An Empirical Approach to Risk Assesment

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

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

AbstractThis paper establishes an investment project's risk by usingestimated net profit variability, determined through theaverage net profit dispersion rate. Then, based on net cashflow variability, NPV variability, the level of risk isdetermined. NPV and its explanatory variables are modeledusing the Monte Carlo simulation and a pilot study todetermine the probability distribution to profit, costs andexpenses associated to cash flow. The social discount rate isused to counterbalance the IRR's fundamental re-investmentcase, since all the cash flow generated by a project mayactually be re-invested at a rate adjacent to the capital cost.

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.

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.

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).

The general expression to calculate NPV is:

NPV = initial investment + NCFt

1+Ka tEquation

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).

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 tEquation 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).

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.

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.

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).

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.

Cash Flow Structure Method of Calculation

Income from Services𝐼𝑛𝑐𝑜𝑚𝑒 =

𝑖=1

𝑛

(𝑑𝐻 ∗ 𝑑𝑎𝑦𝑠 ∗ 𝑣𝑎𝑙𝑢𝑒 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟)/(1 + 𝑡𝑑)𝑖

Direct Cost of Services𝐷. 𝐶𝑜𝑠𝑡 =

𝑖=1

𝑛

(𝑑𝐻 ∗ 𝑑𝑎𝑦𝑠 ∗ 𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟)/(1 + 𝑡𝑑)𝑖

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

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

Operating Margin -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

Gross Profit -60,226 -60,247 10,957 34,638 57,736 59,650 143,896 154,145 163,795

Taxes 0 0 0 0 0 0 0 0 0

Net Income -60,226 -60,247 10,957 34,638 57,736 59,650 143,896 154,145 163,795

Investment -370,622,6

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

Cash Flow -370,622,6 -10,690 -10,711 60,493 84,174 107,272 109,187 193,433 203,681 213,331

$0 $51.68051,0% 44,0% 5,0%

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8-$

80

00

0

-$ 6

00

00

-$ 4

00

00

-$ 2

00

00

$ 0

$ 2

00

00

$ 4

00

00

$ 6

00

00

$ 8

00

00

$ 1

000

00

Val

ue

s x

10

^-5

VPN US$

7,47% 12,22%5,0% 90,0% 5,0%

0

5

10

15

20

25

30

35

40

6%

7%

8%

9%

10%

11%

12%

13%

14%

TIR Mejorada US$

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%.

9,87%

$2

86

47,9%1,9%

47,1% 3,1%-$ 100000

-$ 50000

$ 0

$ 50000

$ 100000

$ 150000

5%

6%

7%

8%

9%

10

%

11

%

12

%

13

%

14

%

15

%

VP

N U

S$

TIRM %

VPN US$ vs TIRM%

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.

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.

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.