Subject:

Break-even analysis
(Usage)

Financial management (Models)

Financial management (Models)

Authors:

Guidry, Flora

Horrigan, James O.

Craycraft, Cathy

Horrigan, James O.

Craycraft, Cathy

Pub Date:

03/22/1998

Publication:

Name: Journal of Managerial Issues Publisher: Pittsburg State University - Department of Economics Audience: Academic; Trade Format: Magazine/Journal Subject: Business; Human resources and labor relations Copyright: COPYRIGHT 1998 Pittsburg State University - Department of Economics ISSN: 1045-3695

Issue:

Date: Spring, 1998 Source Volume: v10 Source Issue: n1

Product:

Product Code: 9915400 Accounting Methods

Accession Number:

20562999

Full Text:

Cost Volume Profit analysis (CVP) is one of the most hallowed, and
yet one of the simplest, analytical tools in management accounting. In a
general sense, it provides a sweeping financial overview of the planning
process (Horngren et al., 1994). That overview allows managers to
examine the possible impacts of a wide range of strategic decisions.
Those decisions can include such crucial areas as pricing policies,
product mixes, market expansions or contractions, outsourcing contracts,
idle plant usage, discretionary expense planning, and a variety of other
important considerations in the planning process. Given the broad range
of contexts in which CVP can be used, the basic simplicity of CVP is
quite remarkable. Armed with just three inputs of data - sales price,
variable cost per unit, and fixed costs - a managerial analyst can
evaluate the effects of decisions that potentially alter the basic
nature of a firm.

However, the simplicity of an analytical tool such as CVP can cut both ways. It can be both its greatest virtue and its major shortcoming. The real world is complicated, no less so in the world of managerial affairs; and a typical analytical model will remove many of those complications in order to preserve a sharp focus. That sharpening is usually achieved in two basic ways: simplifying assumptions are made about the basic nature of the model and restrictions are imposed on the scope of the model. Those simplifications and restrictions impinge on the reality and relevance of analytical models, so attempts to improve them will involve releasing some of their underlying assumptions or broadening their scope. In this article, we propose a variation of the CVP analytical model by broadening its scope to include cost of capital and the related impact of asset structure and risk level on strategic decisions, while at the same time preserving most of its admirable simplicity.

Our variation of the conventional CVP model provides more useful information to management because it focuses on more than operating expenses and sales revenues. Financial managers have long recognized the importance of including cost of capital and business risk variables in capital budgeting decisions (Brigham, 1995). Our model not only incorporates these admittedly important variables but recognizes the fixed and variable nature of capital costs.

Criticisms of CVP Analysis

Most criticisms of CVP relate to its basic underlying assumptions. Economists (Machlup, 1952; Vickers, 1960) have been particularly critical of those assumptions. Their criticisms take many forms, but they all arise from CVP's departures from the standard supply and demand models in price theory economics. Perhaps the most basic difference between CVP analysis and price theory models is that CVP ignores the curvilinear nature of total revenue and total cost schedules. In effect, it assumes that changes in volume have no effect on elasticity of demand or on the efficiency of production factors. Managerial accountants recognize these economic critiques, but they believe nonetheless that CVP analysis is a very useful initial analysis of strategic decisions (Horngren et al., 1994).

Additional criticisms of the underlying nature of CVP analysis arise from its similarities to standard economic models, rather than its differences. Similar to standard economic price theory models, basic CVP analysis usually assumes, among other things, the following: single-stage, single-product manufacturing processes; simple production functions with one causal variable; cost categories limited to only variable or fixed; and data and production functions susceptible to certainty predictions. Further, CVP analysis is typically restricted to one time period in each case. The shortcomings of CVP seem daunting, but CVP is pliable enough to overcome them all, if necessary and desirable. Nonlinear and stochastic CVP models involving multistage, multi-product, multivariate, or multi-period frameworks are all possible, although a single model embracing all of those extensions would seem a radical departure from the whole point of CVP analysis, its basic simplicity.(1) In general, the durability and popularity of CVP analysis undoubtedly reflects the willingness of its users to "live with" the shortcomings revealed by criticisms of its basic nature.

In this article, we are also content to "live with" the basic CVP model. Our concerns lie elsewhere, namely, the somewhat restricted focus of CVP on only sales revenue and operating expenses. That limitation can leave some very important aspects of strategic decisions overlooked. Schneider (1992; 1994), for example, suggests that the scope of CVP analysis ought to be widened to include the impact of managerial compensation schemes on target profit levels. In a similar vein, we propose that the scope of CVP analysis be broadened to overcome three limitations of the model in regard to asset structure and risk. Those three limitations are as follows: CVP does not measure the impact of the decision on wealth; it does not incorporate the effect of asset structure changes required by the decision; and it does not acknowledge the risk created by the decision (Magee, 1975; Cheung and Heaney, 1990; Chan and Yuan, 1990). Some fairly simple extensions of the scope of the basic model can do much to alleviate the shortcomings caused by those limitations.

In the following discussion, each of these three basic limitations of the CVP model will be examined further and some simple extensions of the model will be suggested. Strategic thinking, by definition, considers a broad mix of variables, so even this expanded version of the CVP model may still be subject to the basic criticism that it is too simple, in part, because projects do not exist in isolation. The widespread historic use of the basic version of the CVP model suggests that a simple, parsimonious analysis is indeed an effective first step in thinking about strategic decisions. The expanded version of the CVP model presented here will be developed in that spirit.

Wealth Impacts of CVP Decisions

The first limitation of the basic CVP model that should be addressed is the absence of any measurement of a decision's impact on wealth. The current CVP model focuses on the total level of net profits generated by a decision, which may or may not increase the wealth of the firm. The ultimate effect of a particular decision upon wealth depends on the investment in assets necessary to implement that decision. CVP analysis could be recast completely in present value measures (e.g., see Reinhardt, 1973). While it would probably be ideal to capture wealth effects through present value analyses, the main advantage of CVP analysis, its relative simplicity, would be lessened by the added complexities of present value techniques. A simpler way to incorporate wealth effects in the CVP model would be to include the firm's cost of capital in the analysis.

The key here would be target income, which figures so prominently in CVP analyses. As a simple expansion of the CVP model, target income is defined as the minimum net income acceptable for a particular decision. This minimum income level is formulated as follows: [2]

[NI.sup.T] = [k.sub.o] x [Delta]TA (1.0)

Where:

[NI.sup.T] = target net income; [k.sub.o] = cost of capital; [Delta]TA = total assets required for a decision.

This definition of target income requires the explicit recognition of two more variables in CVP analysis, namely, the cost of capital and the total assets required to implement a decision.(3) The cost of capital would be the minimum rate of return acceptable from the decision and the total assets required for the decision would be any additional, incremental assets that would have to be acquired in order to implement the decision. Admittedly, these additional variables would seem to encroach upon the simplicity of the current version of the CVP model. However, the notion of target income itself implies that some estimates of the cost of capital and the required investment are lurking somewhere in a CVP analysis of this type. Otherwise, the target income itself begs the question of how it was derived.

