Chapter 25 - Uncertainty - Overview PDF

# Chapter 25: Uncertainty - Overview ## Uncertainty - Overview - **Relevance:** Information is applicable to the situation. - **Ease of use:** Information can support decision-making as is, without a lot of effort. - **Integrity:** Information is accurate, consistent, and reliable. - **Timeliness:...

# Chapter 25: Uncertainty - Overview ## Uncertainty - Overview - **Relevance:** Information is applicable to the situation. - **Ease of use:** Information can support decision-making as is, without a lot of effort. - **Integrity:** Information is accurate, consistent, and reliable. - **Timeliness:** Information is available in time to make an effective decision. ## Methods of Communicating Uncertainty - **Probability distributions:** A function that shows the probability as a percentage of different outcomes for an event. - **Payoff tables:** A way to present the expected payoff of the alternative actions by showing the actions an organization may take against the events that cannot be controlled. - **Graphs:** A visual representation of data that can show data as a range or error bar, rather than as a point. ## Lesson 1: Introduction to Uncertainty ### Technical Competencies: - 3.1.1. Evaluates management information requirements. - 3.1.2. Documents and assesses business processes, systems, and data requirements and recommends improvements to meet information needs. ### Learning Outcomes: - Describe decision-making under uncertainty. - Identify the elements of decision-making under uncertainty. - Discuss the effect of the quality of information used in decision-making on uncertainty. - Identify the four elements of quality information used in decision-making on uncertainty. - Identify methods of communicating uncertainty, such as probability distributions, payoff tables, and graphs. ## 25.1 Uncertainty Defined Uncertainty occurs when an action can have more than one outcome and the outcome that will occur is unknown. For example, when someone tosses a coin, there are two possible outcomes: heads up or heads down. For an organization, uncertainty means that it is not possible to know the exact outcome of its actions on future performance. Risk is the potential for uncertainty to impair an organization’s ability to achieve its objectives. When a gambler tosses a coin and places a wager on whether the coin will land heads up or heads down, the gambler is facing risk. Similarly, an organization faces many risks that may impede its ability to meet its strategic and operational objectives, such as its ability to raise sufficient capital or future changes in customer preferences. Most important decisions made in organizations involve actions in the face of uncertainty and, therefore, risk. The management accountant often identifies risks and their possible effects on decision-making to management. This chapter introduces the basics of decision-making under uncertainty. ### 25.1.1 Decision-Making Under Uncertainty The following probability definitions are important to the idea of decision-making under uncertainty: - **Objective criterion:** This is a function expressing the objective, such as minimizing cost, maximizing income, or maximizing market share. - **Set of possible actions:** This is the set of alternative actions the decision maker can undertake to meet the objective. In the case of tossing a coin, there are two wagers (actions): wager the coin will fall heads up or wager it will fall heads down. - **Set of possible events:** This is the set of possible events that occur after actions have been taken that affect the outcome, over which the decision-maker has little or no control. These events are beyond the control of the decision maker and are often called states of nature. In the case of the coin tossing, the possible events are that the coin will fall heads up or heads down. Other possibilities, such as the coin landing on its edge, are excluded. - **Set of probabilities that defines the chance of each event occurring:** In the case of tossing a fair coin, the chance of the coin landing heads up is believed to be half and the chance of it landing heads down is believed to be half. The sum of the probabilities of all possible events must equal one. - **Set of possible outcomes:** Outcomes measure the consequence to the decision maker of each action-event pairing. Decision makers often express the set of outcomes in an outcomes table. The following table for the coin-toss example assumes that the gambler is betting $1 on the coin toss: | Outcome | Heads Up | Heads Down | |---|---|---| | Gambler Bets Heads Up | Win $1 | Lose $1 | | Gambler Bets Heads Down | Lose $1 | Win $1 | Each of these elements has a level of uncertainty. There is no objective way of determining any of them. ## 25.2 Quality of Information When dealing with uncertainty, the quality of information becomes a key consideration for the management accountant. There are four basic dimensions of quality information: relevance, ease of use, integrity, and timeliness. <start_of_image> Table 1: Dimensions of Quality Information | Dimension | Description | |---|---| | Relevance | Information is applicable to the situation. | | Ease of use | Information can support decision-making as is, without a lot of effort. | | Integrity | Information is accurate, consistent, and reliable. | | Timeliness | Information is available in time to make an effective decision. | ## 25.3 Communicating Uncertainty Management accountants have a variety of tools at their disposal that can be used to communicate uncertainty to management and other parties. This section