Introduction

Floriculture in Mexico has grown based on the introduction of new crops such as anthurium, which being originally from Colombia (^{Buldewo et al., 2002}) has found suitable environmental conditions for its establishment in the central region of the state of Veracruz, this tropical ornamental crop has a growing international demand and a good purchase price per floral stem, by their attractive colors (Kamemoto, 1988) and long vase life (^{Islam, 2013}). In Mexico no official statistics are available on anthurium production (SIAP, 2013), however, Murguia et al. (2000) indicate that there are 10 hectares in the state of Veracruz alone, spread into small production units mostly familiar and with low level of technification.

The high cost of mesh shade and plants have limited the crop extension. Investing is defined as the act of incurring in an immediate cost in the hope of obtaining future profits (^{Dixit and Pindyck, 1994}). One of the biggest problems presented in project study and evaluation, is to economically justify the investment of resources in a project facing high volatility and uncertainty conditions (^{Garrido et al., 2010}), ignoring that conditions change over time (^{Domínguez, 2010}).

This is why viable project implementation is required the traditional assessment has limitations when evaluating a project solely under this methodology. There are alternative techniques that are directly related to project administration and management (^{Bacchini, 2007}). The real options theory (^{Myers, 1977}) enables project evaluation and give an approximation of the flexibility value of a project, allowing the evaluator to numerically capture the strategy value (^{Trigeorgis, 1996}; ^{Garrido and Andalaft 2003}).Areal option is present in an investment project, when there is a future possibility of action after solving some current uncertainty (^{Amram and Kulatilaka, 2000}).

In order to determine the economic viability of establishing an anthurium plantation in Cuitláhuac, Veracruz, methodological differences between traditional and real options theories were analyzed, using the binomial model, which is based on simple criteria derived from the use of equivalent portfolios and principles of behavior of arbitration models. Subsequently, the investment project was evaluated, were profitability indicators as NPV, B/C, N/K, IRR and sensitivity analysis were determined. Finally the project was evaluated using traditional techniques and the real options approach to identify its limitations and thus obtain the real value of the investment project taking into account the risk factor.

Then the following concepts for option valuation are listed below:

Value of the underlying asset: in this case the underlying asset is the project itself, where the present value of the project is the present value of expected cash flow to start the project now, which amounts to $ 132 986 (NPV).

Exercise price: this is the cost of expansion, which amounts to $ 520 117.25 and equals 100% of the investment project, i.e. equivalent to setting another production unit.

Variance in the assets value: factors with high volatility, cause uncertainty in estimates of cash flows and therefore in the present value of the underlying asset value. For this project, the anthurium price was considered as the major risk factor.

Expiration date of the option: the period during which the option is viable, being 10 years and may be exercised at any time during the year.

Risk-free rate: this is the annual risk-free rate and is calculated as follows:

CETES: is the interest rate paid by treasury certificates, n ^e : is the expected inflation r: is the real interest rate. CETES after 28 days from the day June 21^st, 2011 amounted to 4.35 and expected inflation was equal to 3.5. With these data, the risk-free rate is calculated as follow: 1.0435/1.001225=1+r; r= 4.22%

The values of the u, d, p and q variables must be calculated.

U= is the coefficient of increase in the value of the underlying asset and is calculated as follows:

d= is the coefficient of decrease in the value of the underlying asset, i.e., measures the amplitude of the asset variation.

p= is the risk neutral probability, the calculation is as follows.

q= (1- p)= 1 - 0.4447574971= 0.555242502

To calculate the probability of each outcome occurring last year, and then obtain the expected value of the project last year, the following formula is required:

Where: T= 10; n= 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 (it is the node number, starting with the top node). p= 0.579474366; 1-p = 0.420525633.

Project evaluation: expansion option

Given this scenario, a 100% expansion is intended for anthurium production. The current value of the investment is $ 132 986.04 (underlying asset value) may rise up to $203 289.39 after a year, if all goes well. If expectations are not met that value could fall to $ 86 995.62. The probability that all is well is p_u= 0.444757497. In this way the calculations are performed up to the 10 period.

Based on the binomial tree of the project value (Figure 1a), we proceed to enhance the calculation of the expansion option. This calculation is performed in two steps, the first is the calculation of the terminal nodes and the second is the calculation of the intermediate nodes to reach the initial node having a value of $ 169 209.26 (Figure 1b ).

Figure 1. Construction of the binomial tree on the data generated by the project: a) overall and for the options of; b) expansion; c) contraction; d) abandonment; and e) strategic, elaboration with own data 

The first step is to calculate the expansion value of the terminal nodes, which is equivalent to increasing 100% the existing capacity less the expansion costs. An example of calculating the expansion value of a terminal node would be the AAD node, which has a value of $ 18 011 900.59 which are obtained from maximizing the value of the expansion option, which is: [2(9 266 008.92) -520 117.25] = $18 011 900.59, versus continue unchanged for the AAD node. In this manner all the expansion values of the terminal nodes are obtained where in some cases the option that maximizes the node value (profits), is to continue with existing operations only.

The AT node has a value of $ 11 624 484.91, at this point there are two options, expand operations or keep the expansion option open for the future, with the hope that market conditions will improve, and the company will have the opportunity to exercise the option and thereby increase its operations in 100%. In this node the expansion value is [2(6 061 554.95) - 520 117.25]= $ 11 602 992.65; however, the value of continuing with the open option is [p (18 011 900.59) + (1-p) (7 410 470.50)*= $11 624 484.91; which is higher than the expansion value. Through the backward induction technique the value of the initial node is estimated at $ 169 209.26, which represents the NPV, and the difference between this and the value obtained using the discounted cash flow is the value of the expansion option, which for this event is: $ 36 223.23.

