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ASSIGMENT # 306 Q : 1 What is meant by the "possible states of nature? ( briefly answer) Q:2What is meant by "prior probabilities?"(Briefly answer) Q:3What do "payoffs" represent in a payoff table?( briefly answer) Q:4What are some criticisms of maximax criterion?( briefly answer) Q:5What are some criticisms of Bayes' decision rule?( briefly answer) Q:6 What are some criticisms of maximin criterion?( briefly answer) 1. The activity, X (patientdays in this case), is plotted on the horizontal axis. Activity is known as the independent variable because it causes variations in the cost. From the scattergraph plot, it is evident that maintenance costs do increase with the number of patient days in an approximately linearfashion. In other words, the points lie more or less along a straight line that slopes upward and to the right. Cost behavior is considered linearwhenever a straight line is a reasonable approximation for the relation between cost and activity. Plotting the data on a scattergraph is an essential diagnostic step that should be performed before performing the highlow method or leastsquares regression calculations. If the scattergraph plot reveals linear cost behavior, then it makes sense to perform the highlow or leastsquares regression calculations to separate the mixed cost into its variable and fixed components. If the scattergraph plot does not depict linear cost behavior, then it makes no sense to proceed any further in analyzing the data. The HighLow Method Assuming that the scattergraph plot indicates a linear relation between cost and activity, the fixed and variable cost elements of a mixed cost can be estimated using the highlow method or the leastsquares regression method. The highlow method is based on the riseoverrun formula for the slope of a straight line. As previously discussed, if the relation between cost and activity can be represented by a straight line, then the slope of the straight line is equal to the variable cost per unit of activity. Consequently, the following formula can be used to estimate the variable cost: To analyze mixed costs with the highlow method, begin by identifying the period with the lowest level of activity and the period with the highest level of activity. The period with the lowest activity is selected as the first point in the above formula and the period with the highest activity is selected as the second point. Consequently, the formula becomes: Page 41 or Therefore, when the highlow method is used, the variable cost is estimated by dividing the difference in cost between the high and low levels of activity by the change in activity between those two points. To return to the Brentline Hospital example, using the highlow method, we first identify the periods with the highest and lowest activityin this case, June and March. We then use the activity and cost data from these two periods to estimate the variable cost component as follows: d Having determined that the variable maintenance cost is 80 cents per patientday, we can now determine the amount of fixed cost. This is done by taking the total cost at either the high or the low activity level and deducting the variable cost element. In the computation below, total cost at the high activity level is used in computing the fixed cost element: Both the variable and fixed cost elements have now been isolated. The cost of maintenance can be expressed as $3,400 per month plus 80 cents per patientday or as: The data used in this illustration are shown graphically in Exhibit 2-7. Notice that a straight line has been drawn through the points corresponding to the low and high levels of activity. In essence, that is what the highlow method doesit draws a straight line through those two points. EXHIBIT 2-7 High-Low Method of Cost Analysis Sometimes the high and low levels of activity don't coincide with the high and low amounts of cost. For example, the period that has the highest level of activity may not have the highest amount of cost. Nevertheless, the costs at the highest and lowest levels of activity are always used to analyze a mixed cost under the highlow method. The reason is that the analyst would like to use data that reflect the greatest possible variation in activity. Page 42 The highlow method is very simple to apply, but it suffers from a major (and sometimes critical) defectit utilizes only two data points. Generally, two data points are not enough to produce accurate results. Additionally, the periods with the highest and lowest activity tend to be unusual. A cost formula that is estimated solely using data from these unusual periods may misrepresent the true cost behavior during normal periods. Such a distortion is evident in Exhibit 2-7. The straight line should probably be shifted down somewhat so that it is closer to more of the data points. For these reasons, leastsquares regression will generally be more accurate than the highlow method. The LeastSquares Regression Method The leastsquares regression method, unlike the highlow method, uses all of the data to separate a mixed cost into its fixed and variable components. A regression line of the form Y = a + bX is fitted to the data, where a represents the total fixed cost and b represents the variable cost per unit of activity. The basic idea underlying the leastsquares regression method is illustrated in Exhibit 2-8 using hypothetical data points. Notice from the exhibit that the deviations from the plotted points to the regression line are measured vertically on the graph. These vertical deviations are called the regression errors. There is nothing mysterious about the leastsquares