Cost-Volume-Profit Analysis Incorporating the Cost of Capital

Abstract

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. …

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