Given the above definition of target income, a CVP analysis could then proceed in the usual fashion suggested. For example, a unit cost approach to CVP analysis could be formulated as follows:

pQ = vQ + FC + ([k.sub.o] x [Delta]TA) (2.0)

Where:

p = selling price per unit; v = variable cost per unit; Q = total quantity of units produced or sold; FC = total fixed costs.

The general thrust of the above CVP analysis would be to determine if a particular pricing policy and cost structure strategy might yield at least a minimum target income level that would meet the firm's cost of capital. An achievement of at least that minimum income level, or more, should preserve or enhance the existing wealth of the firm. As Drucker states in a critique of cost accounting:

"Until a business returns a profit that is greater than its cost of capital, it operates at a loss. Never mind that it pays taxes as if it had a genuine profit. The enterprise still returns less to the economy than it devours in resources. It does not cover its full cost unless the reported profit exceeds the cost of capital. Until then, it does not create wealth; it destroys it" (1995:59).

Introduction of Assets into CVP Analysis

The above introduction of assets into the analysis suggests that a simple framework for analyzing required assets should be incorporated into CVP analysis as well. The notion of variable and fixed assets, somewhat akin to the notion of variable and fixed costs, would be a useful addition to CVP analyses. This notion of variable and fixed assets is a popular tool in financial forecasting in the field of financial management (e.g., see Brigham, 1995). It arises from the simple idea that some proportional relationships may exist between sales or production volume and certain assets. If such proportional relationships can be determined, then an expanded version of the CVP model would allow for a much richer analysis of target income strategies.

The usual approach to asset requirements in financial forecasting is to assume that fixed ratios exist between sales volume and the various current assets of a firm, but the remaining assets are fixed within some relevant volume range. Those ratios are often determined through an analysis of average turnover ratios in a firm's industry or through a study of a firm's own history of turnover ratio levels. The dichotomy of variable and fixed assets can be modified to allow for some assets to have both a variable and fixed component. But, the overall idea is that assets can be analyzed within a variable versus fixed framework just like costs.

In that regard, equation (2.0) above is modified in the following fashion to allow for a variable and fixed analysis of assets as well as costs:

pQ = vQ + FC + [([k.sub.o] x pQ/[R.sub.n]) + ([k.sub.o] x FA)] (3.0)

Where:

[R.sub.n] = normal ratio of sales to current asset;

FA = fixed assets allocated to decision.

In equation (3.0), target income is separated into returns on variable and fixed assets, ([k.sub.o] x pQ/[R.sub.n]) and ([k.sub.o] x FA), respectively. This separation recognizes that the behavior of these two types of assets would normally require different analyses. The operating variable and fixed cost analysis, however, remain unchanged from the basic CVP model. A few additional comments are in order here in regard to equation (3.0) above. First, the expression "pQ./[R.sub.n]" is the estimate of current assets, given the sales volume involved in the CVP analysis. This constant ratio assumption implies that current assets increase and decrease in the exact same percentage changes as sales volume. In some circumstances, this assumption may be too limiting. Second, the fixed assets allocated to the decision may require some entirely different incremental analysis. A particular pricing policy and cost structure strategy may require an increase in the total fixed assets of a firm, but that new increment of fixed assets would presumably not change within some relevant volume range of the proposed strategy.

An interesting variation of equation (3.0) would be to recast it in a contribution margin approach, as follows:

pQ-vQ-([k.sub.o] pQ/[R.sub.n]) = FC+ ([k.sup.o] FA) (3.1)

Contribution margin is normally defined as the income remaining after variable expenses are deducted from sales revenue. In effect, this modified version of equation (3.0) would redefine contribution margin as the net difference between sales and the sum of variable costs plus the minimum required return on the variable assets required for the decision. This version of contribution margin would explicitly recognize that a variable opportunity cost is present in strategic decisions, as well as variable operating costs. While this version of CVP analysis is merely an algebraic manipulation, a separate consideration of variable and fixed resources could allow for new insights within particular decisions. For example, it would allow for a modified version of the break even version of CVP analysis in which the return on fixed assets ([k.sub.o] x FA) would be set to zero. This modified version of break even would imply that the return on fixed capital could possibly be foregone in some circumstances but that return on circulating capital would have to continue for a firm to remain viable.

Risk Considerations in CVP Analysis

The introduction of asset structure into CVP analysis heightens another shortcoming of the traditional CVP model: its lack of attention to operating risk. Intuitively, both cost structure and asset structure would be direct determinants of a firm's operating risk. In general, firms with relatively higher ratios of fixed costs to total costs and fixed assets to total assets would be expected to have higher operating risks. That is, changes in their sales and production volume would have a proportionately greater impact on net income than firms with relatively lower fixed costs and fixed assets. The expanded version of CVP analysis in equation (3.0) includes both of those variables; therefore, a further expansion that included operating risk would seem worthwhile. In other words, every time a CVP analysis presumes a different cost and asset structure, a new operating risk level will emerge.

The logical variable for dealing with this particular shortcoming of CVP analysis is to adjust the cost of capital, [k.sub.o], to include the impact of changes in operating risk caused by cost and asset structure shifts. The field of financial management provides some useful ideas on how to expand the CVP model in light of this shortcoming.

Basically, the cost of capital, [k.sub.o], for a particular strategic decision would be a direct function of the operating risk of the venture that would unfold from that decision. However, defining and measuring that function is an extremely difficult proposition. Two approaches in the field of financial management seem pertinent here, although neither approach is completely satisfactory. The first approach involves measuring a surrogate variable of operating risk, and the second approach involves an analysis of fixed costs that provides a surrogate Beta risk measure for the Capital Asset Pricing Model (CAPM) computation of cost of capital.

In the first approach, a surrogate operating risk measure, the degree of operating leverage, is obtained from the basic data employed in the traditional CVP model (e.g., see Garrison and Noreen, 1994; Hilton, 1994; Zimmerman, 1995; Morse et al., 1996). This risk measure shows the percentage change that can be expected in net income given some change in sales volume. Contribution margin is a key variable in this analysis. It is the income stream that is available to meet fixed expenses and target profit levels. The degree of operating leverage recognizes that contribution margin is an income stream that changes at the same rate as sales volume, while net income will change at a different rate because of the presence of constant fixed costs. Relating those two income measures in ratio form provides an index of the relative sensitivity of net income to changes in sales.

In basic terms, the degree of operating leverage can be defined as follows:

DOL = CM/NI (4.0)

Where:

DOL = degree of operating leverage; CM = contribution margin; NI = net income.

