The coffee market is distinguished for being volatile and uncertain in terms of domestic and international prices. Arabica and Robusta coffee are produced in 23 provinces of Ecuador. A decade-long decline of coffee production prompted the Ecuadorian government to launch a public program for replanting coffee trees towards the end of 2011. A grower’s decision to enter, remain in or exit the coffee sector is based on fluctuating profits from each year’s harvest sale. We analyzed the hypothesis whereby the coffee grower’s decision to leave the sector is explained by volatile and uncertain prices. This paper aimed to evaluate the coffee sector with an application of Real Option Analysis for the period 2002-2012. We also defined entry (H) and exit (L) prices for Arabica and Robusta coffee for the analyzed period. Our findings revealed high H and L prices encourage growers to leave the sector for the most part of the analyzed period. High H and L prices resulted from high variable cost due to increasing wages for farm workers. The Ecuadorian government is developing a policy to help growers make production more efficient, encouraging them to remain in the sector in the long run.

The coffee sector has been one of the most important export sectors in Ecuador. Exports reached 413 million USD (125,070 t) in 1994 but dropped to 261 million USD (51,526 t) in 2012
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Volatile coffee prices create an uncertain environment for growers’ in Ecuador and elsewhere. This uncertainty translates into unstable harvest prices and farm profits. Low-price periods affect growers’ household income in coffee-producing countries, and encourage them to abandon the crop (

To mitigate low prices, alternative strategies such as converting conventional plantations into organic and shading coffee plantations have been evaluated in the literature. Positive benefits include increasing home income (

The Ecuadorian Government was concerned by low coffee production in the last years, and launched a public program to replant coffee trees towards the end of 2011. The program includes technical assistance to improve crop management and credit for growers who established new plantations. Ultimately, it is the farmer’s choice to use this support and invest in renewed plantations and entering a sector characterized by uncertain profitability.

The volatile and uncertain environment, previously described, offers an angle for analysis on the coffee sector in Ecuador before the implementation of the public program. In this paper, we address the following questions: Have coffee growers been inclined to exit the sector due to volatile and uncertain prices for the 2002-2012 period? Which coffee prices triggered the exit decision in the Ecuadorian market? To answer these questions, we used the Real Option Analysis, developed by

The contribution of this work to the literature is two-fold. First, the validation of the hypothesis that volatile and uncertain coffee prices in the Ecuadorian market might explain the growers’ decisions to exit the sector. If we fail to reject it, the conclusion would be that volatile coffee prices might have pushed growers to leave the sector during of the analyzed period. Second, we estimate entry and exit coffee prices for the period 2002-2012 for Arabica and Robusta.

Coffee is produced in 23 Ecuadorian provinces. Geography and climate are apt for the production of Arabica and Robusta coffee (Arabica in highlands and Robusta in lowlands). Manabí is the main producing province with 43.86% of the total bearing area (49,578 planted hectares in 2012 (

Low prices affected the coffee growers’ incentives to maintain or increase the production in following years. Limited use of technology, aging of coffee trees, poor crop management (especially in pruning and insect control activities) and climate anomalies (delayed rainy season) explain the reduction of production and yields (

Coffee prices have been volatile due to variations in world supply (new plantations, frost and coffee bean diseases), established export quotas in the International Coffee Agreement and de-regulation of the market (
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Real Options theory is used to evaluate the implementation of projects as an alternative to the traditional method (Net Present Value) which does not consider volatility and uncertainty in the market. In addition, Real Options analysis is used to understand growers´ decisions concerning agricultural systems and products.

Entry and exit (price or revenues) resulting from the Real Options Analysis helps understand growers’ entry and exit decisions.

Several studies analyze the effect of volatile and uncertain coffee prices on growers.

The model used for coffee Real Options valuation in Ecuador was developed by

The application of the model is based on three steps described by

1) Definition of an idle project’s value. An idle project is the project awaiting initiation, whose value is equal to the option to invest. An idle project requires an amount of money to reinitiate the economic activity.

2) Definition of an active project’s value. An active project’s value is the present value of the net revenues (if the firm operates in the market) added to the value of the abandonment option.

3) Definition of the entry and exit prices of option model. These prices are the same for idle and active projects. This results in two conditions: first, the value of an idle project is equal to that of an active project. Second, the rate change of an idle project’s value is equal to the rate change of an active project. With these conditions, the model will be resolved to determine the entry and exit prices for the coffee activity.

The world market defines the coffee price exogenously. Therefore, it is assumed that it follows a random walk behavior and a geometric Brownian process.

where e is a random value that follows a standardized normal distribution, and dP has a normal distribution, which means dP = µP dt and variance dP = s
^{2}
P
^{2}
dt.

