Refer to the “Whopper to Go” article in The Economist. How can Burger King’s pro
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Question
Refer to the “Whopper to Go” article in The Economist. How can Burger King’s profitability problems be framed in a linear profit model? (Note: Numbers are not required to frame this problem mathematically.)How do linear profit models relate to GAAP-basis income statements?
How well do linear profit models fit the real world?
Why might linear cost models be inappropriate? Why might they not be useful?
Why are linear profit models used in financial decision making?
What are the limitations of using linear profit models in financial decision making?
Explanation / Answer
Conceptually, conventional linear cost-volume-profit (CVP) analysis is a simplified, short term planning technique that evolved as a practical version of the theoretical model of the firm described in economics textbooks.1 From an accounting perspective it is compatible with the direct, or variable costing method of inventory valuation. To use the CVP model, a company must separate total costs into fixed and variable categories using one of the methods described in Chapter 3. Recall from our earlier discussions of these terms that variable costs are those costs that vary with changes in the level of activity. The only activities that are allowed to affect variable costs in traditional cost-volume-profit analysis are production output and sales. Remember that fixed costs are those costs that do not vary with changes in the activity level. Conceptually, fixed costs are not constant. By definition, fixed simply means that these costs are not driven by short run changes in production or sales volume. Although explicit recognition of non production volume related cost drivers is a key concept in activity based costing, the idea is ignored in the conventional linear CVP model.2 Finally, it is important to recognize that the concept of fixed and variable costs is a short run concept. All costs tend to vary in the long run as the company adds to its' capacity to produce and distribute products and services. Therefore, the short run emphasis of CVP analysis tends to conflict with the long run emphasis of activity based costing and the lean enterprise concepts of JIT and TOC. This creates another thought provoking controversial issue. The purpose of this chapter is to describe the assumptions and techniques of the conventional linear cost-volume-profit approach as well as the controversy concerning the compatibility of CVP analysis with ABC and the continuous improvement concepts. The chapter is divided into five main sections. The first section addresses the underlying assumptions of the conventional linear model and the implications of relaxing these assumptions. This section is mainly conceptual and is illustrated with a series of graphs. The second section illustrates the basic planning techniques for a single product company that provide the foundation for more realistic problems. The third section extends the basic analysis to multiproduct companies. Both sections two and three are more mechanical than conceptual and are mainly illustrated with a series of related equations. The fourth section is fairly short, but illustrates how to convert the analysis to a cash flow basis. The last section introduces the controversy associated with the CVP approach as it relates to the newer concepts of ABC, JIT and TOC. Since the CVP methodology is closely related to direct or variable costing, this chapter helps provide a better foundation for the more detailed comparison of direct and absorption costing presented in Chapter 12. ASSUMPTIONS OF CONVENTIONAL LINEAR CVP ANALYSIS Conventional linear cost volume profit analysis is based on five assumptions as follows: 1. Constant sales price. 2. Constant variable cost per unit. 3. Constant total fixed cost. 4. Constant sales mix. 5. Units sold equal units produced. Note that these are the same assumptions that are applicable to the master budget, with the exception of number five. Now we will examine the implications of each assumption. Constant Sales Price To assume that the sales price is constant implies that the company is facing a horizontal demand function as illustrated in Figure 11-1. The implications of a horizontal demand function are that the company can sell any number of units at a constant sales price. Another way to describe this is to say that consumers are willing and able to buy any quantity the company offers for sale at a constant price. Average revenue (AR) is constant and equal to the sales price, (i.e., AR = PX÷X = P) as illustrated in Figure 11-1. The slope of the total revenue function (see Figure 11-2) is equal to the sales price. When the company sells one additional unit, total revenue increases by an amount equal to the sales price of that unit. The fact that the sales price is constant causes the slope of the total revenue function to be constant which results in a linear total revenue function. Another way to describe this is to say that total revenue increases at a constant rate as additional units are sold. A more realistic down sloping demand function (see Figure 11-3) illustrates what economists refer to as the law of demand. This law describes the fundamental idea that consumers are willing and able to buy more at a lower price than a higher