La Hacienda Musa was a long way from Leuven, Belgium. But for Maria Keller, the transition was as natural as it could be. She had spent twenty years in Leuven studying banana genetics at the Catholic University of Leuven’s Laboratory of Tropical Crops, the world center of banana research. She had learned about the challenges the banana-growing industry faced from a variety of diseases, why bananas seemed to be especially susceptible, and how difficult it is to develop new strains of the world’s most popular fruit. But after two decades of study, Maria was ready for something new.

She did her homework, packed her few possessions, and headed to her newly purchased banana plantation in Costa Rica. To say that La Hacienda Musa was already a banana plantation was overstating the case. In fact, Maria owned 100 hectares of previously cleared land on which bananas had never been grown. Because this plot was isolated from established banana-growing operations in Costa Rica, the land should be reasonably free from the most important and virulent of banana diseases, Black Sigatoka, a fungal leaf blight.

The isolation, coupled with Maria’s expert knowledge of banana culture, and especially the new varieties she had brought with her from Belgium, suggested that she ought to be able to make a success of her new venture. The question that faced Maria at the moment was how much, if any, of her 100 hectares should be dedicated to organic bananas. There were good reasons to go organic: top-quality organic produce would command a premium, and her isolated location would be ideal for growing organic bananas. In 2007, Costa Rica had announced its intention to become the first fully carbon-neutral country.

As part of its efforts to offset all Costa Rican carbon emissions, tourists and businesses would pay a voluntary “tax” that would be used to fund conservation, reforestation, and other enterprises that would help move the country toward carbon neutrality. Some of those tax revenues would support organic farming in order to reduce the use of petrochemical-based fertilizers. Although Maria did not expect any rebates that would reduce her costs, she knew that if she went organic, she would receive support in a variety of small ways, such as special soil analyses, access to compost, and help locating workers with organic farming experience.

Any land that was not planted in organic bananas would be used to grow bananas conventionally. Under conventional growing methods, La Hacienda Musa would produce an expected yield of 10 metric tonnes of bananas per hectare. Because of the vagaries of the weather, pests, and diseases, the actual yields were uncertain. Maria had good access to historical data, and so she knew that, with conventional growing methods, the actual yield on her plantation would be approximately normally distributed with mean 10 tonnes per hectare and a standard deviation of 0. 8 tonnes per hectare.

Written by Robert T. Clemen, © 2009. This case was written as a basis for class discussion rather than to illustrate effective or ineffective handling of an administrative situation. Although the case is entirely fictitious, much of the information is taken from Banana: The Fate of the Fruit that Changed the World, by Dan Koeppel, New York: Hudson Street Press (2008). The word “Musa” is the name of the genus in which bananas are classified. The Cavendish variety that is eaten worldwide is a hybrid cross of a male Musa acuminata and a female Musa paradisiacal. 1

The uncertainty associated with organic farming was greater than conventional methods because the methods were less established in general and particularly because less was known about how to mitigate diseases and insect infestations using organic means. Maria estimated that yields would be normally distributed with a mean of 9. 2 tonnes per hectare and a standard deviation of 2. 4 tonnes per hectare. Because of their common dependence on the weather, the yields for organic and conventional bananas were positively correlated, with a correlation coefficient of 0. 0. The prices for bananas were also uncertain. The price (paid to the grower) for conventional bananas was normally distributed with a mean of $220 per tonne and a standard deviation of $28 per tonne. Because large yields for La Hacienda Musa tended to occur at the same time as large yields from other banana plantations, large yields tended to correspond to lower market prices. Thus the market price was negatively correlated with Maria’s yields for conventionally grown bananas, having a correlation coefficient of -0. 50.

Organic bananas would sell at a premium over conventional bananas, but how much this premium would be was uncertain. Maria thought the percentage premium would have a lognormal distribution with a mean of 15% and standard deviation of 2. 5%. (A premium of 5%, for example, meant that the price paid for organic bananas would be 5% more than the price for conventional bananas. ) This premium depended mainly on market factors – how many growers were in the organic business, consumer demand for organic produce – and was independent of all of other uncertainties Maria faced.

