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟)/(1 + 𝑡𝑑) 𝑖
𝐷. 𝐶𝑜𝑠𝑡 =
Direct Cost of Services
𝑖=1
Gross Margin
Income – Costs
Fixed Costs
5% of Income
Depreciation
Straight Line: 20 Years of Works; 5 Pieces of Equipment; 3 Computers
Operating Margin
Income – costs – fixed costs – depreciation
LIBOR Interest Rate Cost
It has a triangular distribution
Fixed Rate Deposit Cost
It has a triangular distribution
Gross Profit
Operating Margin – Interest Costs
Taxes
Net Income
Gross Profit – Taxes
Investment
It has a triangular distribution
Amortization
It is added because it is not an expense
Depreciation
It is added because it is not a disbursement
Cash Flow
Fi

14. Cash Flow Structure
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
Service Billing
246,811
266,876
594,142
709,208
832,797
867,437 1,273,739 1,327,362 1,383,335
Direct Cost of Service
192,733
208,402
463,962
553,817
650,326
677,377
994,655 1,036,529 1,080,238
Gross Margin
54,078
58,474
130,180
155,392
182,471
190,061
279,084
290,833
303,097
Fixed Costs
64,768
69,185
69,687
71,217
75,198
80,874
85,651
87,151
89,766
Depreciation
49,536
49,536
49,536
49,536
49,536
49,536
49,536
49,536
49,536
-60,226
-60,247
10,957
34,638
57,736
59,650
143,896
154,145
163,795
LIBOR
0
0
0
0
0
0
0
0
0
Fixed Rate Deposit Cost
0
0
0
0
0
0
0
0
0
-60,226
-60,247
10,957
34,638
57,736
59,650
143,896
154,145
163,795
0
0
0
0
0
0
0
0
0
-60,226
-60,247
10,957
34,638
57,736
59,650
143,896
154,145
163,795
Amortization
0
0
0
0
0
0
0
0
0
Depreciation
49,536
49,536
49,536
49,536
49,536
49,536
49,536
49,536
49,536
-10,690
-10,711
60,493
84,174
107,272
109,187
193,433
203,681
213,331
Operating Margin
Gross Profit
Taxes
Net Income
Investment
Cash Flow
-370,622,6
-370,622,6

15. $ 100000
$51.680
$ 80000
44,0%
$ 60000
$ 40000
$0
$ 20000
51,0%
$0
-$ 20000
-$ 40000
-$ 60000
-$ 80000
Values x 10^-5
1,8
5,0%
1,6
1,4
1,2
1,0
VPN US$
0,8
0,6
0,4
0,2
0,0

16. 5,0%
90,0%
7,47%
40
12,22%
5,0%
35
30
25
TIR Mejorada US$
20
15
10
5
14%
13%
12%
11%
10%
9%
8%
7%
6%
0

17. With a 44% confidence level, the NPV for the project stands
between 0 and 51,680 dollars for the evaluation period. There is a
51% chance for the value to be below 0. The minimum value
obtained from the simulation was US$ -76.482, and the maximum,
US$79.875. In turn, the IRR, with a 90% confidence level stood
between 7,47% and 12,22% for the period of evaluation.
There was a 5% chance for the value to be below 7,47. The
minimum value obtained from the simulation was 6,4%, and the
maximum, 13,3%.
The IRR and NPV dispersion chart Figure 2 shows that 47,9% of
the simulations got a NPV value above 0, and an IRR between 10%
and 15%. The NPV was negative 47,1% of the times, and the IRR
fluctuated between 5% and 10%.

18. 9,87%
$ 150000
1,9%
47,9%
$ 100000
$ 50000
$286
VPN US$
VPN US$ vs TIRM%
$0
-$ 50000
47,1%
3,1%
TIRM %
15%
14%
13%
12%
11%
10%
9%
8%
7%
6%
5%
-$ 100000

19. It is important to note that the project's total investment has a mean value of
US$370.774, a minimum value of US$343.475, and a maximum value of
US$400.126. It has a 95% chance of ranging between US$355.172 and
US$386.399; a 5% chance of being below US$355.172, and a 5% chance of being
above US$386.399.
With an investment of about US$370,000, which may generate an average NPV of
US$70,000, the institution's fundamental pillars of research, scope and teaching
will be enhanced. The reason is that the academic community, as well as importers
and exporters, are provided with technical and practical tools in the context of
international business for trade treaties and agreements between Colombia and
other countries around the globe.

20. Despite the fact that the financial assessment resulted in a positive balance from the
viewpoint of NPV and IRR, this initiative's relevance lies in the fact that students,
teachers and entrepreneurs will be able to carry out transactions, negotiations and
simulations to gain experience in real situations.
Specifically, students in financial programs will be able to work in stock fields such
as shares, fixed income products, derivatives, commodities, and the foreign exchange
market (Forex) around the world. Similarly, they will be able to assess companies,
analyze risks, execute econometric models, carry out forecasts and Monte Carlo
simulations with financial derivatives transactions, hedging, etc. In short, they will be
able to develop research projects in economics, finance and business.
International trade students will be able to carry out operations related to international
business exports, imports, logistics, tariffs, business transactions, exchange rates and
capital flow analyses.

21. Commercial management students will be able to develop business plans, business
ideas, incubation and post-incubation of production units, and modeling for the
creation of businesses. Likewise, they will be able to assess projects from an
economic, financial, environmental and social point of view.
For the community at large, entrepreneurs, and students, continuous entrepreneurial
consultancy is offered for small and medium-sized enterprises by the Technological
Unit of Entrepreneurship and Innovation (TUEI). The Trading Desk is an
environment in the TdeA Financial Complex. Its purpose is to create a working
environment similar to those in various stock markets such as investment funds
(hegde funds); commercial banks such as Citibank, Deutsche Bank, JP Morgan,
HSBC, Bank of America, etc.; central banks, brokers (financial intermediaries), and
financial institutions in general. The Trading Desk will rely on all the platforms and
tools needed to make decisions to invest in any financial market.