price. When the price is decreased from P1 to P2, the quantity purchased, or demanded, increases from X1 to X2. The total revenue function based on the law of demand is nonlinear as illustrated in Figure 11-4. Total revenue increases at a decreasing rate as additional units are sold. This is because the sale of additional units requires that the company reduce the sales price. Each price corresponds to a specific sales quantity. Thus, average revenue (AR) will be decreasing, rather than constant. Although the assumption of a constant sales price is not realistic, it is defended as a practical way to expedite the planning process within a fairly narrow range of sales activity. The idea that most products are subject to a down sloping demand curve is intuitively obvious, but applying the concept is simply not practical. Most companies sell too many products in a constantly changing economic environment. Today’s demand curve is very likely to be obsolete tomorrow. Constant Variable cost per unit The second assumption of the conventional linear cost-volume-profit approach is that the variable cost per unit of output is constant. This includes two important underlying assumptions: a) input prices are assumed to be constant for all variable inputs such as direct material, direct labor, and the various types of indirect resources represented by variable factory overhead costs and variable selling and administrative expenses, and b) the firm experiences constant productivity, i.e., constant output per variable input. Constant productivity is illustrated in Figure 11-5. When productivity is constant, each new unit of output requires an equal amount of input and thus each unit of output will cost the same amount. This causes both the production function to be linear (see Figure 11-5) and the average variable cost function to be horizontal (see Figure 11-6). Output (X) is placed on the vertical axis in Figure 11-5 because output is the dependent variable, i.e., inputs drive outputs. Output is on the horizontal axis in the other graphs because cost is the dependent variable, i.e., output drives cost. Although it is convenient to assume constant productivity for short run planning purposes, other types of production functions are more realistic when the whole range of production possibilities is considered. When a company begins to expand output from a low volume startup level to a medium volume level, productivity might be expected to increase due to the effects of increased specialization, experience and learning. When productivity is increasing, output increases at an increasing rate (see Figure 11-7) . As variable inputs are added to production, each input generates more output than the previous input. When productivity is increasing, average variable cost per unit will be decreasing as in Figure 11-8. If the company increased production from a medium volume level to a high volume level by continuing to add variable inputs to a fixed size facility, productivity would be expected to decrease as indicated in Figure 11-9. This is because at high volume production levels, the inputs (labor, materials etc.) would become excessive relative to the size of the fixed facility. In the case of decreasing productivity, average variable cost per unit will be increasing as illustrated in Figure 11-10. Each unit will cost more because it requires more inputs to produce. Theoretically, the production and average variable cost functions for the entire range of short run production possibilities will be similar to those illustrated in Figures 11-11 and 11-12. The point where the production function changes directions from increasing to decreasing productivity and the average variable cost function changes from decreasing to increasing cost per unit is referred to as the point of diminishing returns. Output continues to increase beyond this point, but at a decreasing rate. Constant Fixed Costs and The Families of Total Cost Functions A family of total cost functions for the conventional linear model is presented in Figure 11-13. The total variable cost and total cost functions are linear, i.e., they increase at a constant rate, because productivity is assumed to be constant. The total fixed cost function is represented by a horizontal line because of assumption three which eliminates the possibility of a non-output related change in fixed costs during the planning period. No changes in the company’s fixed factors of production can occur. The total cost and total variable cost functions are vertically parallel and separated by the amount of total fixed costs. A comparable family of total cost functions for the theoretical economic model appears in Figure 11-14. The total variable cost and total cost functions increase at a decreasing rate at first in response to increasing productivity. When the inputs are becoming more productive, additional outputs cost less per unit because they require less input. However, when productivity begins to decrease, the total cost and total variable cost functions begin to increase at an increasing rate. In the case of decreasing productivity, the inputs are generating less output per input, thus the unit cost of additional outputs is increasing. The total cost functions in Figure 11-14 are also parallel and separated vertically by the amount of total fixed costs.
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