Drawing upon the usual version of the CVP model, the above leverage relationship can be formulated as follows:

DOL = pQ - vQ / pQ - vQ - FC (4.1)

Note that no new information is required in the equation (4.1) version of operating risk. The numbers employed in a typical CVP analysis would be sufficient to develop this risk measure. While many combinations of product prices and costs are possible, fixed costs are the crucial variable driving the degree of operating leverage. The higher are the fixed costs, the higher is the operating leverage. Other things being equal, the higher a firm's degree of operating leverage, the higher is its overall business operating risk. Over time, a firm with a higher degree of operating leverage can expect a higher variability of its net income stream. In the end result, a higher degree of operating leverage will lead to a higher cost of capital, which in turn means that target income levels in CVP analyses will be relatively higher and more difficult to attain.

It is difficult to stretch this surrogate measure of operating risk beyond the simple hypotheses offered above. That is, the degree of operating leverage measure itself does not tie into the cost of capital figure in a direct analytical manner. Some rough estimates of the quantitative relationship between operating leverage and cost of capital might be obtained from analyses of a group of firms in the same industry or from a time series analysis of a single firm. In most settings, the degree of operating leverage measure would probably serve best as a variable that prompts decision makers to think about the consequences of their strategic decisions on the cost of capital.

In the second approach to incorporating operating risk's effect on the cost of capital, an accounting version of the Capital Asset Pricing Model is employed. In CAPM, the cost of capital of a particular project would be a function of the systematic risk involved in the project's assets. This systematic risk would be the sensitivity of the returns on those assets to broad movements in the economy, usually measured as the returns on all securities in the capital markets. It is formulated as follows:

[k.sub.a] = [k.sub.RF] + [B.sub.a] ([k.sub.M] - [k.sub.RF]) (5.0)

Where:

[k.sub.a] = cost of capital of project assets;

[k.sub.RF] = return on risk free assets;

[k.sub.M] = return on a market portfolio of risky assets;

[B.sub.a] = Beta systematic risk measure of project assets.

In equation (5.0) above, the only variable affected by a firm's strategic decisions is the Beta systematic risk measure. This Beta measure relates the returns on investment of a firm's assets to the average returns on investment of all other firms in the economy, which would be approximated by some index measure of the returns on a market portfolio of risky assets. As the firm changes the cost structures associated with its assets, it also changes the pattern of its cost and income flows relative to all other firms in the economy. As a result, the sensitivity of its asset returns to broad movements in the economy would also change. If a firm's strategic decisions increase [B.sub.a], its cost of capital on the assets associated with those decisions, [k.sub.a], would also increase. Consequently, it would be very useful if accounting data could be used to estimate the systematic risk involved in strategic decisions.

Some ideas from the field of financial management, integrated with some empirical work in accounting, are helpful in regard to linking cost of capital with CVP analyses. The Beta systematic risk measure is the key variable here. Beta risk measures are usually derived from stock market returns, with variable [k.sub.M] representing the return on a market portfolio of securities. Similar Beta risk measures have been developed in accounting and financial management in which a firm's accounting earnings over some time period are related to the average earnings patterns of all firms taken together (White et al., 1994). For example, these earnings variables could be expressed as returns on assets (NI/TA) for variables [k.sub.a] and [k.sub.M] in equation (5.0) above. The systematic risk measures obtained in this approach are referred to as accounting betas. An examination of the underlying origins of accounting betas yields some interesting insights about how CVP analysis could be expanded to incorporate systematic risk measures.

An accounting beta can be thought of as a combination of the individual betas of the various components of net earnings. The present value of the assets necessary for the strategic decision being analyzed can be considered the present values of the net earnings components, as follows (Brealey and Myers, 1991):

[Beta.sub.A] = f([Beta.sub.pQ] - [Beta.sub.vQ] - [Beta.sub.FC]) (6.0)

And:

PV([Delta]TA) = [PV(pQ)-PV(vQ)-PV(FC)] (6.1)

Where:

[Beta.sub.A] = Accounting beta;

PV = Present value.

The two sets of variables above in equations (6.0) and (6.1) can be integrated in light of some simplifying assumptions that are often employed in CVP analysis. If the variable costs (vQ) are perfectly proportional to sales revenue (pQ) and if the fixed costs (FC) are constant within the relevant volume range of a strategic decision, then the systematic risks of variable costs ([Beta.sub.vQ]) and sales revenue ([Beta.sub.pQ]) are equal, and the systematic risk of the fixed costs ([Beta.sub.FC]) is zero. Substituting [Beta.sub.pQ] for [Beta.sub.vQ] and setting [Beta.sub.FC] to zero, equations (6.0) and (6.1) can be integrated by weighting each variable by the present value of sales revenue, PV(pQ), as follows:

BA [multiplied by] PV([Delta]TA) / PV (pQ) = [[Beta.sub.pQ] [multiplied by] PV(pQ)] / PV(pQ) - [[Beta.sub.PQ] [multiplied by] PV(vQ)] / PV (pQ) - [[Beta.sub.FC] [multiplied by] (FC)] / PV (pQ) (7.0)

Since the difference between the present value of revenue, PV(pQ), and variable costs, PV(vQ), equals the present value of freed costs, PV(FC), and the systematic risk of the fixed costs, [Beta.sub.FC], is set at zero, equation (7.0) reduces to the following relationship:

[B.sub.A] = [B.sub.pQ] [multiplied by] [1.0 + PV(FC)]/PV([Delta]TA) (7.1)

Equation (7.1) demonstrates that the accounting beta for a particular strategic decision is determined by the sensitivity of the project's revenue stream to revenue patterns in the general economy and by the project's asset structure. An incorporation of those two variables in CVP analysis would allow for a full consideration of the ultimate wealth impacts of the decision being analyzed. The inclusion of accounting betas in CVP analyses would add two more variables that would have to be estimated, both of which would detract from the basic simplicity of the traditional CVP model. However, rough estimates of a project's revenue beta and asset structure would certainly be feasible and desirable in most cases.

The relative difficulty of estimating each of those additional variables does vary somewhat. The revenue beta would be an estimate of how the cyclical patterns of a project's revenue stream would compare to the aggregate revenue streams in the general economy. This characteristic of a project's market should be considered in making strategic decisions. Most firms should have a good feel for their particular markets from past experience and from information about competitors.

The relationship of the value of freed costs to the total assets to be invested in a project is a bit more difficult to derive. A firm's customary ratio of fixed assets to total assets would seem a useful first approximation. But, a problem exists in that financial accounting systems do not necessarily recognize all of the fixed assets involved in a strategic decision. Certain fixed assets, such as research and development programs or marketing campaigns, are expensed immediately without any consideration for their long-term implications. Thus, the fixed costs relationship in equation (7.1) might be underestimated in many cases when regular accounting data are used.

As stated at the outset, present value analyses might detract too much from the basic simplicity of CVP analysis. However, a present value approach may be the only recourse for estimating the systematic risk created by the fixed assets investment in a particular project. That approach would not be unduly difficult because the necessary data should be obtainable. After all, most of the fixed costs themselves have already been estimated in a traditional CVP analysis, and information about the discount rate is implicit in the target income level set in such an analysis.

