# Cost Volume Profit Analysis: Establishing a Decision Model

Ryan Lagano Professor Van Leer Accounting 200-010 Honors Paper Cost Volume Profit Analysis: Establishing a Decision Model In today’s modern world of businesses and corporations, there is a common goal shared throughout every industry: increase profits. With increases in technology and developing methods, businesses have come far lengths in increasing their profits, or operating income. Controlling costs is the key to a successful operation. Executives and managerial departments are using what they know about costs to create business strategies.

By gathering information on market demand and combining it with a marketing strategy that focuses on higher margin products, companies are able to continue and increase profits and survive. The Cost Volume Profit Analysis is the paramount and most cost efficient way of doing so. By understanding the economic consequences of cost structure, contribution margin, and break-even sensitivity, a business can create a decision model to enhance the company’s profitability. A brief outline is necessary in understanding the Cost Volume Profit analysis (or CVP) and creating a decision model.

In a very general outlook, the CVP looks at how fixed, variable, and mixed costs change with changes in sales volume. The main goal is to determine what factors control costs and see how management can use this information to improve planning and control activity. The first step in any CVP analysis is picking an activity base relative to the nature of the company’s operation. For instance, a retail operation may use output while a manufacturing operation may use input as their base. After establishing a base, it is necessary for the company to identify all fixed, variable, and overhead costs.

This is not an easy task, as what is to be considered one category of cost may change in a different environment. The CVP looks at how each of these costs affects the operating income. Each cost has its own behavior when referring to the CVP analysis. Fixed costs are costs that are relatively constant no matter what the sales volume is. Therefore, as sales volume increases the contribution of fixed cost per unit decreases while the effect of total cost remains constant. Variable costs are those costs considered to change roportionally to change in volume. In this case, as sales volume increases the variable cost per unit stays relatively the same. Thus, the contribution of variable costs to total cost increases as sales volume increases. This proportionality is assumed to be linear, one of the many complaints of the CVP system. Lastly, the mixed costs, or overhead costs are factored in. Overhead cost is a very gray area of costs. It consists of variable and fixed costs. CVP attacks these semivariable costs using two methods: high-low and least squares.

High-low analyzes the extremes of the costs incurred and uses point-slope form to create an estimated linear equation for that certain costs. The least-squares method is a little more costly, but is much more accurate to the actual cost equation by using a line of best fit. Once these costs are sorted and determined, various relationships can be found that help a company make management decisions. Profit, or operating income, is known to be revenue minus the operating and manufacturing costs.

Graphically, the CVP shows two lines, the total costs (in y=mx+b form) and revenue (simply sales price * quantity sold, y=mx form). The intersection of these two lines brings a very interesting and possible the most important result of CVP analysis. This point is the point where the company breaks even, or the level of activity at which operating income is equal to zero. Further mathematical relationships tell management even more about this break-even point and its characteristics. One way CVP analysis goes about this is using the contribution margin. Simply put, it is the amount by which revenue exceeds variable costs.

It states that for every dollar of sales past the break even point, a certain percentage goes towards operating income. The unit contribution margin is just the unit selling price minus the variable cost per unit. The contribution margin ratio is the exact percentage of each sales dollar’s percentage towards revenue. So, prior to break even this percentage of each dollar goes towards covering fixed costs. This is a key relationship as seen late for smaller businesses. Beyond this contribution margin, management may also ask, what does sales need to be?

This can be covered in units or sales dollars. Either way the basic equation is fixed costs plus desired operating income all divided by the contribution margin (units – CM/unit, sales dollars – CM Ratio). Break-even can be calculated using this formula by simply assuming desired operating income is zero. Another elementary relationship given by CVP is the margin of safety. The actual sales for a given time period minus the break even in sales dollars gives the margin of safety. It is a representation of the dollar amount by which sales can decline before operating losses are incurred.

This is crucial for a company to understand what they can endure as far as a downturn in sales. Obviously CVP can answer many various questions management has to ask, but one of the most commonly asked and considered questions is what a company can anticipate as far as a change in operating income. Using the contribution margin ratio, this anticipated change in income can be found by simply multiplying the ratio by the change in sales units. With a common understanding of all of these basic relationships, a business can begin to make a decision model specific to their company.

The basic decision model is a tool using CVP analysis that enables a company to minimize fixed costs and increase profits. Each aspect of the model changes with every managerial decision. A short list of these decisions include: type of unit, categorization of costs, sales price, sales volume, advertising, adding/removing/mixing product lines, accepting or declining a special order, percent operating capacity, increasing or decreasing work force, changing modes of production, and desired operating income. Each decision affects every other decision in some way.

Different departments and sectors of a company can build models using decisions that benefit the company. The type of unit is the first decision necessary towards maximizing profits. This choice is decided by relevance to the customers buying patterns. Each different company must choose a unit that makes sense to their type of product or service. For example a hotel may use rooms rented as their unit while a retailer may decide that each product sold will be a unit. This seemingly elementary step is vital in a business’s success.

