Franchising from a scarcity theory perspective

Starting from the optimization of costs associated with brand positioning and, of course, the increase in demand, the resource scarcity theory was one of the first attempts to explain the reason for the existence of franchising. ^{Oxenfeldt and Kelly (1969)} argue that companies decide to franchise to obtain resources that are scarce and, thus, achieve agile expansion in developing markets (^{Jang & Park, 2019}). Consequently, franchising is presented as an alternative for raising capital (^{Park & Jang, 2018}), especially for small and medium-sized enterprises that generally have difficulty accessing low-cost financing. In this way, companies can overcome capital resource constraints (^{Madanoglu, Castrogiovanni, & Kizildag, 2019}) and expand quickly since franchising requires a lower investment than opening their own point of sale. Thus, they will reach operational and production efficiency levels, which will make it possible, for example, to have better negotiations for raw materials, optimization in advertising expenses, and better access to financing. All of the above is because, as mentioned, the company is working in an already proven activity and with a recognized brand. These factors make it possible for the company to be more competitive and improve its profit margins, not only from the royalties obtained from the franchisee but also from the expansion of demand with the increase of the scope of action of the organization.

Franchising from an agency theory perspective

Another of the theories proposed for franchises is agency, defined as a contract in which the principal agrees with another person (the agent) to perform some activity or provide some service on their behalf. According to ^{Jensen and Meckling (1979)}, the above implies giving the agent a certain amount of authority to make decisions. Accordingly, a franchise can be seen as an agency contract where the franchisee takes the agent position, and the franchisor acts as the principal (^{Sanfelix & Puig, 2018}).

Since both the franchisor and the franchisee benefit economically from the contract, both parties to the relationship are utility maximizers. Thus, ^{Jensen and Meckling (1979)} suggest that there are sufficient reasons to believe that the agent will not always act in the principal's best interest since the agent will seek their own interest. For example, the franchisee could lower the quality of the product in order to increase its profit margin, thus creating the risk of brand deterioration that would affect the franchisor and the other franchisees. However, the benefit on the profit margin would be presented in a short-term position, which leads to avoiding taking into consideration this premise for the projection of future cash flows in the valuation of the franchise, based on the premise that profitability is greater with work based on the common benefit.

Franchising from a real options perspective

Regarding the above theories, the role played by both the franchisor and the franchisee enters into the analysis and valuation exercise from the real options. By definition, a real option exists if one has the right to decide at one or more points in the future, for example, invest or not, sell or not (^{Brix, 2012}). Real options have taken on great importance in the valuation of projects and intangible assets since markets are dynamic, in addition to the fact that projects must be flexible to future investment decisions (^{Quirama & Sepúlveda-Aguirre, 2020, p. 250}). The real options technique facilitates decision-making on investment projects or strategies when there is flexibility (optionality) to make new decisions related to the project or strategy in the future to extend, contract, postpone, or abandon a project.

When considering the various options available to decide on the commercialization of franchises, during the process for the contracting between the parties, several aspects must be taken into account. In legal matters, and given that in Colombia the franchise is categorized as a contract of civil liability, the duration and the territory where the activity will be carried out must be agreed upon between the parties. In addition, so must the clauses that regulate the operation and the package of benefits that the franchisor delivers to the franchise. These may include, as indicated by ^{Rodríguez Alba, Sánchez García, and Mahecha Garzón (2013)}, the transfer of technical know-how or assistance, making it possible for the acquirer to manufacture or commercialize a good or service―in addition to the possibility of early termination of the contract by prior notice. ^{González and Hernández (2016)} point out that breaches of contractual clauses may lead to economically risky consequences for franchisees.

In financial matters, one of the biggest drawbacks in the contracting process is setting the price of the franchise since it must include the pecuniary values resulting from the flexibility of the options and decisions of the franchiser per the clauses previously established in the franchise contract. ^{Baldi and Trigeorgis (2009)} and ^{González, Zuluaga, and Maya (2012)} indicate that this flexibility should be considered when valuing the company and the brand. A large number of publications on franchises are focused on their definition, description, and management, but there are few that attempt to quantify their value. Table 1 presents some of the most relevant contributions in the research of authors on the franchise market.

