Real options represent an extension of the theory of financial options applied to non-financial assets. This theory is based on management’s flexibility to modify its decisions when it identifies changes in the business climate. In this paper, we analyze the characteristics of these financial instruments, their types and valuation, and present some examples of how they can be used in administrative practice.
1. Introduction: Types of Options
Since the 1990s, as international markets began to integrate at an astounding pace and automated systems sprung up that allowed for instantaneous, across-the-globe movements of funds, the complexity of transactions carried out through the financial system has grown exponentially. This situation has been one of the most influential incentives for the creation of innovative financial instruments that meet new needs for hedging and investment and help companies become more competitive and profitable.
One of the most popular and widely-used instruments for investors is what is called an option, which provides a hedge against the volatility and risk of commodity prices, inputs, the exchange rate and other variables. Options enable a company to plan and guarantee the flows it requires, reducing uncertainty in the markets in which it participates.
According to Trigeoris (1999), a financial option is defined as the right, but not the obligation, to purchase (a call or C option) or sell (a put or P option) a specific asset (underlying), paying a given price (strike price) during the life of the instrument or at a specific future date (maturity or expiration date). If the option can be exercised before expiration, it is called an American-style option; if it can only be exercised at expiration, it is known as a European-style option. The value of the contract depends on the amount of the underlying over time, its price, the strike date and interest rates.
Where:
Cis the intrinsic value of a call option
St is the price of the underlying in t; so that t=1,…,n
K is the strike price
P is the intrinsic value of the put option
Following the logic of risk hedging, real options represent an extension of the traditional theory of financial options, but applied to non-financial assets, such as extensions and alternatives in the decisions made regarding productive projects. This theory is based on management’s flexibility to modify its decisions when it identifies changes in the business climate. New information can help it to better adapt its business strategy to minimize new costs or take advantage of expansion opportunities, among other factors.
1 Full-time professor in the Accounting Studies Department at ITAM where she teaches courses on Corporate Finance and Strategic Cost Analysis. E-mail: paulam@itam.mx.
2 Full-time professor in the Business Administration Department at ITAM where he teaches courses on Corporate Finance and Finance Theory. E-mail: jorge.moreno@itam.mx.
Without flexibility in decision-making, the probability distribution of the net present value (NPV) associated with the project would be reasonably symmetrical, in which case traditional valuation methods would be sufficient. However, when management has the opportunity to adapt to changes in financial and economic situations, traditional NPV does not capture this capacity to act. This asymmetry introduced by management’s flexibility is known as the expanded net present value criteria, which reflects two components: traditional NPV from cash flows, and the active part of the project, which incorporates the effect of competition, the synergies generated by a project, the interaction between various phases of the project, and management’s response to all of these factors. This response capacity can be expressed as follows
Thus, we can view investment as a collection of options, or choices, regarding real assets, to which we can apply financial options valuation techniques. Table 1 sums up the similarities between a real option and a stock call option.
Table 1. Similarities between a financial option and a real option
Fuente: Trigeorgis (1999)
Financial and real options are similar in many ways, but not identical, particularly when dealing with noncommercial projects, such as the case of a new product that was not previously on the market. However, when there is difficulty in estimating the parameters shown in the table, we can solve the problem taking a “twin asset” as a reference, meaning one that has a similar risk and return to the project is being considered, and is also interchangeable in the economy. The difference in evaluating a project with a twin asset requires us to adjust the yield of this twin asset according to the additional risk inherent in the project.
Where:
? is the expected return on the project
? is the return on a similar asset a that is found on the market
? is the risk premium of the project, also known as dividen yield
As for the types of applications of real options, Table 2 shows the most common in business management and productive projects. In the next section we will explain in greater detail some of the options contained in the table and will provide a brief example of each one.3
Table 2. Types of real options
Fuente: Trigeorgis (1995)
3 As with financial options, real options can be valued using the methodology of stages or with a continuous time model. In this article we will only explain some options using the stage model. For more information on continuous time valuation, see Dixit and Pindyck (1994).
2. Examples and stage analysis
Company A wants to expand its distribution channels, and has an opportunity to buy 60% of the shares of another company, B, to do so. It will have to invest of 115 million pesos. Upon valuing company B, we find that discounted cash flows total 100 billion pesos, so based on NPV criteria, company A should not acquire company B, because the initial investment is superior to the total amount of discounted cash flows (-115+100 equals -15 <zero).
