Cost Analysis Economic cost – refers to the cost of attracting a resource from its next best alternative use (the opportunity cost concept). Depreciation is a loss of asset value. Economic dep’t is equal to market value minus expected value after 1 yr/total units produced in 1 yr. Unfortunately, it is often difficult, if not impossible, to determine the exact service life of a capital asset and the future changes in its market value. So, accounting dep’t uses the method of allocating the dep’t cost to its useful life (straight line method). Short-run cost output relationships help managers to plan for the most profitable level of output, given the capital resources that are immediately available. Long-run cost-output relationships involve attracting additional capital to expand or contract the plant size and change the scale of operations. Accounting profits, which do not include opportunity costs, are not always a valid indication of the economic profitability (or loss) of an enterprise. Achieving minimum efficient scale is often the key to a successful operations strategy. 2. Inventory valuation The accounting cost is equal to the actual acquisition cost, whereas the economic cost is equal to the current replacement cost. Acquisition cost – the original cost of purchasing the asset. Replacement cost - the amount of money a business must currently spend to replace an essential asset The Meaning and Measurement of Cost Cost simply refers to the sacrifice incurred whenever an exchange or transformation of resources takes place. Accounting vs Economic costs Accountants primarily concerned with identifying highly stable and predictable costs for financial reporting purposes. Measure cost by certain historical outlay of funds. Economists mainly concerned with measuring costs for decision-making purposes. The relevant cost in economic decision making is the opportunity cost of the resources rather than the historical outlay of funds required to obtain the resources. Include the explicit cost but also the implicit opportunity cost 3. Sunk cost of underutilized facilities Sunk cost - A cost incurred regardless of the alternative action chosen in a decision-making problem. Price paid is one measure of cost Interest to bondholders is also a measure of cost Opportunity cost - The value of a resource in its next best alternative use. Opportunity cost represents the return or compensation that must be forgone as the result of the decision to employ the resource in a given economic activity. Sunk cost should not be considered relevant cost because they are unavoidable cost; should seldom be considered in making operating decisions. Short-run cost functions The opportunity cost of the owner’s time is measured by the most attractive salary offer could have received. The opportunity cost of the capital is measured by the profit or return that could have been received if the owner had chosen to employ capital in his or her secondbest (alternative) investment of comparable risk. Economic profit - is defined as the difference between total revenues and these total economic costs, implicit opportunity costs as well as explicit outlays: Economic profit = Total revenues − Explicit costs − Implicit costs 3 substantive distinction of Acctg and Econ cost Rationale: When one recognizes that such first-best and second-best uses change over time, it becomes clear that the historical outlay of funds to obtain a resource at an earlier date (the accounting cost basis) may not be the appropriate measure of opportunity cost in a decision problem today. 1. Depreciation cost measurement Capital assets - A durable input that depreciates with use, time, and obsolescence. Cost function - a mathematical model, schedule, or graph that shows the cost (such as total, average, or marginal cost) of producing various quantities of output. - determines the behavior of costs when output is varied over a range of possible values. The total cost of producing a given quantity of output is equal to the sum of the costs of each of the inputs used in the production process. Fixed costs represent the costs of all the inputs to the production process that are fixed or constant over the short run. Variable costs consist of the costs of all the variable inputs to the production process. Average and marginal cost functions AFC = FC / Q AVC = VC / Q ATC = TC / Q ATC = AFC + AVC Marginal cost - The incremental increase in total cost that results from a one-unit increase in output. Long run cost functions The long-run average cost function (LRAC) consists of the lower boundary or envelope of all these shortrun curves. No other combination of inputs exists for producing each level of output Q at an average cost below the cost that is indicated by the LRAC curve. Volume discounts - Reduced variable cost attributable to larger purchase orders. Learning curve effects and volume discounts in purchasing inputs (so-called external economies of scale) are easily distinguished from internal economies of scale because they depend upon cumulative volume of output no matter how small the production throughput rate per time period. Learning curve relationship - C = aQb C = input cost of Qth unit Q = consecutive units of output produced a = theoretical (or actual) input cost of the first unit of output b = rate of reduction in input cost per unit of output. Because the learning curve is downward sloping, the value of b is normally negative. Optimal Capacity Utilization: Three concepts The Percentage of Learning 1. Optimal output for a given plant size Output rate that results in lowest average total cost for a given plant size. - 2. Optimal plant size for a given output rate Plant size that results in lowest average total cost for a given output. 