There may be some ambiguity involved in choosing what discount rate ought to be used in estimating the present value of fixed costs. The simplest approach would be to assume that the risk of those costs is zero since they are not expected to vary at all in relation to general cyclical movements in the economy. Given that assumption, the appropriate discount rate for determining the present value of the fixed costs, PV(FC), would be simply the risk-free rate of return, [k.sub.RF], as per the CAPM estimate in equation (5.0).

The CAPM viewpoint may seem too simple in this context because these pseudo-assets, the present value of fixed costs, do not necessarily lend themselves to the portfolio diversification effects assumed in CAPM analyses. That is, these assets may embody some unsystematic risks, unique to the firm, which the firm cannot diversify away. Consequently, a discount rate higher than the risk-free rate would be appropriate, which could complicate the analysis necessary for this expanded version of the CVP model.

The use of the risk-free rate, [k.sub.RF], for assessing the risk impact of fixed assets in a strategic decision would be a conservative approach. That discount rate would produce the highest present value of fixed costs in equation (7.1), which in turn would produce the highest estimate of a project's accounting beta, Betas. That higher beta estimate would in turn lead to the highest estimate of the project's cost of capital, [k.sub.a]. Since CVP analysis is not purported to be anything other than a rough first estimate of a strategic decision's impact upon a firm, a conservative estimate of an asset structure's systematic risk level may well be an appropriate approach. But, in any event, the important point is that the impact of asset structure should enter into the strategic thinking in CVP analyses.

An Illustration: Sports Equipment Manufacturing

To illustrate our above proposals, we have drawn upon a standard CVP case expanded with industry asset data (Robert Morris Associates, 1993) to broaden its scope in line with our suggestions. In this case, Hampton Inc. is a small business that manufactures basketballs. The company has a standard ball that sells for $25. At present, the standard ball is manufactured in a plant that relies heavily on direct labor workers. Thus, variable costs are high, totaling $15 per ball. During the current year, the company sold 30,000 standard balls, with the following results:

Sales (30,000 bails) $750,000 Less variable expenses 450,000

Contribution Margin 300,000 Less fixed expenses 210,000

Net income $ 90,000

Using conventional CVP analysis, the company's breakeven point (q) for current period operations was 21,000 balls, calculated as follows:

0 = pq - vq - FC 0 = $25q - $15q - $210,000 q = 21,000 balls

The company's degree of operating leverage (DOL) for current operations was 3.33, calculated as follows:

DOL = (pq - vq) / (pq - vq - FC) DOL = ($750,000 - $450,000) / ($750,000 - $450,000 - $210,000) DOL = 3.33

The company is discussing converting to a new, automated production system to manufacture the standard basketball. The new system would cut variable costs per ball by 40%; however, it would cause annual fixed costs to double. Hampton's average current assets during the year were $385,000. The ratio of sales to current assets was $750,000 / $385,000 or 1.948. The company's fixed assets were $65,000. The proposed production conversion would increase fixed assets to $100,000.

Assets are financed entirely with equity. Market analysis indicates that the current risk-free rate of return is 5% and the market return on stocks is 15%. The company's systematic beta risk ratio is estimated to be 1.50. With the assumptions provided, the company's cost of capital is estimated to be 20%.

[k.sub.a] = [k.sub.RF] + B ([k.sub.a] - [k.sub.RF]) [k.sub.a] = .05 + 1.5 (.15-.05) [k.sub.a] = .20

Breakeven sales and the degree of operating leverage under the proposed production system are estimated using conventional methods, as follows:

0 = $25q - $9q - $420,000 q = 26,250 balls

and

DOL = ($750,000 - $270,000) / ($750,000 - $270,000 - $420,000) DOL = 8.00

Using our expanded version of CVP analysis which incorporates the company's cost of capital, the breakeven point increases to 30,000 units.

$0 = $25q - $15q - $210,000 - .20 ($25q / 1.948) - .20($65,000)

q = 30,000 units

While the company sold 30,000 units last year for a reported net income of $90,000, the net income earned was equal to the company's cost of capital. Under the proposed production system, breakeven sales is estimated at 32,755 units.

$0 = $25q - $9q - $420,000 - .20 ($25q / 1.948) - .20 ($100,000) q = 32,755 units

As previously demonstrated, the automated production system would increase the company's degree of operating leverage. Increased operating leverage tends to increase variability of cash flows and level of firm risk (Zimmerman, 1995). The ratio of fixed assets to total assets would also increase in this proposal. Hence, Hampton's cost of capital could be expected to increase as a result of the proposed production system. Assuming that the increase in DOL increases cost of capital to 25%, the breakeven point would increase as follows:

$0 = $25q - $9q - $420,000 - .25($25q / 1.948) - .25 ($100,000)

q = 34,787 units

In this example, the breakeven points are much higher with our expanded model. The firm will have to increase its volume over current period sales in order to earn the cost of capital in the new production system, a point which the traditional analysis did not reveal. The only variable which remained constant in our analysis was the current asset turnover, S/CA. However, this assumption is probably unrealistic. An automated plant could allow for a higher working capital turnover ratio, but the opposite could be true in certain circumstances. But, once again, note that the traditional analysis ignores this consideration entirely.

Conclusions

CVP analysis is one of the most powerful techniques available in the arsenal of managerial accounting analytical tools. It is a relatively simple planning tool which allows managers to examine the possible impacts of a broad range of decisions. However, the scope of conventional CVP analysis can be broadened with an extended version of its basic model designed to mitigate certain shortcomings. In particular, CVP analysis does not consider the impact of strategic decisions on the wealth of firms, nor does it consider the effect of those decisions on firms' asset structures and risk levels. Those considerations are important because virtually all CVP analyses deal with decisions that alter the asset and cost structures of firms, which means that the risk levels and costs of capital of those firms will also change because of those decisions.

These missing elements in CVP analysis can be filled in with a small number of additional variables. The wealth effects can be included by analyzing the cost of capital of the assets necessary to carry out a decision. The risk level imposed by a decision can be incorporated by considering the degree of operating risk or the systematic risk level as reflected by an accounting beta risk variable. The cost of capital itself can be estimated through an analysis of the revenue patterns and the asset structures involved in a decision. In general, through the use of information that would usually be available in a CVP analysis, the full impact of a strategic decision can be assessed.

1 Similar to Schneider (1992; 1994) our model can be viewed as a variation rather than an extension of the basic CVP model. Schweitzer et al. (1992) provide an excellent discussion of extensions of the basic CVP model, including multi-period and multi-product analyses.

2 Income taxes are assumed away in the ensuing discussion. Manes (1966) remains the best treatment of tax effects in CVP analysis, among other considerations.