discusses three such tools: probability distributions, payoff tables, and graphs. ### 25.3.1 Probability Distributions for Event Uncertainty Decision makers assess event uncertainty, which is uncertainty regarding whether a future event will occur or at what value, using probability distributions. In a discrete probability distribution, each of a finite number of events is assigned a probability of occurring. The result of a coin toss is modeled as a discrete distribution as follows: | Event | Probability | |---|---| | Coin Lands Heads Up | 50% | | Coin Lands Heads Down | 50% | The discrete probability distribution can be further analyzed using expected value, which is the sum of each risk-weighted option when there is event uncertainty. It builds on the discrete probability distribution by arriving at a single expected value to assist with planning. To compute the expected value of sales in the above distribution, each sales amount (outcome) is multiplied by its probability and all of the weights are summed. For a coin toss, the probability of one flip landing heads up is 50%. If the coin was flipped 500 times, the expected value of landing heads up would be 250 times (500 flips x 50% probability of heads up). This does not mean there will be exactly 250 heads up flips in 500 flips total; instead, the expected value represents an amount that is most likely given the probability of each flip being heads. ### 25.3.2 Payoff Tables In decision analysis, the decision maker is facing uncertain acts of nature, where the outcome of the decision is determined either by random acts of nature or by the actions of competitors. Decision makers use payoff tables to set the actions they may take against the events they cannot control to estimate the expected payoff of the alternative actions. Consider an entertainment company that is holding an outdoor concert. Based on prior concerts, it is expected that between 10,000 and 12,000 tickets will be sold. If weather is poor on the date of the concert, revenue from concessions will be significantly lower compared to that of clear weather. The uncertainty in the expected revenue from the concert can be presented as follows: | Tickets Sold | Clear Weather | Poor Weather | |---|---|---| | 10,000 | $750,000 | $550,000 | | 12,000 | $1,000,000 | $800,000 | ### 25.3.3 Graphs Graphs are a useful tool to present uncertainty because they provide a visual representation to management or other users of the possible range of outcomes. Each point on the graph is represented by both an x-value and a y-value. If there is uncertainty in the value, either the x-value or y-value may be a range, rather than a point, called an error bar. An error bar shows the range of each possible value so that users of the graph can visually see the uncertainty in the data. Error lines can also be presented on a graph that highlight the high and low estimates. Consider a glass manufacturer that is thinking about replacing an aging furnace to reduce its electricity costs. Comparing electricity costs of running the old furnace to electricity costs of a new furnace involves uncertainty because the organization’s electricity usage varies and the cost of electricity may change. A graph can be used to show the range of possible electricity costs using error bars, rather than points, and error lines can be used to present the high and low cost estimates, as follows: [Diagram of a graph showing the cost of electricity vs. electricity usage, with error bars representing uncertainty.] ## Lesson 2: Uncertainty - Overview - Summary Problem ### Technical Competencies: - 3.1.1 Evaluates management information requirements. - 3.1.2 Documents and assesses business processes, systems and data requirements and recommends improvements to meet information needs. ### Learning Outcome - Describe uncertainty in decision-making. ### Summary Problem #### Required: 1. Differentiate between risk and uncertainty. Provide an example of uncertainty and risk in the decision-making process. 2. Identify the four basic dimensions of information quality. 3. An organization is forecasting its revenue for the next year and would like to communicate uncertainty in the calculations. Describe how probability distributions, payoff tables, and graphs could be used to present uncertainty in its revenue forecast. #### Solution: 1. An organization is operating in uncertainty when more than one outcome may occur in the future and the outcome is unknown. Risk occurs when uncertainty may prevent an organization from achieving its goals. For example, an organization that manufactures plastic bags has a strategic objective of increasing its net income. The organization is considering adding a paper bag division. There is uncertainty in this decision because management does not know whether the paper bag division will be profitable or not, or what the effect will be on the plastic bag division’s net income. There is risk associated with this decision, as the paper bag division may be unprofitable, causing the organization not to meet its strategic objective of increasing net income. 2. The four basic dimensions of information quality are: - **Relevance:** Information that is appropriate and useful for the given situation. - **Ease of use:** Information that can be used to support decision-making without much effort. - **Integrity:** Information that is: - Accurate (fairly represents the underlying data). - Consistent (in line with other information received). - Reliable (obtained from dependable sources). - **Timeliness:** Information that is received in time to make decisions effectively. 