Project evaluation: contraction option

The only argument that changes is the exercise price, which now stands at $ 53 791.73, representing 50% of total variable costs of the project, since it is thought to contract 50% of operations. First, terminal nodes are calculated choosing the option that maximizes the project profits. The terminal AAD node has a value of $ 9 266 008.92 obtained from maximizing the option value to continue only the existing operations, contrary to exercise the contraction option, because if the company decides to contract operations, the result would be [ (0.5) (9 266 008.92) + 53 791.73= $4 686 796.19 for the ADD node, which is less than the option of continuing with existing operations only. In the terminal AAJ node there is a value obtained by maximizing the value of the contraction option, which is [ (0.5)( 56,910.02) + 53 791.73]= $82 246.74, versus continue unchanged for the AAJ node, thus the option for maximizing profits is to contract the company's operations.

The second step in calculating the value of the contraction option is calculate intermediate nodes, for example, the AT intermediate node has a value of $ 6 061 554.95. At this point the company has two options to choose from, contract the operations or keep the contraction option thereby minimizing losses. Performing these calculations backwards to the starting node, a value of $ 147 894.73 is obtained, the difference between this value and the value obtained through the discounted cash flow ($ 132 986.04) which is $ 14 908.69, is the value of the contraction option.

Project evaluation: abandonment option

The only argument that changes is the exercise price, which now stands at $ 68 054 (representing the salvage or rescue value of the project). In the abandonment option, the exercise price is the liquidation value of the project and for this specific project will be the salvage value of fixed investment, which may be recovered in case the project value falls below the liquidation value, which is $ 68 054.

In Figure 1c, after 10 years, the company has the option to abandon or continue the project the value of continuing can be seen in the AAD, AAE, AAF, AAG, AAH and AAI nodes, where the profit-maximizing decision indicates continuing. The abandonment value occurs in the AAJ, AAK, AAL, AAM and AAN nodes, since they are below the salvage value: $ 68 054.

The second step in calculating the value of the abandonment option is to calculate the intermediate nodes, for example, in the AT intermediate node there is a value of $ 6 061 554.95, higher than the salvage value, therefore in this node the right choice is to continue.

Project evaluation: strategic option

Another option that could be valuable for this project of anthurium production is the strategic option, where the company has the choice of : a) expand current operations in 100% , with an implementation cost of $ 520 117.25; b) contracting operations by 50%, meaning additional savings of$ 53 791.73; c) completely abandon operations sometime within the next 10 years, which would recover the salvage value of $ 68 054; and d) continue without changes, the calculation of value for this option uses almost the same arguments as in the expansion, contraction and abandonment options, where the only argument that changes is the exercise price, which will now be selected from the options enumerated above.

In order to obtain the new project value (expanded NPV) and the value of the strategic option with the real options approach, the binomial method is used with the project value (Figure 1a) and proceed to calculate the value of strategic option for which it is noted that the AAD terminal node has a value of $ 18 011 900.59, obtained from maximizing the expansion, contraction, abandonment and continue unchanged options. At the end of the 10 years, the company has the option to choose how to continue through these operations. In the AAD node the expansion value is [2(9 266 008.92) - 520,117.25] = $18 011 900.59; the contraction value is [ (0.5) (9 266 008.92) + 53 791.73]= $4 686 796.19; the value of the abandonment option is $ 68 054 and finally the value of continuing existing operations is $ 9 266 008.92. Therefore the decision that maximizes profits is to expand operations in the AAD node.

The value of the strategic option is not equal to the sum of the individual options, the reason for this is that a company can never contract and expand its operations at the same time on the same node, on the other hand, in this project and particularly the contraction option excludes the abandonment option, thus with the strategic option and using the binomial method the interaction of the different operation types can be captured.

The establishment of an anthurium plantation in Cuitláhuac, Veracruz, is justified by being a tropical crop (^{Buldewo et al., 2002}) and by the local conditions, good quality production is feasible throughout the year which guarantees a good market price (Kamemoto, 1988), the economic assessment has shown that the project is viable and guarantees options in the implementation and can be expanded, contracted or abandoned as needed according to the interests of the company members (^{Garrido et al., 2010}), which would be ensuring the investment and obtaining long-term profits (^{Dixit and Pindyck, 1994}). The real options methodology enables the analysis and evaluation of the investment project, which shows significant differences in NPV with and without flexibility.

Conclusions

Following indicators obtained with traditional evaluation, the anthurium project is financially viable and profitable for establishment in Cuitláhuac, Veracruz, however, this methodology assumes an investment opportunity project, i.e, unable to incorporate either uncertainty or managerial flexibility in decision-making.

The company has the option to expand operations in 100%, thus increasing NPV from $132 986.04 to $169 209.26, where the difference is the value of the expansion option. Conversely, contracting operations by 50%, would change the NPV from $132 986.04 to $147 894.73, where the difference is the value of the contraction option. The option of completely abandoning operations is available if market conditions make the project unprofitable, then the NPV would increase from $132 986.04 to $145 798.53 where the difference represents the value ofthe abandonment option.