regression method. It simply computes the regression line that minimizes the sum of these squared errors. The formulas that accomplish this are fairly complex and involve numerous calculations, but the principle is simple. EXHIBIT 2-8 The Concept of Least-Squares Regression Fortunately, computers are adept at carrying out the computations required by the leastsquares regression formulas. The datathe observed values of X and Yare entered into the computer, and software does the rest. In the case of the Brentline Hospital maintenance cost data, a statistical software package on a personal computer can calculate the following leastsquares regression estimates of the total fixed cost (a) and the variable cost per unit of activity (b): Therefore, using the leastsquares regression method, the fixed element of the maintenance cost is $3,431 per month and the variable portion is 75.9 cents per patientday. In terms of the linear equation Y = a + bX, the cost formula can be written as where activity (X) is expressed in patientdays. Appendix 2A discusses how to use Microsoft Excel to perform leastsquares regression calculations. For now, you only need to understand that leastsquares regression analysis generally provides more accurate cost estimates than the highlow method because, rather than relying on just two data points, it uses all of the data points to fit a line that minimizes the sum of the squared errors. The table below compares Brentline Hospital's cost estimates using the highlow method and the leastsquares regression method: d When Brentline uses the leastsquares regression method to create a straight line that minimizes the sum of the squared errors, it results in estimated fixed costs that are $31 higher than the amount derived using the highlow method. It also decreases the slope of the straight line resulting in a lower variable cost estimate of $0.759 per patientday rather than $0.80 per patientday as derived using the highlow method. Page 44 IN BUSINESS THE ZIPCAR COMES TO COLLEGE CAMPUSES Zipcar is a car sharing service based in Cambridge, Massachusetts. The company serves 13 cities and 120 university campuses. Members pay a $50 annual fee plus $7 an hour to rent a car. They can use their iPhones to rent a car, locate it in the nearest Zipcar parking lot, unlock it using an access code, and drive it off the lot. This mixed cost arrangement is attractive to customers who need a car infrequently and wish to avoid the large cash outlay that comes with buying or leasing a vehicle. In this section of the chapter, we discuss how to prepare traditional and contribution format income statements for a merchandising company.3Merchandising companies do not manufacture the products that they sell to customers. For example, Lowe's and Home Depot are merchandising companies because they buy finished products from manufacturers and then resell them to end consumers. The Traditional Format Income Statement Traditional income statements are prepared primarily for external reporting purposes. The lefthand side of Exhibit 2-9 shows a traditional income statement format for merchandising companies. This type of income statement organizes costs into two categoriescost of goods sold and selling and administrative expenses. Sales minus cost of goods sold equals the gross margin. The gross margin minus selling and administrative expenses equals net operating income. EXHIBIT 2-9 Comparing Traditional and Contribution Format Income Statements for Merchandising Companies (all numbers are given) The cost of goods sold reports the product costs attached to the merchandise sold during the period. The selling and administrative expenses report all period costs that have been expensed as incurred. The cost of goods sold for a merchandising company can be computed directly by multiplying the number of units sold by their unit cost or indirectly using the equation below: Page 45 For example, let's assume that the company depicted in Exhibit 2-9purchased $3,000 of merchandise inventory during the period and had beginning and ending merchandise inventory balances of $7,000 and $4,000, respectively. The equation above could be used to compute the cost of goods sold as follows: Although the traditional income statement is useful for external reporting purposes, it has serious limitations when used for internal purposes. It does not distinguish between fixed and variable costs. For example, under the heading \"Selling and administrative expenses,\" both variable administrative costs ($400) and fixed administrative costs ($1,500) are lumped together ($1,900). Internally, managers need cost data organized by cost behavior to aid in planning, controlling, and decision making. The contribution format income statement has been developed in response to these needs. The Contribution Format Income Statement The crucial distinction between fixed and variable costs is at the heart of the contribution approach to constructing income statements. The unique thing about the contribution approach is that it provides managers with an income statement that clearly distinguishes between fixed and variable costs and therefore aids planning, controlling, and decision making. The righthand side of Exhibit 2-9 shows a contribution format income statement for merchandising companies. The contribution approach separates costs into fixed and variable categories, first deducting variable expenses from sales to obtain thecontribution margin. For a merchandising company, cost of goods sold is a variable cost that gets included in the \"Variable expenses\" portion of the contribution format income statement. The contribution margin is the amount remaining from sales