We also have the following information: the project value can increase by 120% or decline by 80% in each period, according to the demand for the product being sold. There are similar projects whose average yield is 20% and risk-free rate is 4%. The cash flow tree for company B is as follows:
Table 3: Estimated trajectory of underlying (Figures in millions)
2.1 Option to defer
Depending on the economic or political situation, certain projects can wait for their value to justify the initial outlay; accordingly, management has the right, but not the obligation, to make the investment in the following period. The option to defer can be viewed as an American-style call option, in which the underlying is the cash flow in each natural state (V in Table 3) and the strike price, the initial updated investment (I) at a rate of 8%. The general formula for this category is as follows:
Taking the data from this example, let us say that company A has the option to defer acquisition of company B for up to two periods. Again, this option is similar to an American-style call option, so management must decide whether to exercise the option before its expiration or to wait for flows in the following period.
The restated value of the initial investment is for t1=115 pesos, x the value by which the investment increases, which is equal to 124.20 pesos; and for the following period t2 =124.2 x 1.08 = 134.136 pesos. The intrinsic value of the option to defer is represented by Figure 1.
Figure 1. Intrinsic value of option to defer
If management decides it would be better not to invest in t0 or wait to invest in the following period, this option can be viewed as a European-style option, discounting the expected flows from the future period, weighted by the risk-neutral probability and using the risk-free rate as the discount rate.
Table 4. Value of the option evaluated as European-style (figures in millIons)
To make a decision, we must compare the option to wait or to exercise before expiration. We take the highest result in each node of these two trees. In this case, the company would benefit more from waiting until the second year to invest, provided flows remain around 135 million pesos. As the table shows us, management should wait until the following period to acquire company B, so the value of the option to wait is the same as shown in Figure 2.
Investing any earlier would mean sacrificing the option to wait. Investment at this point would only be justified if V>I1 + Option. The difference between this model and a decision-making tree is that we take the risk free rate and risk-neutral probabilities to value the option, which avoids distortions that could be created by the use of subjective rates imposed by management.
2.2. Option to expand
Once the project is underway, management has the flexibility to change its initial decision. If conditions are favorable, the company may choose to increase the scale of production by a certain percentage (%X), at an additional cost (I2). This alternative is similar to an American-style call option:
Let us assume that the company in this example has the opportunity to expand the production of Company B by 100% starting from the first period, at an additional cost of 90 million pesos. The intrinsic value of the option would be as shown in Figure 3, while the value of this flexibility is 116 million pesos, which is almost 17 million pesos more than the additional project value estimated under the traditional system of discounted cash flows (Table 4).
Table 5. Intrinsic value of the option to expand (figures in millions)
Table 6. Value of the option evaluated as European-style (figures in millions)
Waiting for the last period to expand the scale of operations would be equivalent to valuing the option as European-style. Once this is done, we compare the values of the results node to node and we choose the highest. Finally, the highest values must be discounted at t0 to determine the value of the option to expand.
Similarly, if market conditions are favorable, management may decide to operate below its theoretic production capacity and keep costs down. This alternative is similar to an American-style put option on the part of the project that can be reduced, with the strike price equal to the cost savings:
In the example, if demand for the product does not respond as administration had planned, starting from the third period, it may decide to scale back its operations by 40%, in other words, to keep the company working at 60% of its installed capacity, which would avoid variable costs amounting to 45 pesos. The intrinsic value of the option is shown in Table 7:
Table 7. Intrinsic value of the option to reduce scale (figures in millions)
But there is also the possibility of waiting until the last period to decide whether or not to reduce the scale of production. In this case, the option can be evaluated as European-style (Table 8)
Table 8. Value of the option evaluated as European-style (figures in millions)
Once this is done, we compare node to node and choose the highest, so the highest values must be discounted through time t0 to determine the value of the option to reduce scale. As Figure 5 shows, it would be better to reduce the scale of operation in the two nodes of the first period, to attain an expanded present value of 103 million pesos.
2.3. Option to abandon
As an alternative to the choice of reducing the scale or suspending operations, there is always the possibility of abandoning the project altogether in exchange for obtaining the salvage value of the assets used in the project. This option may be valued as an American-style put option, comparing the salvage value with the project value at each of the nodes.
