Management And Accounting Web

Summary by Scott Ingram

Master of Accountancy Program

University of South Florida, Summer 2003

The cost-volume-profit (CVP) model was designed to be used in conjunction with a traditional cost accounting system. Through a set of simplifying assumptions, CVP analysis develops equations to represent a product’s cost and revenue functions. The purpose of this article is to demonstrate how CVP analysis can be used with an activity based costing (“ABC”) system.

**The four main objectives of the article are outlined below**:

**1. Development of a mathematical model showing the relationship between a product’s revenue function and its ABC derived cost function.**

ABC differs from traditional cost accounting systems because it allocates the cost of overhead to activities and then to products through identified cost drivers. ABC treats all costs as variable when calculating a unit cost, but production level changes and relevant ranges test this assumption. The author developed the following set of relational equations to help derive the effects of variability in the unit, batch and product-level costs on a product’s profitability:

The calculations are somewhat involved as indicated above. The quantity produced and sold (Q_{i}) and the number
of batches (B_{j,i}) must be determined jointly since the number of batches depends on Q_{i}. This requires an approximation to be
calculated based on expected batch sizes using equation (3). Although a detailed explanation of the approach is beyond the scope of this summary, according to
Kee, it provides a way for managers to better estimate the impacts of product mix and batch size changes on profitability.

**2. Explaining how the CVP model can be used to determine the rate of change in profitability in respect to changes in demand.**

The starting point for any CVP analysis is the computation of a product quantity needed to break even and earn a specific level of profitability. In contrast to traditional accounting systems, an ABC system’s use of batch-level activities creates a step-type cost and profit function. The author created a difference equation to capture the discrete, rather than continuous, nature of this cost function (See equation 4 above). The result of the calculation is a defined unit interval size and each interval’s corresponding increase or decrease in accounting income.

A graph of this data allows managers to visually identify the sales volume needed to break even and to earn a specific level of profitability. Managers can also see how far sales demand would have to decrease for the product to become unprofitable.

**3. Explaining how the CVP model can be used to determine the change in profit given a change in one or more of a product’s underlying parameters.**

There are many cost and price parameters used in a CVP analysis. It is important for managers to be able to estimate the effects that changes in these parameters will have on a product’s profitability. The author uses the example of a product’s price reduction as a result of competitive pressures. When the new price information is inserted in the equations above, a new break even and target profitability product quantity are calculated. In Kee's example, when product price was decreased, both the break even and the target profitability product quantity increased. Using this approach, managers can determine the maximum price reduction allowed before practical capacity would be exceeded.

**4. Using CVP to evaluate the financial impacts of product and process improvements that are generated through the use of ABC.**

ABC is very useful for modeling how a firm’s support and production activities will be used in manufacturing a product. When process improvements are proposed, the mix of resources needed to manufacture a product and the relationship between the product’s profitability and sales volume are affected. Use of the author’s approach allows managers to estimate the affect any proposed process improvement has on a product’s sales volume and profitability.

**Summary**

Though the usefulness of CVP analysis has been criticized for its reliance on simplifying assumptions, this article demonstrates that it can be very effective in helping managers understand the effects of changes in ABC cost assumptions and market variability on product profitability. The step by step approach illustrated by the author coupled with the use of an extensive quantitative example, make this article a valuable tool for any production manager.

The author suggests that future CVP research is needed on: (1) the incorporation of cost of capital as a product cost, (2) the incorporation of facility-level costs and (3) the evaluation of multiple products.

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