Franchising as an intangible

So far, it has been emphasized that the value of franchises underlies the Know-how. Therefore, an intangible asset is valued during the franchise valuation process. ^{Vélez (2016)} states that an intangible's value is subjective and adds that some authors criticize the valuation exercise because of the subjectivity and uncertainty involved. However, valuation methods provide a guideline to negotiate.

The valuation of a franchise, like that of any other intangible asset, should be done at fair value, which means that it should include market expectations and assumptions about risks inherent to the asset, and, as indicated in ^{Flórez (2019)}, it is necessary to determine the specific asset that is the object of the measurement, the main (or most advantageous) market for the asset, and the ideal valuation techniques, taking into account the availability of data with which to develop variables that represent the assumptions that market participants would use when pricing the asset (^{Flórez, 2019}).

Calculation of 𝐾_𝑒

Obtaining the approximate K_e for each project is a complicated task since there is a possibility of underestimating or overestimating the calculated cost rate. It is assumed that the risk and capital structure of the company remain constant (^{García & Montes, 2018}) and that there is no debt because the capital structure that the future franchisee will assume is unknown. The methodology for its calculation is based on the CAPM model (Capital Asset Pricing Model).

Where R_LR = risk-free rate; β = measure of the sensitivity of the stock of the company to the market; and R_M= market return.

The methodology used for this work is the CAPM model adjusted to emerging countries such as Colombia, proposed by ^{Beltrán, Ravelo, and España (2018)}. These authors take the United States market as a basis, given that the assumptions of the model propose an efficient market where investors seek to maximize their profit by demanding higher profitability versus higher risk assumed. Moreover, these do not influence market prices. The model has three components: (i) K_lrusd risk-free rate, (ii)

US equity market risk premium PR _usd, and (iii) Colombia country risk premium, given by Equation (3), where this factor is calculated with credit default swaps (CDS).

The data obtained for May 6, 2020, were:

Table 3 presents the K_e discount rates in dollars and pesos for each company under study.

The classic NPVs of the companies are presented in Table 4

Stochastic NPV and volatility calculations

Once the classic NPVs are obtained, this work proceeds to the simulation of different scenarios using the Risk Simulator software with 10,000 events and using the 12345 seed, where it is assumed that the input variables (see Table 5) have a BETA probability distribution (PERT), since there is no historical information to perform a distribution analysis of the variables. The NPV is also taken as the output forecast variable.

According to ^{Antikarov and Copeland (2001)}, the NPV without flexibility is the most objective approach to the market value of a project. Therefore, the simulation of the cash flows provides a reliable estimate of the volatility of the investment. Thus, the volatility of the franchise was taken as the value obtained by the Monte Carlo simulation with a confidence level of 95%. Table 5 presents the uncertainty variables taken for the Monte Carlo simulation in each company, as well as the stochastic NPV values and the volatilities obtained.

NPV calculation with flexibility

Once the stochastic NPV and an estimate of volatility are obtained, the NPV is calculated with the flexibility to include in the project the future decisions that the franchisor may make according to the clauses of the contract, thus determining the real options associated with each possible decision. For this exercise, a clause is proposed that gives the franchisor the option to convert the franchised unit into its own unit. The franchisor can exercise the option when the franchisee fails to comply with the conditions of the contract and at the expiration of the contract, which is five years. Given the characteristics of the contract clause, the franchisor's decision resembles an American sale option to abandon, in which the franchisor has the right to terminate the contract at any time.

The valuation was performed based on the binomial tree methodology, and four phases were considered. The first phase is the input parameters of each option. Underlying asset (S) = present value of the projected cash flows without initial investment for each type of franchise; K = initial franchise costs assumed by the franchisee (I); rf = risk-free rate (TES trading rate, July 20); σ= volatility obtained by Monte Carlo simulation; t = time of the franchise contract.

As the second phase, the model variable (u, d, p, q) must be calculated (Table 6), where U are the factors that increase and decrease the PV of the cash flows, respectively. They are determined by expressions (6) and (7), while the probabilities p and q are mathematical elements that allow us to discount the cash flows using the risk-free rate and were obtained by applying Equations (8) and (9).

In the third phase, the value of S is projected based on the upward u and downward d movements of the present value of the cash flows of each company.