Let us assume that the company has conducted an analysis of the real-estate market to determine the trajectory of the salvage values of the assets of Company B (see Table 9).
Table 9. Estimated trajectory of Company B assets (figures in millions)
The next step is to compare node to node and find what would be more beneficial to the company. If we assume that this option can be exercised starting in t1, the company must choose the maximum value between abandoning or continuing the project, in other words, obtaining the intrinsic value of this option (Table 10).
Table 10. Intrinsic value of the option to abandon (figures in millions)
As with the previous options, management can also wait until the last period to make a decision, which would mean considering the option as European-style with risk-neutral probability (Table 11):
Table 11. Value of the option evaluated as European-style(figures in millions)
As in the preceding cases, we must compare the intrinsic value of the European-style option to abandon and choose the highest value. Finally, the highest values must be discounted across time t0 to determine the final value of the option. According to this valuation, we find the best decision would be to sell the subsidiary company during the last period, provided is at the highest node; otherwise, it would be best to retain the shares of Company B.
3. Conclusions
Real options are a much more powerful tool than the traditional present value methodology because they incorporate administrators’ optimal reaction to changes in the business climate for the company or the project managed.
The analysis of these instruments enables us to assemble variant financial and market scenarios, so their study and evaluation is more complex because more parameters must be calculated. One of the most important parameters in evaluating real options is the volatility of the project, because this depends on the modeling of the underlying’s trajectory, as well as the probabilities assigned to relevant events that are taken into account.
Real options are increasingly popular among investors and project managers; but for the Mexican market it is still difficult to estimate the values of the key parameters. This difficulty arises from the lack of complementary information on the project, and on the flows that will be valued, for example a long series of the products that will be sold or variations in the number of units sold. However, the ability to take advantage of investment opportunities and lock in competitive advantages against rivals are good reasons for a company to begin allocating resources to compiling this type of information, and thus to use real options in deciding whether or not to undertake new productive projects.?
References
Amram, M.y Kulatilaka N. Real Options, Managing Strategic Investment in a Uncertain World, HBS Press, 1999.
Dixit, A.K. y Pindyck, R.S.Investment under UncertaintyPrincenton University Press,1994
Trigeorgis, L. Real Options in Capital Investment, Models, Strategies, and Applications. Praeger, Westport, Connecticut, London, 1995.
Trigeoris, L. Real Options, Managerial Flexibility and Strategy in Resource Allocation, Fourth printing, The MIT Press, 1999.
The value of alternatives for change: What is real options?
By: Paula Beatriz Morales1
and Jorge Omar Moreno2
Real options represent an extension of the theory of financial options applied to non-financial assets. This theory is based on management’s flexibility to modify its decisions when it identifies changes in the business climate. In this paper, we analyze the characteristics of these financial instruments, their types and valuation, and present some examples of how they can be used in administrative practice.
1. Introduction: Types of Options
Since the 1990s, as international markets began to integrate at an astounding pace and automated systems sprung up that allowed for instantaneous, across-the-globe movements of funds, the complexity of transactions carried out through the financial system has grown exponentially. This situation has been one of the most influential incentives for the creation of innovative financial instruments that meet new needs for hedging and investment and help companies become more competitive and profitable.
One of the most popular and widely-used instruments for investors is what is called an option, which provides a hedge against the volatility and risk of commodity prices, inputs, the exchange rate and other variables. Options enable a company to plan and guarantee the flows it requires, reducing uncertainty in the markets in which it participates.
According to Trigeoris (1999), a financial option is defined as the right, but not the obligation, to purchase (a call or C option) or sell (a put or P option) a specific asset (underlying), paying a given price (strike price) during the life of the instrument or at a specific future date (maturity or expiration date). If the option can be exercised before expiration, it is called an American-style option; if it can only be exercised at expiration, it is known as a European-style option. The value of the contract depends on the amount of the underlying over time, its price, the strike date and interest rates.
Where:
Following the logic of risk hedging, real options represent an extension of the traditional theory of financial options, but applied to non-financial assets, such as extensions and alternatives in the decisions made regarding productive projects. This theory is based on management’s flexibility to modify its decisions when it identifies changes in the business climate. New information can help it to better adapt its business strategy to minimize new costs or take advantage of expansion opportunities, among other factors.
