Cost-volume-profit analysis incorporating the cost of capital.

Cost-volume-profit (CVP) analysis is a mathematical representation of the economics of producing a product. The relationships between a product's revenue and cost functions expressed within the CVP model are used to evaluate the financial implications of a wide range of strategic and operational decisions. For example, CVP analysis is employed to assess the financial implications of product mix, pricing, and product and process improvement decisions. Perhaps equally important, CVP analysis facilitates measuring the sensitivity of a product's profitability to variations in one or more of its underlying parameters. Finally, CVP analysis may be used to determine the trade-offs in profitability and risk from alternative product design and production possibilities. In effect, CVP is a quantitative model for developing much of the financial information relevant for evaluating resource allocation decisions.

Despite its widespread application, CVP analysis is frequently criticized for its use of simplifying assumptions, such as deterministic and linear cost and revenue functions. Additionally, CVP is disparaged for its focus on a single product and its single-period analysis. However, as noted by Guidry et al.: "Non-linear and stochastic CVP models involving multistage, multi-product, multivariate, or multi-period frameworks are all possible, although a single model embracing all of these extensions would seem a radical departure from the whole point of CVP analysis, its basic simplicity" (1998: 75). Horngren et al. (2000) note that firms across a variety of industries have found the simple CVP model to be helpful in both strategic and long-run planning decisions. Furthermore, a survey of management accounting practices indicates that CVP analysis is one of the most widely used techniques (Garg et al., 2003). However, Horngren et al. (2000) warn that, in situations where revenue and cost are not adequately represented by the simplifying assumption of CVP analysis, managers should consider more sophisticated approaches to financial analysis.

An implicit assumption, and one that is frequently overlooked in evaluating the use of CVP analysis, involves its treatment of the cost of capital. CVP analysis, like other managerial accounting techniques and models, uses accounting profitability as the primary decision criterion for evaluating resource allocation decisions. CVP analysis, like other managerial accounting techniques, ignores the cost of capital and treats it as if it were zero. However, the opportunity cost of the funds invested in the assets used to manufacture a product is a cost the same as the cost of operating resources, such as direct material, labor, and overhead. The failure of CVP analysis to incorporate the cost of capital into a product's cost function can lead to underestimating a product's cost, while overstating its profitability. For products that require a significant investment of capital, ignoring the opportunity cost of invested funds may lead to accepting products whose rate of return is less than the firm's cost of capital. In effect, traditional CVP analysis encourages managers to select products that destroy, rather than create, economic value for the firm. Finally, using an accounting measure of profitability creates a bias to employ capital relative to operating resources because the cost of capital is not reflected in a product's cost like those of operational resources. Therefore, product designers and developers may employ investment funds beyond the point where the marginal benefit of the last dollar of capital used is equal to its marginal cost.

The purpose of this article is to illustrate how the cost of capital may be incorporated into CVP analysis. It develops the mathematical relationship between a product's discounted operating income after taxes less the cost of capital and the product's price, costs, invested funds, and sales quantity. From this relationship, the sales quantity needed to earn a rate of return equal to the firm's cost of capital may be estimated. Incorporating the cost of capital into the CVP model enables managers to determine the value added (destroyed) for a given level of sales. Finally, the article illustrates how the modified CVP model facilitates evaluating the economic implications of alternative investment and cost structures and process improvement of the activities used to manufacture a product.

The remainder of this article is organized as follows. The next section discusses the different approaches to the economic analysis of a product. The following section discusses how the cost of capital may be incorporated into the measurement of a product's cost. The subsequent section derives a mathematical expression for calculating the discounted value of a product's operating income after taxes less the cost of capital used to earn the operating profit. In the next section, a numerical example is used to illustrate how CVP analysis may be developed from the present value of a product's operating income after taxes less the cost of capital. The subsequent section examines the use of the CVP model for assessing the economics of a program of process improvement. The final section presents the summary and conclusions of the paper.

PRODUCT MIX DECISIONS AND CVP ANALYSIS

The selection of which products to produce, which to abandon, and which to postpone is one of the most critical decisions confronting a firm's management. The products selected from the product mix decision determine the revenue, profit, and cash flow of the firm's operations. Perhaps equally important, the products selected determine, in part, the firm's competitive position vis-a-vis its competitors. The profit and cash flow from the products selected currently provide the funds required to develop and produce products in the future. A final, but frequently overlooked, aspect of product mix decisions involves the investment in long-term assets used to manufacture a product. The investments in these assets, once committed, are frequently difficult and/or costly to reverse. Therefore, once a product enters production, the firm may find it difficult to avoid economic losses.

CVP analysis is generally implemented with financial data taken from the firm's accounting system. Financial data is readily available, as well as congruent, with the accounting profit objective inherent in the use of CVP analysis. The financial data needed for CVP may be taken from either a traditional cost accounting or an activity-based costing (ABC) system. Traditional cost accounting systems allocate overhead to products based on one or more volume-based measures of activity. However, products consume overhead resources based on batch-, product-, facility-, and complexity-, as well as volume- or unit-level, activities. Consequently, traditional cost accounting systems can systematically misallocate overhead to products. Kaplan and Cooper (1998) assert that it is not unusual for firms using a traditional cost accounting system to find that 20% of their products earn 300% of their profit, while the remaining 80% either break even or incur a loss and collectively lose 200% of the firm's profitability. CVP analysis based on data from a traditional cost accounting system may be expected to lead to similar distortions in modeling a product's cost. Consequently, the CVP model developed in this article is based on ABC, rather than a traditional cost accounting system.

CVP analysis is used to measure the economic characteristics of manufacturing a proposed product. Based on accounting data, the CVP model is used to determine the sales quantity needed to break even, as well as the sales quantity required to earn a desired profit or profit margin. Managers then compare a product's expected sales with the sales quantities required to break even and/or earn a target profit margin to determine whether the product should be produced.

Cost-volume-profit, like all financial models, is based on a set of simplifying assumptions that reduce the complexity of a resource allocation decision to make decision making more tractable. To understand a financial model and its usefulness, its assumptions and their role in a decision must be understood. For example, CVP is a one-period model of a product's profitability, although the product may have an economic life of several years. CVP analyses treat a product's life as a single period, or evaluate a single period of its life, such as a year, and extrapolate the one-period's result over the product's life. Managers can use either approach for evaluating a product's profitability with CVP analysis and for making the product mix decision.