The fourth phase corresponds to the options tree. Here the value obtained at the end of the Stree is compared with the current investment in the franchise by choosing the maximum between this value and zero according to expression (10).

Finally, it was adjusted backward from the final moment to the initial moment with probabilities p and 1 − p by finding the risk-weighted average and discounting it to the present with the risk-free rate using Equation (11) to obtain the value of the real option at time zero. Table 6 presents the parameters for the option calculations of the three companies.

Figure 2 presents the evolution of the underlying asset and the valuation of the real option for company A.

Source: calculations and creation by the authors

Figure 2 Underlying asset tree and real option valuation tree for company A  

Once the valuation process was completed, the values of the real options seen in Table 7 were obtained.

The flexible NPV is given by Equation (12)

Calculation of royalty rate

The next step is calculating the royalty rate for each franchise determined by Equation (13), applying the methodology proposed by ^{Kotliarov (2011)}.

The values of A, B, C and D are calculated as follows:

Table 9 presents the variables taken into account to obtain the royalty rate and the royalty results for each company when there is no initial fee.

To determine the probability, this work took into account the indications of ^{Kotliarov (2011)}, who suggests that the probability of obtaining income of the independent or non-franchised entrepreneur (Wind) depends on the survival rate of the franchising companies, the economic sector, and the geographic area. In order to obtain this figure (Wind), the study took into account the data published by ^{Espinosa, Molina, and Vera (2015)}, where it is indicated that in the commerce and industry sectors, 33% of the companies fail; these are the sectors to which companies A and C belong, respectively. Meanwhile, in the service sector, to which company B belongs, the failure rate is 31%. In general, in the main geographical sector of the franchises, the value of non-success is 27.10%. Concerning the probability of obtaining the income produced by the franchise (Wfr), the data published by Portafolio (2017) was taken into account, where it is indicated that 70% of franchises in Colombia survive more than five years.

The additional probability of earning income from know-how (Wsup) is calculated as the difference between Wind and Wfr.

Initial fee

As mentioned above, the determination of the initial fee (IF) value depends on the franchisor, and together with the royalty rate, it is configured as a way to recover the invested values. Therefore, several IF scenarios were taken into account to calculate the royalty rate when there is a r_IF fee, based on Equation (15) proposed by ^{Kotliarov (2011)}. The fee values are calculated as a percentage of the flexible NPV of each company. The simulation showed that when the ratio of initial royalty to franchise revenues is equal to the initial fee when there is no fee r, it does not make sense to calculate a new r_IF, since the value of r_IF = r.

Table 10 presents an initial fee simulation and royalties for the three companies. In the case of company A, for example, for an initial fee of 267,085,257, it would charge the franchisee a royalty rate of 5% of the franchise revenues. This simulation gives the franchisor alternatives to structure an attractive commercial offer. It can also be observed that as the initial fee increases, the royalty rate decreases. This is due to the fact that the sum of the values calculated by the royalty rate and the fee cannot exceed the fee without royalties (royalties = 0). On the other hand, Table 10 summarizes the NPV and the free cash flows for the three companies from the perspectives of the franchisee and the franchisor. It can be seen that the franchise of Company C is not financially viable from the franchisee's point of view since the NPV is negative.

In this case, it is evident that franchises overcome resource constraints and make company growth possible at a lower cost than would be incurred to position their own brand (^{Madanoglu, Castrogiovanni, & Kizildag, 2019}). It also demonstrates that the valuation of franchises generally performed with traditional models is deterministic, i.e., it does not consider elements that make decisionmaking flexible in a changing environment.

It is important to highlight that, in order to determine the value of the franchise and the royalty rate proposed in this work, it is necessary to rigorously analyze the economic value of the franchise from the franchisee's perspective since the franchisee must make their own studies to make a rational decision. Moreover, they should perform the valuation in different capital structure scenarios, considering the initial investment and royalty, among other factors (^{Gillis, Combs, & Yin, 2018}).

Franchisors can make future decisions based on the real options model to mitigate some risks. For the above, clauses are stipulated that affect the contract value. Such impacts caused by future decisions can be previously contemplated since this model incorporates volatility through simulations (^{Casson, 2015}). This justifies the reason for the valuation using real options (Pareja & Cadavid, 2016).