3 An implicit assumption here, and in the remainder of this discussion, is that assets invested in a project will be continuously renewed. That is, a perpetual asset, rather than a finite life asset, will be assumed. A similar, but slightly more "complicated" analysis can be developed for finite life assets by depreciating the assets on an annuity basis at the appropriate cost of capital (e.g., see Brealey and Myers, 1991: 219-223).

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-----. 1994. "How To Include Earnings-based Bonuses In Cost-Volume-Profit Analysis." Journal of Managerial Issues 2 (Summer): 231-240.

Schweitzer, Marcell, Ernst Trossmann, and Gerald H. Lawson. 1992. Break-even Analyses: Basic Model, Variants, Extensions. New York: John Wiley & Sons.

Vickers, Douglas. 1960. "On the Economics of Break-Even." Accounting Review 35 (July): 405-412.

White, Gerald I., Ashwinpaul C. Sondhi, and Dov Fried. 1994. The Analysis and Use of Financial Statements. New York: John Wiley & Sons.

Zimmerman, Jerold L. 1995. Accounting For Decision Making and Control. Chicago: Richard D. Irwin.

However, the simplicity of an analytical tool such as CVP can cut both ways. It can be both its greatest virtue and its major shortcoming. The real world is complicated, no less so in the world of managerial affairs; and a typical analytical model will remove many of those complications in order to preserve a sharp focus. That sharpening is usually achieved in two basic ways: simplifying assumptions are made about the basic nature of the model and restrictions are imposed on the scope of the model. Those simplifications and restrictions impinge on the reality and relevance of analytical models, so attempts to improve them will involve releasing some of their underlying assumptions or broadening their scope. In this article, we propose a variation of the CVP analytical model by broadening its scope to include cost of capital and the related impact of asset structure and risk level on strategic decisions, while at the same time preserving most of its admirable simplicity.

Our variation of the conventional CVP model provides more useful information to management because it focuses on more than operating expenses and sales revenues. Financial managers have long recognized the importance of including cost of capital and business risk variables in capital budgeting decisions (Brigham, 1995). Our model not only incorporates these admittedly important variables but recognizes the fixed and variable nature of capital costs.

Criticisms of CVP Analysis

Most criticisms of CVP relate to its basic underlying assumptions. Economists (Machlup, 1952; Vickers, 1960) have been particularly critical of those assumptions. Their criticisms take many forms, but they all arise from CVP's departures from the standard supply and demand models in price theory economics. Perhaps the most basic difference between CVP analysis and price theory models is that CVP ignores the curvilinear nature of total revenue and total cost schedules. In effect, it assumes that changes in volume have no effect on elasticity of demand or on the efficiency of production factors. Managerial accountants recognize these economic critiques, but they believe nonetheless that CVP analysis is a very useful initial analysis of strategic decisions (Horngren et al., 1994).

Additional criticisms of the underlying nature of CVP analysis arise from its similarities to standard economic models, rather than its differences. Similar to standard economic price theory models, basic CVP analysis usually assumes, among other things, the following: single-stage, single-product manufacturing processes; simple production functions with one causal variable; cost categories limited to only variable or fixed; and data and production functions susceptible to certainty predictions. Further, CVP analysis is typically restricted to one time period in each case. The shortcomings of CVP seem daunting, but CVP is pliable enough to overcome them all, if necessary and desirable. Nonlinear and stochastic CVP models involving multistage, multi-product, multivariate, or multi-period frameworks are all possible, although a single model embracing all of those extensions would seem a radical departure from the whole point of CVP analysis, its basic simplicity.(1) In general, the durability and popularity of CVP analysis undoubtedly reflects the willingness of its users to "live with" the shortcomings revealed by criticisms of its basic nature.

In this article, we are also content to "live with" the basic CVP model. Our concerns lie elsewhere, namely, the somewhat restricted focus of CVP on only sales revenue and operating expenses. That limitation can leave some very important aspects of strategic decisions overlooked. Schneider (1992; 1994), for example, suggests that the scope of CVP analysis ought to be widened to include the impact of managerial compensation schemes on target profit levels. In a similar vein, we propose that the scope of CVP analysis be broadened to overcome three limitations of the model in regard to asset structure and risk. Those three limitations are as follows: CVP does not measure the impact of the decision on wealth; it does not incorporate the effect of asset structure changes required by the decision; and it does not acknowledge the risk created by the decision (Magee, 1975; Cheung and Heaney, 1990; Chan and Yuan, 1990). Some fairly simple extensions of the scope of the basic model can do much to alleviate the shortcomings caused by those limitations.

In the following discussion, each of these three basic limitations of the CVP model will be examined further and some simple extensions of the model will be suggested. Strategic thinking, by definition, considers a broad mix of variables, so even this expanded version of the CVP model may still be subject to the basic criticism that it is too simple, in part, because projects do not exist in isolation. The widespread historic use of the basic version of the CVP model suggests that a simple, parsimonious analysis is indeed an effective first step in thinking about strategic decisions. The expanded version of the CVP model presented here will be developed in that spirit.

Wealth Impacts of CVP Decisions

The first limitation of the basic CVP model that should be addressed is the absence of any measurement of a decision's impact on wealth. The current CVP model focuses on the total level of net profits generated by a decision, which may or may not increase the wealth of the firm. The ultimate effect of a particular decision upon wealth depends on the investment in assets necessary to implement that decision. CVP analysis could be recast completely in present value measures (e.g., see Reinhardt, 1973). While it would probably be ideal to capture wealth effects through present value analyses, the main advantage of CVP analysis, its relative simplicity, would be lessened by the added complexities of present value techniques. A simpler way to incorporate wealth effects in the CVP model would be to include the firm's cost of capital in the analysis.

The key here would be target income, which figures so prominently in CVP analyses. As a simple expansion of the CVP model, target income is defined as the minimum net income acceptable for a particular decision. This minimum income level is formulated as follows: [2]

[NI.sup.T] = [k.sub.o] x [Delta]TA (1.0)

Where:

[NI.sup.T] = target net income; [k.sub.o] = cost of capital; [Delta]TA = total assets required for a decision.

This definition of target income requires the explicit recognition of two more variables in CVP analysis, namely, the cost of capital and the total assets required to implement a decision.(3) The cost of capital would be the minimum rate of return acceptable from the decision and the total assets required for the decision would be any additional, incremental assets that would have to be acquired in order to implement the decision. Admittedly, these additional variables would seem to encroach upon the simplicity of the current version of the CVP model. However, the notion of target income itself implies that some estimates of the cost of capital and the required investment are lurking somewhere in a CVP analysis of this type. Otherwise, the target income itself begs the question of how it was derived.

Given the above definition of target income, a CVP analysis could then proceed in the usual fashion suggested. For example, a unit cost approach to CVP analysis could be formulated as follows:

pQ = vQ + FC + ([k.sub.o] x [Delta]TA) (2.0)

Where:

p = selling price per unit; v = variable cost per unit; Q = total quantity of units produced or sold; FC = total fixed costs.

