| Course | BUS 540 Managerial Economics |
|---|---|
| Module | Module 7 |
| Paper type | Decision analysis under risk |
| Length | About 1,068 words, 6 pages |
| Format | APA 7 student paper |
| School | Aspen University |
| Program | MBA |
| Updated | October 2026 |
Free sample paper for BUS 540 Module 7
Three Frosty Nights in Ten Springs: Expected Value, Risk and the Price of Information for a Cherry Orchard
Student Name
MBA Program, Aspen University
BUS 540: Managerial Economics
Instructor Name
Month Day, Year
Three Frosty Nights in Ten Springs: Expected Value, Risk and the Price of Information for a Cherry Orchard
Grand Traverse Bay Orchards, a composite family farm near Traverse City, Michigan, grows tart cherries on 160 acres. Cherry trees bloom in spring, and a hard frost after bloom can kill the blossoms and destroy most of the year's crop. The owners have faced several damaging frosts in recent decades and are deciding among three responses: install wind machines, tall fans that pull warmer air down into the orchard on cold, still nights; buy crop insurance that pays a share of frost losses; or continue without protection. This paper applies decision analysis under risk to the choice.
The Decision and the Probabilities
The uncertain event is whether a damaging frost occurs after bloom in a given year. The orchard's records for the past 20 springs show six years with frost damage that cut the crop by more than half, a probability of 6 in 20, or 0.30. The owners recognize that climate may be changing this probability, a point the analysis returns to below.
The consequences of each option, stated as yearly costs and losses, are based on the orchard's records, equipment quotes and an insurance agent's quote.
| Option | Fixed yearly cost | Loss in a frost year | Loss in a normal year |
|---|---|---|---|
| Do nothing | $0 | $210,000 | $0 |
| Wind machines | $38,000, including financing, fuel and maintenance | $40,000 | $0 |
| Crop insurance covering 75% of losses | $52,000 premium | $52,500, the uncovered 25% | $0 |
Expected Costs
The expected cost of each option is its fixed cost plus the probability-weighted loss (Baye & Prince, 2022). Doing nothing has an expected cost of 0.30 times $210,000, or $63,000 a year. Wind machines cost $38,000 plus 0.30 times $40,000, or $50,000. Insurance costs $52,000 plus 0.30 times $52,500, or $67,750. On expected value alone, wind machines are the best choice, saving $13,000 a year compared with doing nothing and $17,750 compared with insurance. Insurance is the most expensive on average because premiums include the insurer's costs and profit.
The Decision Tree
The decision can be drawn as a tree. A square decision node branches into the three options. Each option leads to a round chance node with two branches: frost, with probability 0.30, and no frost, with probability 0.70. At the end of each branch is the total cost for that year: $210,000 or $0 for doing nothing; $78,000 or $38,000 for fans; $104,500 or $52,000 for insurance. Folding back the tree, multiplying each end value by its probability and adding, gives the expected costs above.
Looking Beyond the Average
Expected value assumes the orchard can absorb the variation, but a single bad year matters to a family farm with loans to pay. The worst case for doing nothing is a $210,000 loss, which would force the owners to borrow against their land. The worst case for fans is $78,000, and for insurance $104,500. Fans have both the lowest expected cost and the smallest worst case, which makes the choice unusually clear.
How People Weigh Risk
Kahneman and Tversky (1979) found that people evaluate outcomes as gains and losses relative to a reference point rather than as final wealth, that losses loom larger than equal gains, and that people overweight outcomes that are certain relative to those that are merely probable. Their prospect theory helps explain the owners' feelings. Paying a certain $38,000 a year for fans feels like a sure loss, while doing nothing offers a chance of losing nothing. Yet the owners also describe the frost years as devastating, consistent with loss aversion. Recognizing these tendencies helps them separate their feelings about paying for protection from the numbers.
The Value of Better Information
Raiffa (1968) showed how to value information before buying it: compare the expected outcome when deciding with the information to the expected outcome when deciding without it. Suppose that, with fans installed, the owners could also rent portable heaters for the season for $15,000, which would cut a frost year's loss from $40,000 to $15,000. Without knowing whether frost will come, renting has an expected cost of $15,000 plus 0.30 times $15,000, or $19,500, compared with 0.30 times $40,000, or $12,000, for not renting, so the owners would not rent. If they knew in advance that a frost was coming, they would rent only in frost years, giving an expected cost of 0.30 times $30,000, or $9,000. Perfect information would therefore be worth $12,000 minus $9,000, or $3,000 a year. A private long-range frost forecasting service offered at $4,500 a year costs more than perfect information would be worth, and its forecasts are far from perfect, so it should be declined.
Other Ways to Reduce the Risk
The three options are not the only tools. Overhead irrigation can protect blossoms by coating them in ice that releases heat as it forms, but it requires large volumes of water and can break limbs. Planting later-blooming varieties lowers exposure but takes years to pay off as young trees mature. Selling part of the crop under contracts with fixed prices spreads price risk but not frost risk. The owners considered these and set them aside for now, because each either addresses a different risk or takes too long to help. Naming them shows that the comparison was made among realistic alternatives.