1 Full-time professor in the Accounting Studies Department at ITAM where she teaches courses on Corporate Finance and Strategic Cost Analysis. E-mail: paulam@itam.mx.
2 Full-time professor in the Business Administration Department at ITAM where he teaches courses on Corporate Finance and Finance Theory. E-mail: jorge.moreno@itam.mx.
Without flexibility in decision-making, the probability distribution of the net present value (NPV) associated with the project would be reasonably symmetrical, in which case traditional valuation methods would be sufficient. However, when management has the opportunity to adapt to changes in financial and economic situations, traditional NPV does not capture this capacity to act. This asymmetry introduced by management’s flexibility is known as the expanded net present value criteria, which reflects two components: traditional NPV from cash flows, and the active part of the project, which incorporates the effect of competition, the synergies generated by a project, the interaction between various phases of the project, and management’s response to all of these factors. This response capacity can be expressed as follows
Thus, we can view investment as a collection of options, or choices, regarding real assets, to which we can apply financial options valuation techniques. Table 1 sums up the similarities between a real option and a stock call option.
Table 1. Similarities between a financial option and a real option
Fuente: Trigeorgis (1999)
Financial and real options are similar in many ways, but not identical, particularly when dealing with noncommercial projects, such as the case of a new product that was not previously on the market. However, when there is difficulty in estimating the parameters shown in the table, we can solve the problem taking a “twin asset” as a reference, meaning one that has a similar risk and return to the project is being considered, and is also interchangeable in the economy. The difference in evaluating a project with a twin asset requires us to adjust the yield of this twin asset according to the additional risk inherent in the project.
Where:
As for the types of applications of real options, Table 2 shows the most common in business management and productive projects. In the next section we will explain in greater detail some of the options contained in the table and will provide a brief example of each one.3
Table 2. Types of real options
Fuente: Trigeorgis (1995)
3 As with financial options, real options can be valued using the methodology of stages or with a continuous time model. In this article we will only explain some options using the stage model. For more information on continuous time valuation, see Dixit and Pindyck (1994).
2. Examples and stage analysis
Company A wants to expand its distribution channels, and has an opportunity to buy 60% of the shares of another company, B, to do so. It will have to invest of 115 million pesos. Upon valuing company B, we find that discounted cash flows total 100 billion pesos, so based on NPV criteria, company A should not acquire company B, because the initial investment is superior to the total amount of discounted cash flows (-115+100 equals -15 <zero).
We also have the following information: the project value can increase by 120% or decline by 80% in each period, according to the demand for the product being sold. There are similar projects whose average yield is 20% and risk-free rate is 4%. The cash flow tree for company B is as follows:
Table 3: Estimated trajectory of underlying (Figures in millions)
2.1 Option to defer
Depending on the economic or political situation, certain projects can wait for their value to justify the initial outlay; accordingly, management has the right, but not the obligation, to make the investment in the following period. The option to defer can be viewed as an American-style call option, in which the underlying is the cash flow in each natural state (V in Table 3) and the strike price, the initial updated investment (I) at a rate of 8%. The general formula for this category is as follows:
Taking the data from this example, let us say that company A has the option to defer acquisition of company B for up to two periods. Again, this option is similar to an American-style call option, so management must decide whether to exercise the option before its expiration or to wait for flows in the following period.
The restated value of the initial investment is for t1=115 pesos, x the value by which the investment increases, which is equal to 124.20 pesos; and for the following period t2 =124.2 x 1.08 = 134.136 pesos. The intrinsic value of the option to defer is represented by Figure 1.
Figure 1. Intrinsic value of option to defer
If management decides it would be better not to invest in t0 or wait to invest in the following period, this option can be viewed as a European-style option, discounting the expected flows from the future period, weighted by the risk-neutral probability and using the risk-free rate as the discount rate.
Table 4. Value of the option evaluated as European-style (figures in millIons)
To make a decision, we must compare the option to wait or to exercise before expiration. We take the highest result in each node of these two trees. In this case, the company would benefit more from waiting until the second year to invest, provided flows remain around 135 million pesos. As the table shows us, management should wait until the following period to acquire company B, so the value of the option to wait is the same as shown in Figure 2.