revenues after variable expenses have been deducted. This amount contributes toward covering fixed expenses and then toward profits for the period. The contribution format income statement is used as an internal planning and decisionmaking tool. Its emphasis on cost behavior aids costvolumeprofit analysis (such as we shall be doing in a subsequent chapter), management performance appraisals, and budgeting. Moreover, the contribution approach helps managers organize data pertinent to numerous decisions such as productline analysis, pricing, use of scarce resources, and make or buy analysis. All of these topics are covered in later chapters. Cost Classifications for Decision Making LO2-7 Understand cost classifications used in making decisions: differential costs, opportunity costs, and sunk costs. Costs are an important feature of many business decisions. In making decisions, it is essential to have a firm grasp of the concepts differential cost, opportunity cost, and sunk cost. Differential Cost and Revenue Decisions involve choosing between alternatives. In business decisions, each alternative will have costs and benefits that must be compared to the costs and benefits of the other available alternatives. A difference in costs between any two alternatives is known as a differential cost. A difference in revenues (usually just sales) between any two alternatives is known asdifferential revenue. Page 46 A differential cost is also known as an incremental cost, although technically an incremental cost should refer only to an increase in cost from one alternative to another; decreases in cost should be referred to asdecremental costs. Differential cost is a broader term, encompassing both cost increases (incremental costs) and cost decreases (decremental costs) between alternatives. The accountant's differential cost concept can be compared to the economist's marginal cost concept. In speaking of changes in cost and revenue, the economist uses the terms marginal cost and marginal revenue. The revenue that can be obtained from selling one more unit of product is called marginal revenue, and the cost involved in producing one more unit of product is called marginal cost. The economist's marginal concept is basically the same as the accountant's differential concept applied to a single unit of output. Differential costs can be either fixed or variable. To illustrate, assume that Natural Cosmetics, Inc., is thinking about changing its marketing method from distribution through retailers to distribution by a network of neighborhood sales representatives. Present costs and revenues are compared to projected costs and revenues in the following table: d According to the above analysis, the differential revenue is $100,000 and the differential costs total $85,000, leaving a positive differential net operating income of $15,000 in favor of using sales representatives. In general, only the differences between alternatives are relevant in decisions. Those items that are the same under all alternatives and that are not affected by the decision can be ignored. For example, in the Natural Cosmetics, Inc., example above, the \"Other expenses\" category, which is $60,000 under both alternatives, can be ignored because it has no effect on the decision. If it were removed from the calculations, the sales representatives would still be preferred by $15,000. This is an extremely important principle in management accounting that we will revisit in later chapters. Opportunity Cost and Sunk Cost Opportunity cost is the potential benefit that is given up when one alternative is selected over another. For example, assume that you have a parttime job while attending college that pays $200 per week. If you spend one week at the beach during spring break without pay, then the $200 in lost wages would be an opportunity cost of taking the week off to be at the beach. Opportunity costs are not usually found in accounting records, but they are costs that must be explicitly considered in every decision a manager makes. Virtually every alternative involves an opportunity cost. A sunk cost is a cost that has already been incurred and that cannot be changed by any decision made now or in the future. Because sunk costs cannot be changed by any decision, they are not differential costs. And because only differential costs are relevant in a decision, sunk costs should always be ignored. Page 47 To illustrate a sunk cost, assume that a company paid $50,000 several years ago for a specialpurpose machine. The machine was used to make a product that is now obsolete and is no longer being sold. Even though in hindsight purchasing the machine may have been unwise, the $50,000 cost has already been incurred and cannot be undone. And it would be folly to continue making the obsolete product in a misguided attempt to \"recover\" the original cost of the machine. In short, the $50,000 originally paid for the machine is a sunk cost that should be ignored in current decisions. IN BUSINESS THE ECONOMICS OF DRIVING YOUR DREAM CAR The costs of buying, insuring, repairing, and garaging ultraluxury vehicles can be very expensive. For example, the purchase price alone for a new Lamborghini or Bentley can easily exceed $300,000. Thus, Gotham Dream Cars offers an alternative to customers who want to drive ultraluxury cars while avoiding the exorbitant costs of ownership. It sells fractional shares in luxury carsthe minimum price starts at $9,000 for 20 drivingdays. George Johnson is a Gotham Dream Cars customer who spent $30,000 for 90 drivingdays in two types of ultraluxury vehicles. He noted that \"it's not worth it to buy one of these cars when you have to fix them.