The investment value V (P,t) is a function of variables price (P) and time (t). By a second-order Taylor Series, dV can be approximated as:

Terms dP and dt in the limit would tend to zero. Thus, the terms
^{2}
= σ
^{2}
p
^{2}
dt in

Replacing

The

where the terms

Next, we can take the expected value of both sides of

In equilibrium, an expected capital gain of an idle project would be equal to the return of the investment (V
_{0}
(P) dt). With V
_{0}
(p) being the idle project to be initiated,

Dividing by dt, we have:

The solution of the differential equation is the following: V
_{0}
(P) = AP
^{-α}
+ BP
^{ß}
, A and B constants are estimated in a later section, and where the α and ß are equal as:

The value of an idle project V
_{0}
(P) is defined as AP
^{-α}
+ BP
^{ß}
. If the market price is close to zero, it means that there are no incentives to initiate the project (the option is worthless), and so V
_{0}
(P) = 0, to have this fact, the constant A must be equal zero
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In equilibrium, for an active project, the normal return is equal to the addition of expected capital gain and net revenue flow:

Replacing the term

Reordering all the terms of equation above and equal to 0, we obtain:

The solution of

The solution shows the net revenue flow expressed as
^{-α}
+ BP
^{ß}
). If the market price tends to infinity (P → ∞), the option abandonment would tend to be zero. Considering the value of α>0 and ß>1, the abandonment option would be zero (AP
^{-α}
+ BP
^{ß}
= 0), only if B constant takes a value of zero
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H is the entry price that defines the firm’s entry decision. The value of the option of invest V
_{0}
(H) must be equal to the expected value of the executed project (V
_{1}
(H)) minus the investment cost (K), and so, the value-match condition is:

Also, the smooth-pasting condition requires that the two value functions meet tangentially:

The firm’s exit decision is defined by the price L, so the abandonment option V
_{0}
(L) must be equal to the expected value of the project (V
_{1}
(L)) added to the abandonment cost X. Therefore, the value-match condition is:

And the smooth-pasting condition requires that the two values functions meet tangentially:

We obtain four equations that solve the entry (H) and exit (L) prices. Substituting V
_{0}
(H), V
_{1}
(H), V
_{0}
(L) and V
_{1}
(L) in the Eqs.

First, we must estimate (µ, σ
^{2}
and ρ) with the coffee price and banking rate series. Then, the estimated variables are replaced in

where W
_{H}
= C + K and W
_{L}
= C - ρL. With these variables and equations, we define the H and L prices for Arabica and Robusta coffee for the period 2002-2012, and therefore growers’ entry or exit decision in this volatile and uncertain sector.

The Ecuadorian Arabica and Robusta coffee annual prices (USD/lb) for the period 1990-2012 were obtained from the (ICO) International Coffee Organization, denominated in nominal terms. Future coffee prices are negotiated in the New York and London markets. Thus, world coffee prices are exogenous variables that affect the Ecuadorian prices directly.

We supposed that the coffee price follows a random walk behavior as:

where P
_{t-1}
is the price of the previous year, and u
_{t}
is the error term that follows a random walk with value 0 and constant variance. To determinate if Ecuadorian coffee prices follow a random walk behavior, it is necessary to perform the Unit Root Test (λ=1). We used the Augmented Dickey-Fuller test to validate the unit root with three possible models for each series: without constant, with constant as well as with constant and trend, where P
_{t}
= P
_{t}
- P
_{t-1}
and δ= λ-1.

This test was performed for Arabica and Robusta price series. In each model, we incorporated lagged terms to analyze, with most accurately, the existence of the unit root. For Arabica series results, none of the models rejects the null hypothesis at a confidence level of 95%. However, for Robusta series results, two of three models cannot reject the null hypothesis at confidence level of 95%
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Now, we get the returns (Φ = ln(

This information is obtained from the (BCE) Central Bank of Ecuador (2002-2012). In Ecuador, the financial system is divided into segments. The banking interest rate varies according to the segments. However, agricultural growers do not have access to the conventional Ecuadorian banking system because many of them do not have any collateral. For this reason, it is the public bank that provides loans to agricultural growers. For banking data, we select the interest rate that banks used for the period January 2002-June 2007. Since mid-2007, a new regulation of the financial system created segments according to the amount of credit money that the clients applied for. Therefore, we select the PYMES (small and medium firms) segment, which is for clients requiring a loan equal to or less than USD 200,000 for the period August 2007-December 2012. This segment corresponds to the amount of money that growers required for the investment in the coffee activity.