3. Optimal plant size Plant size that achieves minimum long-run average total cost. Only when optimal output increases to Q3, where the firm will build the universally least cost optimal plant size represented by SAC3, will further opportunities for cost reduction cease. Short-run average total cost with underutilization of capacity at Point A or overutilization of capacity at Point B is always higher than the minimum average total cost in the long run (LRAC) fundamentally because the production manager can vary plant and equipment in the long run, matching capacity to his or her output requirements. ECONOMIES AND DISECONOMIES OF SCALE The long-run average total cost LRAC function is hypothesized to decline as the flow rate of throughput rises over the lower range of operations scale and is hypothesized to remain flat or rise over the higher range of scale. Declining long-run average total cost reflects internal economies of scale at one of 3 levels: the product level, the multiproduct plant level, or the firm level of operations. 1. Product-Level Internal Economies of Scale A number of different sources of declining cost are associated with producing one product (say, PCs) at a higher rate of throughput per day. Special-purpose equipment; production process can be broken down into a series of smaller tasks; workers can be assigned to the tasks for which they are most qualified. Learning curve effect - Declining unit cost runs attributable to greater cumulative volume. - defined as the proportion by which an input (or its associated cost) is reduced when output is doubled, can be estimated as follows: L = C2 / C1 × 100% C1 = input (or cost) for the Q1 unit of output C2 = cost for the Q2 = 2Q1 unit of output 2. Plant-Level Internal Economies of Scale Sources of scale economies at the plant level include capital investment, overhead, and required reserves of maintenance parts and personnel. With respect to capital investment, capital costs tend to increase less than proportionately with the productive capacity of a plant, particularly in process-type industries. Another source of plant-level scale economies is overhead costs, which include such administrative costs as management salaries and paperwork documentation associated with regulatory compliance. Overhead costs can be spread over a higher volume of throughput in a larger plant or facility, thus reducing average costs per unit. 3. Firm-Level Internal Economies of Scale associated with the overall size of the multiplant firm. One possible source of firm-level scale economies is in distribution. For example, multiplant operations may permit a larger firm to maintain geographically dispersed plants. Delivery costs are often lower for a geographically dispersed operation compared with a single (larger) plant. raising capital funds. Because flotation costs increase less than proportionately with the size of the security (stock or bond) issue, average flotation costs per dollar of funds raised is smaller for larger firms. marketing and sales promotion. These scale economies can take such forms as (1) quantity discounts in securing advertising media space and time, or (2) the ability of the large firm to spread the fixed costs of advertising each period over greater throughput. Diseconomies of Scale Rising long-run average costs as the level of output is increased. A primary source of diseconomies of scale associated with an individual production plant is transportation costs. Another possible source of plant diseconomies is labor requirements; higher wage rates or costly worker recruiting and relocation programs may be required to attract the necessary personnel. Finally, large-scale plants are often inflexible operations designed for long production runs of one product, based often on forecasts of what the target market wanted in the past “Flat Rock was built to make a few parts at very high volumes. But the plant turned out to be very inflexible for conversion to making new types and different sizes of engine blocks. Sometimes you really can be too big.” The Overall Effects Diseconomies of Scale Economies and minimum efficient scale (MES) - The smallest scale at which minimum costs per unit are attained. Over this extended middle-scale range, average costs per unit are relatively constant. However, expansion beyond the maximum efficient scale eventually will result in problems of inflexibility, lack of managerial coordination, and rising long-run average total costs. SUMMARY Cost is defined as the sacrifice incurred whenever an exchange or transformation of resources takes place. Different approaches are used in measuring costs, depending on the purposes for which the information is to be used. For financial reporting purposes, the historical outlay of funds is usually the appropriate measure of cost, whereas for decision making purposes, it is often appropriate to measure cost in terms of the opportunities forgone or sacrificed. A cost function is a schedule, graph, or mathematical relationship showing the minimum achievable cost (such as total, average, or marginal cost) of producing various quantities of output. Short-run total costs are equal to the sum of fixed and variable costs. Marginal cost is defined as the incremental increase in total cost that results from a one-unit increase in output. The short-run average variable and marginal cost functions of economic theory are hypothesized to be U-shaped, first falling and then rising as output is increased. Falling short-run unit costs are attributed to the gains available from specialization in the use of capital and labor. Rising short-run unit costs are attributed to diminishing returns in production. The theoretical long-run average cost function is often found to be L-shaped due to the frequent presence of scale economies and frequent absence of scale diseconomies. Economies of scale are attributed primarily to specialization and other features of the production process or the factor markets, whereas diseconomies of scale are attributed primarily to problems of coordination and inflexibility in large-scale organizations. Volume discounts in purchasing inputs and learning curve effects, both of which result from a larger cumulative volume of output, can be distinguished from scale effects, which depend on the firm’s rate of production throughput per time period. Learning curve advantages often, therefore, arise in smallscale plants able to make long production runs. Minimum efficient scale is achieved by a rate of output sufficient to reduce long-run average total cost to the minimum possible level. Smaller rates of output imply smaller plant sizes to reduce unit cost, albeit to higher levels than would be possible if a firm’s business plan could support minimum efficient scale production.