The general thrust of the above CVP analysis would be to determine if a particular pricing policy and cost structure strategy might yield at least a minimum target income level that would meet the firm's cost of capital. An achievement of at least that minimum income level, or more, should preserve or enhance the existing wealth of the firm. As Drucker states in a critique of cost accounting:

"Until a business returns a profit that is greater than its cost of capital, it operates at a loss. Never mind that it pays taxes as if it had a genuine profit. The enterprise still returns less to the economy than it devours in resources. It does not cover its full cost unless the reported profit exceeds the cost of capital. Until then, it does not create wealth; it destroys it" (1995:59).

Introduction of Assets into CVP Analysis

The above introduction of assets into the analysis suggests that a simple framework for analyzing required assets should be incorporated into CVP analysis as well. The notion of variable and fixed assets, somewhat akin to the notion of variable and fixed costs, would be a useful addition to CVP analyses. This notion of variable and fixed assets is a popular tool in financial forecasting in the field of financial management (e.g., see Brigham, 1995). It arises from the simple idea that some proportional relationships may exist between sales or production volume and certain assets. If such proportional relationships can be determined, then an expanded version of the CVP model would allow for a much richer analysis of target income strategies.

The usual approach to asset requirements in financial forecasting is to assume that fixed ratios exist between sales volume and the various current assets of a firm, but the remaining assets are fixed within some relevant volume range. Those ratios are often determined through an analysis of average turnover ratios in a firm's industry or through a study of a firm's own history of turnover ratio levels. The dichotomy of variable and fixed assets can be modified to allow for some assets to have both a variable and fixed component. But, the overall idea is that assets can be analyzed within a variable versus fixed framework just like costs.

In that regard, equation (2.0) above is modified in the following fashion to allow for a variable and fixed analysis of assets as well as costs:

pQ = vQ + FC + [([k.sub.o] x pQ/[R.sub.n]) + ([k.sub.o] x FA)] (3.0)

Where:

[R.sub.n] = normal ratio of sales to current asset;

FA = fixed assets allocated to decision.

In equation (3.0), target income is separated into returns on variable and fixed assets, ([k.sub.o] x pQ/[R.sub.n]) and ([k.sub.o] x FA), respectively. This separation recognizes that the behavior of these two types of assets would normally require different analyses. The operating variable and fixed cost analysis, however, remain unchanged from the basic CVP model. A few additional comments are in order here in regard to equation (3.0) above. First, the expression "pQ./[R.sub.n]" is the estimate of current assets, given the sales volume involved in the CVP analysis. This constant ratio assumption implies that current assets increase and decrease in the exact same percentage changes as sales volume. In some circumstances, this assumption may be too limiting. Second, the fixed assets allocated to the decision may require some entirely different incremental analysis. A particular pricing policy and cost structure strategy may require an increase in the total fixed assets of a firm, but that new increment of fixed assets would presumably not change within some relevant volume range of the proposed strategy.

An interesting variation of equation (3.0) would be to recast it in a contribution margin approach, as follows:

pQ-vQ-([k.sub.o] pQ/[R.sub.n]) = FC+ ([k.sup.o] FA) (3.1)

Contribution margin is normally defined as the income remaining after variable expenses are deducted from sales revenue. In effect, this modified version of equation (3.0) would redefine contribution margin as the net difference between sales and the sum of variable costs plus the minimum required return on the variable assets required for the decision. This version of contribution margin would explicitly recognize that a variable opportunity cost is present in strategic decisions, as well as variable operating costs. While this version of CVP analysis is merely an algebraic manipulation, a separate consideration of variable and fixed resources could allow for new insights within particular decisions. For example, it would allow for a modified version of the break even version of CVP analysis in which the return on fixed assets ([k.sub.o] x FA) would be set to zero. This modified version of break even would imply that the return on fixed capital could possibly be foregone in some circumstances but that return on circulating capital would have to continue for a firm to remain viable.

Risk Considerations in CVP Analysis

The introduction of asset structure into CVP analysis heightens another shortcoming of the traditional CVP model: its lack of attention to operating risk. Intuitively, both cost structure and asset structure would be direct determinants of a firm's operating risk. In general, firms with relatively higher ratios of fixed costs to total costs and fixed assets to total assets would be expected to have higher operating risks. That is, changes in their sales and production volume would have a proportionately greater impact on net income than firms with relatively lower fixed costs and fixed assets. The expanded version of CVP analysis in equation (3.0) includes both of those variables; therefore, a further expansion that included operating risk would seem worthwhile. In other words, every time a CVP analysis presumes a different cost and asset structure, a new operating risk level will emerge.

The logical variable for dealing with this particular shortcoming of CVP analysis is to adjust the cost of capital, [k.sub.o], to include the impact of changes in operating risk caused by cost and asset structure shifts. The field of financial management provides some useful ideas on how to expand the CVP model in light of this shortcoming.

Basically, the cost of capital, [k.sub.o], for a particular strategic decision would be a direct function of the operating risk of the venture that would unfold from that decision. However, defining and measuring that function is an extremely difficult proposition. Two approaches in the field of financial management seem pertinent here, although neither approach is completely satisfactory. The first approach involves measuring a surrogate variable of operating risk, and the second approach involves an analysis of fixed costs that provides a surrogate Beta risk measure for the Capital Asset Pricing Model (CAPM) computation of cost of capital.

In the first approach, a surrogate operating risk measure, the degree of operating leverage, is obtained from the basic data employed in the traditional CVP model (e.g., see Garrison and Noreen, 1994; Hilton, 1994; Zimmerman, 1995; Morse et al., 1996). This risk measure shows the percentage change that can be expected in net income given some change in sales volume. Contribution margin is a key variable in this analysis. It is the income stream that is available to meet fixed expenses and target profit levels. The degree of operating leverage recognizes that contribution margin is an income stream that changes at the same rate as sales volume, while net income will change at a different rate because of the presence of constant fixed costs. Relating those two income measures in ratio form provides an index of the relative sensitivity of net income to changes in sales.

In basic terms, the degree of operating leverage can be defined as follows:

DOL = CM/NI (4.0)

Where:

DOL = degree of operating leverage; CM = contribution margin; NI = net income.

Drawing upon the usual version of the CVP model, the above leverage relationship can be formulated as follows:

DOL = pQ - vQ / pQ - vQ - FC (4.1)

Note that no new information is required in the equation (4.1) version of operating risk. The numbers employed in a typical CVP analysis would be sufficient to develop this risk measure. While many combinations of product prices and costs are possible, fixed costs are the crucial variable driving the degree of operating leverage. The higher are the fixed costs, the higher is the operating leverage. Other things being equal, the higher a firm's degree of operating leverage, the higher is its overall business operating risk. Over time, a firm with a higher degree of operating leverage can expect a higher variability of its net income stream. In the end result, a higher degree of operating leverage will lead to a higher cost of capital, which in turn means that target income levels in CVP analyses will be relatively higher and more difficult to attain.