Coffee is a perennial tree that is productive for up to 20 years. According to the information published by the Ecuadorian Ministry of Agriculture (MAGAP), and shown in the

Now, we can estimate Arabica and Robusta costs (USD/lb).
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For Robusta coffee, sowing is the largest cost item for the first year (USD 760). Fertilizer and cultural labor represent 82.58% of the total cost for the second year. During our analysis period (2002-2012), the values were adjusted to the inflation rate (agrochemical products, seeds, etc.) and labor wage for each year. During 2012, the cost of establishing a coffee hectare was USD 2,783.15. We could estimate cost K to be 5.49 USD/lb in 2012, this value is calculated by dividing establishment cost per hectare by the average coffee yield (MAGAP data).

To estimate the variable cost per unit (C), we considered as a reference the activities of the third year that the MAGAP has estimated to a value of 1,691 USD/ha for 2013. Harvest was the highest cost in that year (USD 766) due to the wages paid. With the variable cost adjusted to the data and average yield for each year, we could estimate variable C for the whole analyzed period. It is important to note that coffee beans are sold without any transformation process. The model assumes an infinite life project (renewal of the trees and fixed assets). In our case, growers do not have any irrigation system, which means that they do not to require fixed assets. For 2012, we estimated C cost as 3.65 USD/lb; this cost includes variable cost and the cost for growers to renew the trees every 20 years (infinite project assumption).

We tried to estimate the abandonment cost per lb (X), but we did not find any official information (costs of tree-cutting and land-clearing). Therefore, we considered an estimated cost of 16 units of labor per hectare (MAGAP defines that 16 units of labor are required to clear the land before planting Robusta coffee; we will consider that the same amount of labor is necessary to clear the land of coffee trees and switch to another crop). For the 2002-2012 period, we considered MAGAP and the basic Ecuadorian wage to estimate X value for each year. For 2012, the daily wage for land preparation activities in the agricultural sector was USD 10-12.70 depending on the province (

Also,

For 2012, we obtained K (7.64 USD/lb), C (3.85 USD/lb) and L (0.32 USD/lb) costs. It was possible to verify that only the K cost had significant difference between both varieties. This results from the investment made in the first year: sowing, land preparation and fertilization activities demand more resources for Arabica coffee, the main reason being that more trees have to be planted per hectare.

We estimated H and L prices for Arabica and Robusta coffee.
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The L price defines the exit decision for the activity. By comparing L prices with paid prices to Ecuadorian growers, we observed that L prices are above paid prices in most years (except in 2011). Thus, an average coffee grower would be inclined to exit the sector in most of analyzed years. This is consistent with the decreasing number of hectares in the coffee harvest. The decreasing trend started in 2004, despite increasing coffee prices. In Ecuador, the costs agrochemicals products and wages have increased continuously. Variable cost (C) has also experienced an increased tendency, lifting the L price upwards.

The paid prices received by Robusta growers did not cover C costs in any year. Thus, the coffee activity does not generate profits and coffee growers would incur economic losses if they continued in the activity. We observe that L line was above paid price in all analyzed periods, indicating that coffee prices were too low for current growers. This supports the conclusion that average Ecuadorian coffee growers would take the exit decision every year since 2002.

Our findings indicate that, for both coffee varieties, volatile and uncertain prices as well as increasing costs, forced growers to exit the sector. More specifically, variable representing the expected rate of market growth exhibited negative values for Robusta in 2002 and for Arabica in 2002-2003. Since 2004, has positive values caused by the high upward trend experienced in the world and Ecuadorian coffee market. This upward movement would be attractive to new (enter) and current (renewal of hectares) growers; nonetheless it did not have the expected effect in the Ecuadorian coffee market. This is explained by the increasing labor costs, which cause K and C values to increase, in turn triggering high values of H and L prices; the average yield would be measured as an indirect force that pushes K and C costs up. The average coffee yield for Ecuadorian growers is considered low (0.1- 0.3 t/ha) if it is compared with some of the major principal coffee-producing countries. However, even if the average coffee yield improves in the next years, this would not guarantee that K and C would decrease to the necessary extent due to the increasing wage costs in previous years.

For each coffee variety, we performed a sensitivity analysis to evaluate how changes on the variables influence the entry (H) and exit (L) prices. We used @Risk software to perform the sensitivity analysis for year 2012
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^{2}
(the variance rate of price market), we simulated values between 5% and 35% and obtain H prices ranging from 6.72 to 13.05 USD/lb. If market volatility increases, H increases. For variable C, with a value between 0.05 and 5.00 USD/lb we obtained H prices of 2.44 and 12.2 USD/lb. Therefore, if the grower faces a higher cost C each year, the H price would be higher.