\" In essence, Johnson compared the costs of ownership with the rental costs and decided to rent. Source: David Kiley, \"My LamborghiniToday, Anyway,\" BusinessWeek, January 14, 2008, p. 17. Summary In this chapter, we have discussed ways in which managers classify costs. How the costs will be used for assigning costs to cost objects, preparing external reports, predicting cost behavior, or decision makingwill dictate how the costs are classified. For purposes of assigning costs to cost objects such as products or departments, costs are classified as direct or indirect. Direct costs can be conveniently traced to cost objects. Indirect costs cannot be conveniently traced to cost objects. For external reporting purposes, costs are classified as either product costs or period costs. Product costs are assigned to inventories and are considered assets until the products are sold. At the point of sale, product costs become cost of goods sold on the income statement. In contrast, period costs are taken directly to the income statement as expenses in the period in which they are incurred. For purposes of predicting how costs will react to changes in activity, costs are classified into three categoriesvariable, fixed, and mixed. Variable costs, in total, are strictly proportional to activity. The variable cost per unit is constant. Fixed costs, in total, remain the same as the activity level changes within the relevant range. The average fixed cost per unit decreases as the activity level increases. Mixed costs consist of variable and fixed elements and can be expressed in equation form as Y = a + bX, where X is the activity, Y is the total cost, a is the fixed cost element, and b is the variable cost per unit of activity. If the relation between cost and activity appears to be linear based on a scattergraph plot, then the variable and fixed components of a mixed cost can be estimated using the highlow method, which implicitly draws a straight line through the points of lowest activity and highest activity, or the least squares regression method, which uses all of the data points to compute a regression line that minimizes the sum of the squares errors. The traditional income statement format is used primarily for external reporting purposes. It organizes costs using product and period cost classifications. The contribution format income statement aids decision making because it organizes costs using variable and fixed cost classifications. For purposes of making decisions, the concepts of differential cost and revenue, opportunity cost, and sunk cost are vitally important. Differential costs and revenues are the costs and revenues that differ between alternatives. Opportunity cost is the benefit that is forgone when one alternative is selected over another. Sunk cost is a cost that occurred in the past and cannot be altered. Differential costs and opportunity costs should be carefully considered in decisions. Sunk costs are always irrelevant in decisions and should be ignored. Page 48 Review Problem 1: Cost Terms Many new cost terms have been introduced in this chapter. It will take you some time to learn what each term means and how to properly classify costs in an organization. Consider the following example: Porter Company manufactures furniture, including tables. Selected costs are given below: 1. The tables are made of wood that costs $100 per table. 2. The tables are assembled by workers, at a wage cost of $40 per table. 3. 4. 5. Workers assembling the tables are supervised by a factory supervisor who is paid $38,000 per year. Electrical costs are $2 per machinehour. Four machinehours are required to produce a table. The depreciation on the machines used to make the tables totals $10,000 per year. The machines have no resale value and do not wear out through use. 6. The salary of the president of the company is $100,000 per year. 7. The company spends $250,000 per year to advertise its products. 8. Salespersons are paid a commission of $30 for each table sold. 9. Instead of producing the tables, the company could rent its factory space for $50,000 per year. Required: Classify these costs according to the various cost terms used in the chapter. Carefully study the classification of each cost. If you don't understand why a particular cost is classified the way it is, reread the section of the chapter discussing the particular cost term. The termsvariable cost and fixed cost refer to how costs behave with respect to the number of tables produced in a year. Solution to Review Problem 1 d Page 49 Review Problem 2: HighLow Method The administrator of Azalea Hills Hospital would like a cost formula linking the administrative costs involved in admitting patients to the number of patients admitted during a month. The Admitting Department's costs and the number of patients admitted during the immediately preceding eight months are given in the following table: d Required: 1. 2. Use the highlow method to estimate the fixed and variable components of admitting costs. Express the fixed and variable components of admitting costs as a cost formula in the form Y = a + bX. Solution to Review Problem 2 1. The first step in the highlow method is to identify the periods of the lowest and highest activity. Those periods are November (1,100 patients admitted) and June (1,900 patients admitted). The second step is to compute the variable cost per unit using those two data points: d The third step is to compute the fixed cost element by deducting the variable cost element from the total cost at either the high or low activity. In the computation below, the high point of activity is used: 2. The cost formula is Y = $9,500 + $3X