Finally, the costs associated with growing bananas were uncertain and approximately normally distributed with a mean of $1800 per hectare and a standard deviation of $300 per hectare. Because the uncertainty in growing costs was primarily due to labor rates and water use, the growing costs were identical under the two growing methods. These costs were uncorrelated with the other uncertainties. Maria smiled to herself as she realized that her dilemma was actually quite simple to state: how much of her land should she plant in organic bananas and how much in conventional? Although the question seemed straightforward, the answer was not obvious!

Download La_Hacienda_Musa. xlsx. Using it as a starting point, create a simulation model to answer the following questions: 1. (6 points) Suppose that Maria Keller plants all 100 hectares in organic bananas. Create a risk profile for her total profit. What is her expected (mean) total profit? What is the probability of a loss (i. e. , negative profit)? 2. (2 points) What is the probability that organically grown bananas will be more profitable per hectare than conventionally grown bananas? 3. (2 points) Suppose that Keller plants 50 hectares in organic and 50 in conventional bananas.

Create a risk profile for her total profit. What is the expected total profit in this scenario? What are the 10th, 50th, and 90th percentiles for profit? 4. (4 points) Maria asks you to look at five possibilities: 0, 25, 50, 75, and 100 hectares planted in organic bananas, and the balance conventional. Use Crystal Ball to analyze these five possibilities. Provide statistics for Maria’s total profit in each possibility, and create a trend chart in order to compare the distributions. 5. (2 points) Based on your analysis, what advice would you give Maria to help her decide how many hectares to plant in organic?

To help stimulate growth in the supply of organic produce, Dole (the fruit and vegetable company) is contemplating giving growers like Maria Keller a guaranteed minimum price (GMP) for organic bananas. For example, if the GMP were $260 per tonne, Maria would get $260 per tonne or the market price, whichever was greater. Dole’s hope is that such a price guarantee would help overcome growers’ concerns about the risks of growing bananas organically. 6. (5 points) Assume the GMP is $260 per tonne, and that Maria plants all 100 hectares in organic bananas. Create a risk profile for Maria’s total profit. What is her expected profit?

What is the probability of a loss? How does this compare to her risk profile without the GMP? 7. Dole has asked you to help them understand how the GMP will affect them. Their incremental cost per tonne of organic bananas can be calculated as the difference between what they would pay per tonne under the GMP program and what they would pay without the GMP. (In other words, some of the time the price is the same, when the market price exceeds the GMP. Other times the GMP is larger than the market price, and so they would be paying more. ) a. (3 points) If the GMP is $260, create the risk profile for Dole’s incremental cost per tonne.

What is the expected value? What is the probability that the incremental cost is zero? What is the probability that the incremental cost is greater than $10. 00? What is the 90th percentile? b. (2 points) Dole’s managers have argued about what the GMP should be. One suggestion is that on average, Dole’s incremental cost should be no more than $2. 00 per tonne. Find a GMP that gives Dole an expected incremental cost per tonne of $2. 00. If Dole uses this GMP, what is the probability that the incremental cost is zero? c. Another manager has argued that the GMP should be set to protect the farmers against the low end of the price range.

The suggestion is to set the GMP at the 25th percentile of the organic price distribution. i. (2 points) What is the 25th percentile of the organic price? If Dole uses this value as its GMP, what is its expected incremental cost per tonne, and what is the probability that the incremental cost per tonne is less than or equal to $10? ii. (2 points) Consider the effect on Maria’s profit of a GMP equal to 25th percentile of the organic price. Assuming she plantc. is all 100 acres in organic, create an overlay chart showing her profit risk profiles with the GMP and without (from Q1). What is the difference in the mean? In the standard deviation?