For L price, µ (expected rate of the market growth) and (capital cost) were the two most significant variables. We simulated variable µ values ranging from -50% to 10%, raising L between 3.33 USD/lb and 0.70 USD/lb. Our results showed the inverse relation of µ and L, as expected; as high coffee prices would encourage growers to continue producing coffee instead of exiting the sector. With variable ρ values between 7.5% and 30%, L prices varied between 0.09 and 1.82 USD/lb. There was a direct relation between ρ and L: if decreases for coffee growers, L will also decrease. This has an obvious policy conclusion: if access to capital can be obtained at lower interest rates, growers might be stimulated to remain in the coffee sector.

^{2}
and C are the most important variables affecting H prices. In the sensitivity analysis, we modeled values in a range of 5% - 35% to simulate the effect of volatility in H price (6.10 - 10.85 USD/lb). In our simulation, we could find a direct relation between σ
^{2}
and H: if σ
^{2}
increases for coffee activity, a high H price is obtained. Therefore, new coffee growers would not start up a plantation, and current growers would not replant the trees. Variable σ
^{2}
is more important for Robusta than for Arabica growers, based on the coffee simulation analyses. This suggests that Robusta coffee growers were exposed to more volatility and price uncertainty than Arabica coffee growers. For variable C, we simulated values ranging from 0.05 to 5.00 USD/lb and obtained H prices between 2.07 and 12.92.

We also characterized an inverse relation of µ and L: if µ increases in the coffee market, the L price adopts a low value. This market movement would encourage current coffee growers to remain in business, but increasing costs would compromise the crop profits. When variable was simulated with values ranging from 7.5% to 30%, we obtained L prices between 0.11 and 1.62 USD/lb. The direct relation of µ and L implies that any increase in µ forces L to increase as well.

Additionally, coffee growers were affected by increasing input costs, especially by the cost of labor for sowing, maintenance and harvesting activities. This reduces the profits and inflates L prices, encouraging growers to exit the coffee activity despite periods of high coffee prices.

The results show that volatile and uncertain coffee prices may have been the major reason for growers to leave the sector during the period 2002-2012. Our sensitivity analysis highlights the importance of C (variable cost) in the definition of entry and exit coffee prices for both varieties. In year 2012, C had a value of 3.85 USD/lb for Arabica coffee and 3.65 USD/lb for Robusta coffee.

Simulations carried out on the variable µ (expected rate of the market growth) show that an increase in the value of causes a reduction in L prices for both coffee varieties. This would postpone the exit decision of current growers. At the same time, increasing K and C costs discourage current growers from staying in the activity due to the high production cost. The net effect of and increasing costs (K and C) is a slight reduction of L prices. Thus, the incentives to stay in the activity are low.

Low s
^{2}
values reduced entry coffee prices, which would be attractive for new growers if C and K costs were not high. The net effect was a slight reduction of H price that did not encourage investment in new hectares or renewal of existing hectares. Price stabilization and risk-management mechanisms have been proposed to reduce the volatile and uncertain nature of the sector, but its successful application depends on transparency, fairness and intermediaries in the process (

An option to improve the growers’ household income is turning into organic growing and shading the coffee plantations. These coffee production systems would fetch better prices than the conventional system, but costs and premium prices would not guarantee high profits in the long run according to an evaluation in other coffee producing countries (

The increasing farming costs forced all inefficient growers to leave the sector, a hypothesis that is proved by the exit prices obtained in the model. H and L coffee prices would be signs of profitable activity despite the volatility and uncertainty of the sector. The Ecuadorian government implemented a program offering technical and financial support. This policy only improves the harvest in the short or medium term. The main problem remains in the volatile and uncertain prices and increasing cost of production in the long term, which coffee growers have to face each year. The government and coffee growers must work together towards efficient production: finding a way to have an attractive and profitable activity despite of volatility and uncertainty.

We thank anonymous referees for helpful comments and suggestions.

Values expressed in current United States Dollars.

Arabica classification of International Coffee Organization (ICO)

If A ≠ 0 and P → 0 inV0(P), there would be a value of the option to enter, that situation is not logical, because firms do not have incentive to enter with P → 0. So, the constant A must be equal to 0.

If B ≠ 0 and P → ∞ in V1(P), there would be a value of the abandonment option, that situation is not logical, because with a p → ∞ a firm never has incentive to take exit decision. So, the constant B must equal be to 0.

The results data and test execution are available from the author upon request.

The MAGAP published the cost farm structure in: http://sinagap.agricultura.gob.ec/insumos-cafe.

Paid price data is adjusted to coffee cherry prices according to the COFENAC information.

We selected the last year (2012) for the sensitivity analysis due to its more complete historical information to determine the distribution for each variable of the model.