Investing any earlier would mean sacrificing the option to wait. Investment at this point would only be justified if V>I1 + Option. The difference between this model and a decision-making tree is that we take the risk free rate and risk-neutral probabilities to value the option, which avoids distortions that could be created by the use of subjective rates imposed by management.
2.2. Option to expand
Once the project is underway, management has the flexibility to change its initial decision. If conditions are favorable, the company may choose to increase the scale of production by a certain percentage (%X), at an additional cost (I2). This alternative is similar to an American-style call option:
Let us assume that the company in this example has the opportunity to expand the production of Company B by 100% starting from the first period, at an additional cost of 90 million pesos. The intrinsic value of the option would be as shown in Figure 3, while the value of this flexibility is 116 million pesos, which is almost 17 million pesos more than the additional project value estimated under the traditional system of discounted cash flows (Table 4).
Table 5. Intrinsic value of the option to expand (figures in millions)
Table 6. Value of the option evaluated as European-style (figures in millions)
Waiting for the last period to expand the scale of operations would be equivalent to valuing the option as European-style. Once this is done, we compare the values of the results node to node and we choose the highest. Finally, the highest values must be discounted at t0 to determine the value of the option to expand.
Similarly, if market conditions are favorable, management may decide to operate below its theoretic production capacity and keep costs down. This alternative is similar to an American-style put option on the part of the project that can be reduced, with the strike price equal to the cost savings:
In the example, if demand for the product does not respond as administration had planned, starting from the third period, it may decide to scale back its operations by 40%, in other words, to keep the company working at 60% of its installed capacity, which would avoid variable costs amounting to 45 pesos. The intrinsic value of the option is shown in Table 7:
Table 7. Intrinsic value of the option to reduce scale (figures in millions)
But there is also the possibility of waiting until the last period to decide whether or not to reduce the scale of production. In this case, the option can be evaluated as European-style (Table 8)
Table 8. Value of the option evaluated as European-style (figures in millions)
Once this is done, we compare node to node and choose the highest, so the highest values must be discounted through time t0 to determine the value of the option to reduce scale. As Figure 5 shows, it would be better to reduce the scale of operation in the two nodes of the first period, to attain an expanded present value of 103 million pesos.
2.3. Option to abandon
As an alternative to the choice of reducing the scale or suspending operations, there is always the possibility of abandoning the project altogether in exchange for obtaining the salvage value of the assets used in the project. This option may be valued as an American-style put option, comparing the salvage value with the project value at each of the nodes.
Let us assume that the company has conducted an analysis of the real-estate market to determine the trajectory of the salvage values of the assets of Company B (see Table 9).
Table 9. Estimated trajectory of Company B assets (figures in millions)
The next step is to compare node to node and find what would be more beneficial to the company. If we assume that this option can be exercised starting in t1, the company must choose the maximum value between abandoning or continuing the project, in other words, obtaining the intrinsic value of this option (Table 10).
Table 10. Intrinsic value of the option to abandon (figures in millions)
As with the previous options, management can also wait until the last period to make a decision, which would mean considering the option as European-style with risk-neutral probability (Table 11):
Table 11. Value of the option evaluated as European-style(figures in millions)
As in the preceding cases, we must compare the intrinsic value of the European-style option to abandon and choose the highest value. Finally, the highest values must be discounted across time t0 to determine the final value of the option. According to this valuation, we find the best decision would be to sell the subsidiary company during the last period, provided is at the highest node; otherwise, it would be best to retain the shares of Company B.
3. Conclusions
Real options are a much more powerful tool than the traditional present value methodology because they incorporate administrators’ optimal reaction to changes in the business climate for the company or the project managed.
The analysis of these instruments enables us to assemble variant financial and market scenarios, so their study and evaluation is more complex because more parameters must be calculated. One of the most important parameters in evaluating real options is the volatility of the project, because this depends on the modeling of the underlying’s trajectory, as well as the probabilities assigned to relevant events that are taken into account.
Real options are increasingly popular among investors and project managers; but for the Mexican market it is still difficult to estimate the values of the key parameters. This difficulty arises from the lack of complementary information on the project, and on the flows that will be valued, for example a long series of the products that will be sold or variations in the number of units sold. However, the ability to take advantage of investment opportunities and lock in competitive advantages against rivals are good reasons for a company to begin allocating resources to compiling this type of information, and thus to use real options in deciding whether or not to undertake new productive projects.?
References