3. **Probability distribution:** A probability distribution presents the probability of a number of possible outcomes. The organization could create a number of forecasts of annual revenue and assign a probability to each possible forecast. This would allow decision makers to determine which revenue forecast is the most likely. In addition, an expected value for annual revenue could be calculated by multiplying the possible revenue outcomes with the probabilities. **Payoff table:** A payoff table shows possible outcomes when facing future uncertain acts of nature. The organization could use a payoff table to show the possible revenue forecast depending on different ways competitors may compete. **Graph:** Graphs can be used to communicate uncertainty through showing data ranges, such as error bars, instead of data points. The organization could present a monthly forecast of revenue as a graph that presents each month’s revenue estimate as an error bar. This would show decision makers to quickly view the range of possible outcomes for revenue each month. ## Practice Problem 1 (20 minutes) Mary, the president and general manager of Down the Road Construction Co. (Down the Road), is considering how much to bid on a government contract. Mary has determined that the company’s cost to complete the contract will be $5,000,000. Bids must be made in multiples of $100,000. Based on the historical pattern of winning bids for similar contracts, Mary has put together the following table of bids and the probability of each one being accepted: | Bid | Probability of Winning | |---|---| | $5,100,000 | 30% | | $5,200,000 | 25% | | $5,300,000 | 15% | | $5,400,000 | 10% | | $5,500,000 | 5% | | $5,600,000 | 0% | #### Required: 1. Describe uncertainty and risk as it relates to Down the Road’s bid on the government contract. 2. Describe the following decision-making elements for Down the Road: - Objective criterion - Set of possible actions - Set of possible events - Set of probabilities that defines each chance of occurring - Set of possible outcomes ## Practice Problem 2 (25 minutes) Rashad is a management accountant for a beer company in Eastern Canada. He has been assigned to develop a five-year forecast of the organization’s revenues and costs, using sensitivity analysis. Rashad has been given the following types of data: - Internally generated demand data for the past 10 years, showing consumer adoption by age, gender, education level, and socio-economic standing. - Temperature, rainfall, interest rates, employment rates, and economic growth rates for the past 10 years from various Canadian government websites. - Expectations from economic analysts for the upcoming year, with respect to economic growth, employment rates, and exchange rates. - The Farmers’ Almanac’s annual weather forecast, which predicts that the upcoming year will have mild temperatures with an average level of rainfall. The organization’s main raw material is Canadian-grown hops, of which the price varies based on the weather each summer. The beer is sold only in Eastern Canada. #### Required: 1. Assess the data integrity for each type of data used by Rashad in preparing the forecast (that is, relevance, ease of use, integrity, and timeliness). 2. Discuss the use of professional skepticism with the data provided to Rashad and the implications to the beer company if professional skepticism is not used. ## Solution to Practice Problem 1 ### Competencies: - 3.1.1 Evaluates management information requirements (Entry - Level B). - 3.1.2 Documents and assesses business processes, systems and data requirements and recommends improvements to meet information needs (Entry - Level C). ### Knowledge Item: - Information and decision-making - Framing information recognizing uncertainty (Entry - Level C). - Transformation of data to decision relevant criteria (Entry - Level C). ### a) Uncertainty and Risk Uncertainty describes a situation in which more than one possible outcome can occur, and the outcome is unknown. Mary is putting in a bid for a government contract, and the government may accept her bid or a competitor’s bid, so there is more than one possible outcome. It is unknown which contractor will be selected prior to the government making its selection, so the outcome of the situation is unknown. Risk is the potential that uncertainty will affect an organization's ability to achieve its objectives. For Down the Road, the objective is likely to maximize profit, so putting in a winning bid would help the organization to achieve that objective. However, it is unknown whether Down the Road’s bid or a competitor’s bid will be accepted. There is a risk that Down the Road will not win the contract, which would not provide profit for the organization. ### b) Decision-Making Elements #### Objective Criterion Mary would like Down the Road’s bid to be accepted for the government contract. #### Set of Possible Actions Mary has already decided to bid and is now determining how much to bid. Down the Road can bid for the government contract in increments of $100,000. The lowest bid is $5,100,000, because total costs of the contract are $5,000,000, and a bid any lower would not give Down the Road any profit. The maximum bid should be $5,600,000, because a higher bid does not have any probability of winning. #### Set of Possible Events Other construction companies will also be bidding on the government contract. The government will accept one bid, either from Down the Road, or another construction company. #### Set of Probabilities that Defines Each Chance of Occurring The probabilities of each possible bid of Down