It is difficult to stretch this surrogate measure of operating risk beyond the simple hypotheses offered above. That is, the degree of operating leverage measure itself does not tie into the cost of capital figure in a direct analytical manner. Some rough estimates of the quantitative relationship between operating leverage and cost of capital might be obtained from analyses of a group of firms in the same industry or from a time series analysis of a single firm. In most settings, the degree of operating leverage measure would probably serve best as a variable that prompts decision makers to think about the consequences of their strategic decisions on the cost of capital.

In the second approach to incorporating operating risk's effect on the cost of capital, an accounting version of the Capital Asset Pricing Model is employed. In CAPM, the cost of capital of a particular project would be a function of the systematic risk involved in the project's assets. This systematic risk would be the sensitivity of the returns on those assets to broad movements in the economy, usually measured as the returns on all securities in the capital markets. It is formulated as follows:

[k.sub.a] = [k.sub.RF] + [B.sub.a] ([k.sub.M] - [k.sub.RF]) (5.0)

Where:

[k.sub.a] = cost of capital of project assets;

[k.sub.RF] = return on risk free assets;

[k.sub.M] = return on a market portfolio of risky assets;

[B.sub.a] = Beta systematic risk measure of project assets.

In equation (5.0) above, the only variable affected by a firm's strategic decisions is the Beta systematic risk measure. This Beta measure relates the returns on investment of a firm's assets to the average returns on investment of all other firms in the economy, which would be approximated by some index measure of the returns on a market portfolio of risky assets. As the firm changes the cost structures associated with its assets, it also changes the pattern of its cost and income flows relative to all other firms in the economy. As a result, the sensitivity of its asset returns to broad movements in the economy would also change. If a firm's strategic decisions increase [B.sub.a], its cost of capital on the assets associated with those decisions, [k.sub.a], would also increase. Consequently, it would be very useful if accounting data could be used to estimate the systematic risk involved in strategic decisions.

Some ideas from the field of financial management, integrated with some empirical work in accounting, are helpful in regard to linking cost of capital with CVP analyses. The Beta systematic risk measure is the key variable here. Beta risk measures are usually derived from stock market returns, with variable [k.sub.M] representing the return on a market portfolio of securities. Similar Beta risk measures have been developed in accounting and financial management in which a firm's accounting earnings over some time period are related to the average earnings patterns of all firms taken together (White et al., 1994). For example, these earnings variables could be expressed as returns on assets (NI/TA) for variables [k.sub.a] and [k.sub.M] in equation (5.0) above. The systematic risk measures obtained in this approach are referred to as accounting betas. An examination of the underlying origins of accounting betas yields some interesting insights about how CVP analysis could be expanded to incorporate systematic risk measures.

An accounting beta can be thought of as a combination of the individual betas of the various components of net earnings. The present value of the assets necessary for the strategic decision being analyzed can be considered the present values of the net earnings components, as follows (Brealey and Myers, 1991):

[Beta.sub.A] = f([Beta.sub.pQ] - [Beta.sub.vQ] - [Beta.sub.FC]) (6.0)

And:

PV([Delta]TA) = [PV(pQ)-PV(vQ)-PV(FC)] (6.1)

Where:

[Beta.sub.A] = Accounting beta;

PV = Present value.

The two sets of variables above in equations (6.0) and (6.1) can be integrated in light of some simplifying assumptions that are often employed in CVP analysis. If the variable costs (vQ) are perfectly proportional to sales revenue (pQ) and if the fixed costs (FC) are constant within the relevant volume range of a strategic decision, then the systematic risks of variable costs ([Beta.sub.vQ]) and sales revenue ([Beta.sub.pQ]) are equal, and the systematic risk of the fixed costs ([Beta.sub.FC]) is zero. Substituting [Beta.sub.pQ] for [Beta.sub.vQ] and setting [Beta.sub.FC] to zero, equations (6.0) and (6.1) can be integrated by weighting each variable by the present value of sales revenue, PV(pQ), as follows:

BA [multiplied by] PV([Delta]TA) / PV (pQ) = [[Beta.sub.pQ] [multiplied by] PV(pQ)] / PV(pQ) - [[Beta.sub.PQ] [multiplied by] PV(vQ)] / PV (pQ) - [[Beta.sub.FC] [multiplied by] (FC)] / PV (pQ) (7.0)

Since the difference between the present value of revenue, PV(pQ), and variable costs, PV(vQ), equals the present value of freed costs, PV(FC), and the systematic risk of the fixed costs, [Beta.sub.FC], is set at zero, equation (7.0) reduces to the following relationship:

[B.sub.A] = [B.sub.pQ] [multiplied by] [1.0 + PV(FC)]/PV([Delta]TA) (7.1)

Equation (7.1) demonstrates that the accounting beta for a particular strategic decision is determined by the sensitivity of the project's revenue stream to revenue patterns in the general economy and by the project's asset structure. An incorporation of those two variables in CVP analysis would allow for a full consideration of the ultimate wealth impacts of the decision being analyzed. The inclusion of accounting betas in CVP analyses would add two more variables that would have to be estimated, both of which would detract from the basic simplicity of the traditional CVP model. However, rough estimates of a project's revenue beta and asset structure would certainly be feasible and desirable in most cases.

The relative difficulty of estimating each of those additional variables does vary somewhat. The revenue beta would be an estimate of how the cyclical patterns of a project's revenue stream would compare to the aggregate revenue streams in the general economy. This characteristic of a project's market should be considered in making strategic decisions. Most firms should have a good feel for their particular markets from past experience and from information about competitors.

The relationship of the value of freed costs to the total assets to be invested in a project is a bit more difficult to derive. A firm's customary ratio of fixed assets to total assets would seem a useful first approximation. But, a problem exists in that financial accounting systems do not necessarily recognize all of the fixed assets involved in a strategic decision. Certain fixed assets, such as research and development programs or marketing campaigns, are expensed immediately without any consideration for their long-term implications. Thus, the fixed costs relationship in equation (7.1) might be underestimated in many cases when regular accounting data are used.

As stated at the outset, present value analyses might detract too much from the basic simplicity of CVP analysis. However, a present value approach may be the only recourse for estimating the systematic risk created by the fixed assets investment in a particular project. That approach would not be unduly difficult because the necessary data should be obtainable. After all, most of the fixed costs themselves have already been estimated in a traditional CVP analysis, and information about the discount rate is implicit in the target income level set in such an analysis.

There may be some ambiguity involved in choosing what discount rate ought to be used in estimating the present value of fixed costs. The simplest approach would be to assume that the risk of those costs is zero since they are not expected to vary at all in relation to general cyclical movements in the economy. Given that assumption, the appropriate discount rate for determining the present value of the fixed costs, PV(FC), would be simply the risk-free rate of return, [k.sub.RF], as per the CAPM estimate in equation (5.0).

