La Hacienda Musa was located far away from Leuven, Belgium. However, Maria Keller easily adjusted to the change. Maria had dedicated twenty years to studying banana genetics at the Laboratory of Tropical Crops, which was the global hub for banana research at the Catholic University of Leuven. During her time there, Maria became knowledgeable about the obstacles faced by the banana-growing industry due to various diseases, the vulnerability of bananas, and the challenges involved in creating novel varieties of this highly popular fruit. Nonetheless, after two decades of focus on this subject, Maria felt prepared for a fresh endeavor.
After completing her homework, Maria packed her belongings and set off for her recently acquired banana plantation in Costa Rica. However, it would be an exaggeration to call La Hacienda Musa an existing banana plantation. In reality, Maria now owned 100 hectares of land that had been cleared previously but never used for banana cultivation. Due to its isolation from established banana farms in Costa Rica, this plot of land is expected to be relatively disease-free, specifically from Black Sigatoka, a highly contagious and destructive fungal leaf blight that affects bananas.
Maria’s extensive knowledge of banana culture, as well as her isolation and the new varieties she brought from Belgium, made her feel confident about succeeding in her new venture. The current dilemma for Maria is determining how much, if any, of her 100 hectares should be allocated for organic bananas. There are several compelling reasons for going organic: high-quality organic products would fetch higher prices, and her remote location provides ideal conditions for cultivating organic bananas. Furthermore, Costa Rica had declared its goal in 2007 to become the world’s first completely carbon-neutral country.
An optional “tax” will be implemented for tourists and businesses in Costa Rica to counterbalance carbon emissions. The generated revenue will be used for conservation, reforestation, and other initiatives to achieve carbon neutrality. A portion of the funds will be dedicated to promoting organic farming to reduce reliance on petrochemical-based fertilizers. Maria knew that choosing organic methods wouldn’t result in cost savings, but she was aware that specialized soil analysis, access to compost, and assistance in finding skilled organic farmers would be provided.
Any land not planted in organic bananas would be used for conventional banana growth. La Hacienda Musa’s expected yield was 10 metric tonnes of bananas per hectare using conventional methods. However, actual yields were uncertain due to weather, pests, and diseases. Maria had historical data showing that the actual yield on her plantation would follow a normal distribution with a mean of 10 tonnes per hectare and a standard deviation of 0.8 tonnes per hectare.
This text was written by Robert T. Clemen in 2009. It serves as a basis for class discussion and does not aim to demonstrate effective or ineffective handling of an administrative situation. Although the case is entirely fictional, much of the information is sourced from Banana: The Fate of the Fruit that Changed the World, a book by Dan Koeppel, published by Hudson Street Press in 2008. The term “Musa” refers to the genus in which bananas are classified. The variety of banana known as Cavendish, which is consumed worldwide, is a hybrid combining a male Musa acuminata and a female Musa paradisiacal. 1
The uncertainty of organic farming is greater than conventional methods because they are less established and there is less knowledge about how to combat diseases and insect infestations using organic practices. According to Maria’s estimates, the yields for organic bananas would follow a normal distribution, with an average of 9.2 tonnes per hectare and a standard deviation of 2.4 tonnes per hectare. Both organic and conventional banana yields were positively correlated (correlation coefficient = 0.0), as they depended on the weather conditions. The price paid to growers for conventional bananas also followed a normal distribution, with an average of $220 per tonne and a standard deviation of $28 per tonne. When La Hacienda Musa had high yields, other banana plantations tended to have high yields as well, resulting in lower market prices (correlation coefficient of -0.50 between Maria’s conventionally grown banana yields and market price).
Organic bananas were anticipated to be priced higher than conventional bananas. The premium percentage for this price disparity was assumed to adhere to a lognormal distribution, with an average of 15% and a standard deviation of 2.5%. For instance, if the premium amounted to 5%, it indicated that the organic bananas would be priced 5% more than the conventional ones. The magnitude of this premium relied on market factors like the quantity of organic growers and consumer demand for organic produce. Maria experienced no other uncertainties impacting this premium.
Ultimately, the expenses associated with cultivating bananas remained uncertain, amounting to an average of $1800 per hectare and a standard deviation of $300 per hectare. These costs were consistent across both growing methods and unrelated to any other uncertainties. Maria recognized that her predicament revolved around determining the optimal allocation of her land for organic banana cultivation versus conventional banana cultivation. Nevertheless, finding the solution to this query proved to be challenging!
Download La_Hacienda_Musa. xlsx. Use it as a starting point to create a simulation model for the following questions:
1. (6 points) Create a risk profile for Maria Keller’s total profit if she plants all 100 hectares in organic bananas. Determine her expected mean total profit and the probability of a loss (negative profit).
2. (2 points) Calculate the probability of organically grown bananas being more profitable per hectare compared to conventionally grown bananas.
3. (2 points) Consider Keller planting 50 hectares of organic bananas and 50 hectares of conventional bananas.
Create a risk profile to determine the total profit. Calculate the expected total profit and identify the 10th, 50th, and 90th percentiles for profit. Maria wants to explore five possibilities: planting 0, 25, 50, 75, and 100 hectares with organic bananas while the rest are conventional. Utilize Crystal Ball to analyze these options. Provide profit statistics for each possibility and create a trend chart to compare the distributions. Based on the analysis, offer advice to Maria on the optimal number of hectares to plant organically.
To encourage the growth of organic produce, Dole is considering offering a guaranteed minimum price (GMP) to growers such as Maria Keller for organic bananas. This GMP would ensure that Maria receives either $260 per tonne or the market price, whichever is greater. The purpose of this price guarantee is to address growers’ worries about the risks involved in growing organic bananas.
Assuming the GMP is $260 per tonne and Maria uses all 100 hectares for planting organic bananas, let’s analyze the risk profile for her total profit and determine her expected profit.
Dole is interested in understanding question #7, which pertains to the probability of a loss and its comparison to their risk profile without the GMP. To assist them, they can determine their incremental cost per tonne of organic bananas by calculating the difference between what they would pay under the GMP program and what they would pay without it. If the market price exceeds the GMP, there will be no change in price. However, if the market price falls below the GMP, Dole will have to pay more. A thorough examination is needed to establish Dole’s risk profile for their incremental cost per tonne, assuming that the GMP remains at $260.
What are the expected value, probability of zero incremental cost, probability of incremental cost greater than $10.00, and 90th percentile?
(2 points) Dole’s managers have debated the ideal GMP. One proposal suggests that on average, Dole’s incremental cost should not exceed $2.00 per tonne. Determine a GMP that yields an expected incremental cost per tonne of $2.00 for Dole. If this GMP is used, what is the probability of having zero incremental cost?
c. Another manager argues for setting the GMP to safeguard farmers against the lower end of the price range.
The proposal is to establish the GMP at the 25th percentile of the organic price.
i. (2 points) What is the 25th percentile of the organic price? In the case that Dole adopts this value as its GMP, what would be its expected incremental cost per tonne, and what is the likelihood that the incremental cost per tonne is $10 or less?
ii. (2 points) Take into consideration the impact on Maria’s profit with a GMP equivalent to the 25th percentile of the organic price. Assuming she plants all 100 acres in organic, generate an overlay chart displaying her profit risk profiles with and without the GMP (from Q1). What is the difference in the mean? What about the standard deviation?