the Road being accepted is as follows: | Bid | Probability of Winning | |---|---| | $5,100,000 | 30% | | $5,200,000 | 25% | | $5,300,000 | 15% | | $5,400,000 | 10% | | $5,500,000 | 5% | | $5,600,000 | 0% | #### Set of Possible Outcomes There are two possible outcomes: Down the Road’s bid is accepted or it is not accepted. The outcomes result in the following: | Outcome | Description | |---|---| | Down the Road’s bid is accepted | Down the Road receives revenue based on the accepted bid and incurs $5 million in expenses. However, $5 million is an estimate, and costs may be higher or lower than expected. This would have an impact on Down the Road’s profitability. | | Down the Road’s bid is not accepted | Down the Road does not receive any revenue or incur any expenses from the contract. | ## Solution to Practice Problem 2 ### Competencies: - 3.1.1 Evaluates management information requirements (Entry - Level B). - 3.1.2 Documents and assesses business processes, systems and data requirements and recommends improvements to meet information needs (Entry - Level C). ### Knowledge Item: - Information and decision-making - Dimensions of information quality (relevance, ease of use, integrity, timeliness (Entry - Level C). - Professional skepticism regarding data (Entry - Level C). ### a) Data Integrity Assessment #### Internally generated demand data (consumer adoption by age, gender, education level, and socio-economic standing over past 10 years) - **Relevance:** This data is directly related to the organization’s customers, which increases its relevance. However, it is past data, so the demographic information about customers may not be relevant to future customers, decreasing its relevance. - **Ease of use:** Since this data came from the organization, it is likely in a format that is easy for Rashad to use. - **Integrity:** The customer data likely has high integrity, assuming the organization has adequate controls over the data. - **Timeliness:** The organization already has this demand data, so it is timely. #### Government website data (temperature, rainfall, interest rates, rates of employment, and economic growth rates over the past 10 years) - **Relevance:** Past weather and economic data may not be relevant because it is from the past and will not necessarily predict the future. However, correlations may be made between past weather and economic data and sales and demand that may be useful for future forecasting. - **Ease of use:** Given that the data is from a variety of websites, it would likely need to be aggregated and analyzed before it can be used. - **Integrity:** The source is Canadian government websites, so the data would have high integrity because federal agencies and departments are required to meet rigorous standards to ensure accurate, consistent, and reliable data. - **Timeliness:** Although this information relates to the past, it is timely in the sense that the data was published in a timely manner and is readily available on government websites. #### Economic analyst data (forecasted economic growth, employment rates, and exchange rates) - **Relevance:** The forecasted economic growth is likely to be relevant because the company’s sales could grow in a similar manner. However, the growth forecast is only for one year, so its relevance is limited to next year, while Rashad is required to prepare a five-year forecast. The exchange rates are unlikely to be relevant to the forecast because exchange rates probably do not impact the beer company’s future costs or revenue, given that the raw materials are grown in Canada and the beer is sold locally. - **Ease of use:** Analyst data generally comes from reports or websites, so the data is unlikely to be in a format that can be used immediately by Rashad. - **Integrity:** The data from economic analysts is related to the future, so whether it is reliable is difficult to know. However, if these analysts have a history of accurate predictions, the data may be reliable. To know whether the data is consistent, Rashad would have to compare it with similar data from additional sources, which may be difficult to obtain. Overall, the data may or may not have integrity, but it would be difficult for Rashad to judge. - **Timeliness:** The economic analyst data exists already and can be used, so it is timely. #### Farmer’s Almanac (annual forecasted temperature and rainfall) - **Relevance:** Weather affects the price of hops, so future weather data is likely to be relevant. - **Ease of use:** The data contained in the Farmers’ Almanac is general weather information, rather than specific temperatures and weather patterns. Therefore, it would be difficult for Rashad to use this information to predict the future price of hops and to use it in the forecast. - **Integrity:** This data is anecdotal and is unlikely to be accurate, consistent, and reliable. - **Timeliness:** The Farmer's Almanac is available in advance of a season, so this data is timely. Other responses are acceptable if supported. ### b) Professional Skepticism A management accountant must use professional skepticism when using the data to create a financial forecast with a sensitivity analysis. For Rashad, this means critically examining the data to ensure that it meets the dimensions of quality information described above. If the data used is not considered with professional skepticism before being incorporated into the financial forecast, the result may not be an accurate representation of the organization’s future results. As a result, using the forecast to make decisions might not be in the best interest of the organization.