The CAPM viewpoint may seem too simple in this context because these pseudo-assets, the present value of fixed costs, do not necessarily lend themselves to the portfolio diversification effects assumed in CAPM analyses. That is, these assets may embody some unsystematic risks, unique to the firm, which the firm cannot diversify away. Consequently, a discount rate higher than the risk-free rate would be appropriate, which could complicate the analysis necessary for this expanded version of the CVP model.

The use of the risk-free rate, [k.sub.RF], for assessing the risk impact of fixed assets in a strategic decision would be a conservative approach. That discount rate would produce the highest present value of fixed costs in equation (7.1), which in turn would produce the highest estimate of a project's accounting beta, Betas. That higher beta estimate would in turn lead to the highest estimate of the project's cost of capital, [k.sub.a]. Since CVP analysis is not purported to be anything other than a rough first estimate of a strategic decision's impact upon a firm, a conservative estimate of an asset structure's systematic risk level may well be an appropriate approach. But, in any event, the important point is that the impact of asset structure should enter into the strategic thinking in CVP analyses.

An Illustration: Sports Equipment Manufacturing

To illustrate our above proposals, we have drawn upon a standard CVP case expanded with industry asset data (Robert Morris Associates, 1993) to broaden its scope in line with our suggestions. In this case, Hampton Inc. is a small business that manufactures basketballs. The company has a standard ball that sells for $25. At present, the standard ball is manufactured in a plant that relies heavily on direct labor workers. Thus, variable costs are high, totaling $15 per ball. During the current year, the company sold 30,000 standard balls, with the following results:

Sales (30,000 bails) $750,000 Less variable expenses 450,000

Contribution Margin 300,000 Less fixed expenses 210,000

Net income $ 90,000

Using conventional CVP analysis, the company's breakeven point (q) for current period operations was 21,000 balls, calculated as follows:

0 = pq - vq - FC 0 = $25q - $15q - $210,000 q = 21,000 balls

The company's degree of operating leverage (DOL) for current operations was 3.33, calculated as follows:

DOL = (pq - vq) / (pq - vq - FC) DOL = ($750,000 - $450,000) / ($750,000 - $450,000 - $210,000) DOL = 3.33

The company is discussing converting to a new, automated production system to manufacture the standard basketball. The new system would cut variable costs per ball by 40%; however, it would cause annual fixed costs to double. Hampton's average current assets during the year were $385,000. The ratio of sales to current assets was $750,000 / $385,000 or 1.948. The company's fixed assets were $65,000. The proposed production conversion would increase fixed assets to $100,000.

Assets are financed entirely with equity. Market analysis indicates that the current risk-free rate of return is 5% and the market return on stocks is 15%. The company's systematic beta risk ratio is estimated to be 1.50. With the assumptions provided, the company's cost of capital is estimated to be 20%.

[k.sub.a] = [k.sub.RF] + B ([k.sub.a] - [k.sub.RF]) [k.sub.a] = .05 + 1.5 (.15-.05) [k.sub.a] = .20

Breakeven sales and the degree of operating leverage under the proposed production system are estimated using conventional methods, as follows:

0 = $25q - $9q - $420,000 q = 26,250 balls

and

DOL = ($750,000 - $270,000) / ($750,000 - $270,000 - $420,000) DOL = 8.00

Using our expanded version of CVP analysis which incorporates the company's cost of capital, the breakeven point increases to 30,000 units.

$0 = $25q - $15q - $210,000 - .20 ($25q / 1.948) - .20($65,000)

q = 30,000 units

While the company sold 30,000 units last year for a reported net income of $90,000, the net income earned was equal to the company's cost of capital. Under the proposed production system, breakeven sales is estimated at 32,755 units.

$0 = $25q - $9q - $420,000 - .20 ($25q / 1.948) - .20 ($100,000) q = 32,755 units

As previously demonstrated, the automated production system would increase the company's degree of operating leverage. Increased operating leverage tends to increase variability of cash flows and level of firm risk (Zimmerman, 1995). The ratio of fixed assets to total assets would also increase in this proposal. Hence, Hampton's cost of capital could be expected to increase as a result of the proposed production system. Assuming that the increase in DOL increases cost of capital to 25%, the breakeven point would increase as follows:

$0 = $25q - $9q - $420,000 - .25($25q / 1.948) - .25 ($100,000)

q = 34,787 units

In this example, the breakeven points are much higher with our expanded model. The firm will have to increase its volume over current period sales in order to earn the cost of capital in the new production system, a point which the traditional analysis did not reveal. The only variable which remained constant in our analysis was the current asset turnover, S/CA. However, this assumption is probably unrealistic. An automated plant could allow for a higher working capital turnover ratio, but the opposite could be true in certain circumstances. But, once again, note that the traditional analysis ignores this consideration entirely.

Conclusions

CVP analysis is one of the most powerful techniques available in the arsenal of managerial accounting analytical tools. It is a relatively simple planning tool which allows managers to examine the possible impacts of a broad range of decisions. However, the scope of conventional CVP analysis can be broadened with an extended version of its basic model designed to mitigate certain shortcomings. In particular, CVP analysis does not consider the impact of strategic decisions on the wealth of firms, nor does it consider the effect of those decisions on firms' asset structures and risk levels. Those considerations are important because virtually all CVP analyses deal with decisions that alter the asset and cost structures of firms, which means that the risk levels and costs of capital of those firms will also change because of those decisions.

These missing elements in CVP analysis can be filled in with a small number of additional variables. The wealth effects can be included by analyzing the cost of capital of the assets necessary to carry out a decision. The risk level imposed by a decision can be incorporated by considering the degree of operating risk or the systematic risk level as reflected by an accounting beta risk variable. The cost of capital itself can be estimated through an analysis of the revenue patterns and the asset structures involved in a decision. In general, through the use of information that would usually be available in a CVP analysis, the full impact of a strategic decision can be assessed.

1 Similar to Schneider (1992; 1994) our model can be viewed as a variation rather than an extension of the basic CVP model. Schweitzer et al. (1992) provide an excellent discussion of extensions of the basic CVP model, including multi-period and multi-product analyses.

2 Income taxes are assumed away in the ensuing discussion. Manes (1966) remains the best treatment of tax effects in CVP analysis, among other considerations.

3 An implicit assumption here, and in the remainder of this discussion, is that assets invested in a project will be continuously renewed. That is, a perpetual asset, rather than a finite life asset, will be assumed. A similar, but slightly more "complicated" analysis can be developed for finite life assets by depreciating the assets on an annuity basis at the appropriate cost of capital (e.g., see Brealey and Myers, 1991: 219-223).

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-----. 1994. "How To Include Earnings-based Bonuses In Cost-Volume-Profit Analysis." Journal of Managerial Issues 2 (Summer): 231-240.

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