If a unit of sale is chosen that does not make sense or is too large or too small in quantity, any information regarding productivity of the company (such as sales) will be rendered irrelevant and any decision based on the information will not reflect a probable strategies to improve corporate earnings. The categorization of costs is the company’s responsibility of labeling each cost as fixed, variable or mixed. By correctly grouping each cost, management can then take it a step further and see what combination of decisions will reduce costs the most.

The operating and unit costs of a company are what decide the total cost. With costs correctly categorized, a company can accurately see if something like an increase in produced units will increase or decrease expected profits. Sales price is crucial to a company’s success. As consumers, it is known that prices change frequently. This is a strategy used by management in an effort to reduce costs and increase earnings. As management knows, price must reflect the cost of production. If cost of production increases, as must sales price.

Yet, an attempt to increase price while productions costs hold constant is where CVP analysis will show if this decision is beneficial. An increase in sales price is likely to decrease the number of sales units. If the change in expected income is greater than zero as using the accounting formula’s then the choice is advantageous. If prices are too high in a competitive market, the desired operating costs go down. The price must be set based on its worth to the customer and not on the cost of production. Therefore, it is clear that sales price and sales volume are intertwined.

As discussed previously, variable costs and mixed costs increase as sales volume increases. The increase in sales income must be greater than the increase in costs. If this is true, a company would be wise in increasing its sales volume. The amount to increase by is decided by a maximizing level of contribution per unit. This analysis can be seen by a graphical representation of the relationship between cost and contribution per unit. If the derivative is taken of the function, the maximizing value shall be where the derivative equals zero and the second derivative is greater than zero.

Although the initial function is not necessarily linear, there will still be only one maximum due to the behavior of the line. Another crucial step in increasing success is management’s decisions in advertising. Advertising will increase sales volume, yet will increase fixed costs by the cost of advertising and by the increase in variable costs due to the higher sales volume. For a beneficial advertising decision the contribution of the extra sales volume must be greater than the newly acquired costs.

A company’s production and work force are important in making decision to better earning opportunities. As sales volume increases for whatever reason, the production must increase as well. A business must analyze how they will account for this increase in production. First, they must decide if they should have the workers work more, or if they should hire new workers. Requiring more of the current workers will increase their wages and the hours they work. Hiring new employees will keep wages constant yet increase the payroll.

Each cost must be analyzed and compared to each unit. This is a decision largely influenced by a plant manager. By determining the projected income over a relative period of time, the company can then make an educated decision to increase profitability. Hand in hand with the labor decision, a company must decide its percent operating capacity. Increased volume puts pressure on a company’s production capabilities. An increase in work labor is needed while increasing the operating activity percent. For every company there is an operating capacity ideal for maximizing profits.

This can be estimated relative to the operation of the company yet for any business it is in the range of 45 to 80 percent. Lastly, a business must decide on a product line, or range of product line. When more than two products are incorporated in a company, as is usually the case, in order to use the cost volume profit analysis, the contribution margins of each product must be averaged. Therefore, the company will shift to the product with a higher contribution margin ratio. One easy way for a company to do this is to have their own substitute product.

By keeping a mixture of sales between one product and a product of higher value, the company can minimize costs and not have to worry about losing business to competitors with lower valued products, as long as they do not completely exclude their own higher valued product. As beneficial as the CVP analysis is, there are still flaws that many businesses complain about. CVP analysis makes some assumptions that do not hold true in the real business world. First, it assumes that everything produced is sold. Many companies lose acquire sunk costs due to situations like for manufacturing products with faults.

These situations can not be predicted and are therefore ignored. Another assumption CVP makes is its linear functions of cost for a single product in a determined period. There will always be some unpredictability to non linear costs, yet the CVP does a good job to at least estimate costs. Another complaint that managers and business have with CVP analysis is its ignorance of the cost of capital. By not including the cost of capital into the analysis, total cost can be understated while overstating profitability.

The costs invested in the assets used to for production is a cost equal to the cost of operating resources. This would lead to investment in funds beyond where the marginal contribution of the last dollar of capital used is the same as its marginal cost. Incorporating the cost of capital into the CVP analysis allows managers to determine the added value for a certain level of sales. In order to account for the cost of capital, a firm must use the activity based costing (ABC) system. This is due to product mix and that many times, a small percentage of the product can produce a large percent of the profits.

CVP analyses production over a certain period, however, the economic life of a product may be greater than this period. By extrapolating the period over the life of the product, mangers can evaluate profitability accurately. Lastly, CVP is ignorant to opportunity cost. Incorporating the cost of capital into a product’s cost allows product mix decisions to be spot on with capital budgeting decisions. When existing capital assets will be used to manufacture a product, failure to consider the cost of capital is implicitly assuming that these assets have an abandonment value of zero.

It is very likely that current assets can be sold or used by the company. The cost of capital should be incorporated into a product’s cost whether new or existing assets are used to manufacture a proposed product. The cost volume profit analysis is a useful accounting tool for managerial decision. Specific decision models can be created to allow firms to minimize costs and maximize profits. With a thorough understanding of controlling costs firms can make accurate changes that will allow them to expand their profitability and success.