Sensitivity to the Probability
The recommendation depends on the frost probability. If the probability fell to 0.20, doing nothing would cost $42,000 in expectation and fans $46,000, reversing the ranking. If it rose to 0.40, the advantage of fans would grow. Because warmer winters can bring earlier bloom and greater exposure to late frosts, the owners believe the probability is more likely to rise than fall, which strengthens the case for fans.
Recommendation
The orchard should install wind machines, which have the lowest expected cost and the smallest worst-case loss at the estimated frost probability. It should decline the forecasting service and review the decision if records over the next five years suggest the frost probability has fallen below about 0.25.
Conclusion
Decision analysis turned an anxious choice into a structured one. Expected value favored wind machines, the worst-case comparison confirmed the choice, prospect theory explained the owners' hesitation, and Raiffa's method showed that extra information was not worth its price. The analysis also identified the one number that could change the answer, the probability of frost, and set a rule for revisiting it.
References
Baye, M. R., & Prince, J. T. (2022). Managerial economics and business strategy (10th ed.). McGraw Hill.
Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), 263-291. https://doi.org/10.2307/1914185
Raiffa, H. (1968). Decision analysis: Introductory lectures on choices under uncertainty. Addison-Wesley.
Reading the BUS 540 Module 7 assignment instructions
Most real business choices are bets on events no one controls, so BUS 540 devotes a module to deciding well when outcomes depend on chance. A single uncertain decision is analyzed below from probabilities to recommendation. Define the alternatives and the uncertain events, and estimate probabilities from data where possible. Compute the expected value or expected cost of each option, showing each step. Use a decision tree or table to make the structure clear. Look beyond expected value to the spread of outcomes, including the worst case. Discuss how decision-makers' attitudes toward risk affect the choice, with research. Calculate the value of additional information if relevant. Recommend a decision and say what would change it.
How this BUS 540 Module 7 example is built
The paper opens with Grand Traverse Bay Orchards, 160 acres of tart cherries, and three options. Twenty springs of records show six damaging frosts, a probability of 0.30. A table lists each option's fixed yearly cost and loss in a frost year: doing nothing loses $210,000 in a frost year; fans cost $38,000 a year and limit the loss to $40,000; insurance costs $52,000 and covers 75% of losses. Expected costs are $63,000, $50,000 and $67,750. A worst-case comparison shows fans also have the smallest maximum loss. Kahneman and Tversky's Econometrica article explains loss aversion and why the owners' discomfort with doing nothing is predictable. Raiffa's Decision Analysis supplies the method for valuing information, and a calculation shows a $4,500 long-range forecast service is not worth buying. The recommendation is fans, with conditions.
Where the marks sit in the BUS 540 Module 7 rubric
Decision analysis papers in an MBA economics course are marked on correct expected value calculations, a clear structure such as a decision tree, attention to risk beyond the average and thoughtful use of research on how people judge risk. This example derives the probability from the orchard's own records and shows each expected cost calculation, so the grader can check the arithmetic. It compares worst cases as well as expected values, which recognizes that a firm can be ruined by one bad year even if an option looks good on average. Kahneman and Tversky's Econometrica article and Raiffa's book supply the theory of risk attitudes and the method for valuing information, and Baye and Prince's text supplies the expected value framework. The calculation of the value of perfect information shows a skill that instructors reward at this level.
BUS 540 Module 7 help: mistakes that cost marks
The most common error in Module 7 is computing expected value without stating where probabilities came from. Use data where possible and explain any judgment. Another mistake is mixing costs and losses inconsistently; keep all figures in the same terms, such as yearly cost. Show every calculation. Do not stop at expected value; examine the range of outcomes and the worst case, since businesses with limited cash cannot always play the averages. Discuss risk attitudes and how they might change the choice. If you calculate the value of information, compare it with the information's price. Draw a decision tree or table so the structure is clear. Finally, test how sensitive your recommendation is to the probability estimate, since that is often the most uncertain number in the analysis.
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BUS 540 Module 7 questions, answered
What does BUS 540 Module 7 usually ask for?
Aspen's BUS 540 covers decisions under risk and uncertainty in this module, so analyzing a business decision with expected value, decision trees and risk attitudes is typical. Check your classroom prompt.
What is expected value?
The probability-weighted average of the outcomes of a decision, found by multiplying each outcome by its probability and adding the results.
What is the expected value of perfect information?
The most a decision-maker should pay to learn the outcome of an uncertain event before deciding, equal to the improvement in expected value that knowing it would bring.
Where can I find a free BUS 540 Module 7 sample paper?
The full analysis appears above: a cherry orchard choosing among frost fans, insurance and doing nothing, with expected costs, a decision tree, worst cases, prospect theory and the value of information.
What is loss aversion?
The tendency, documented by Kahneman and Tversky, for people to weigh losses more heavily than gains of the same size.