Question

Respond to this:

Identify the costs of a current or past project. Share your perspective on whether each cost is variable, fixed or mixed. If you list a cost as variable, describe what causes the cost to vary. If you list a cost as mixed, attempt to calculate the cost formula using the high-low method. Explain how knowing the costs are variable, fixed or mixed can help you manage a project budget.

Prototype part cost = variable. As we buy more volume, the cost per piece is lower.

Prototype tooling cost = fixed

Prototype build labor = variable. Depending on the length of a build, the labor cost will differ.

Design labor cost (time required to produce a design) = variable. Depending on number of hours needed to finish a design, the overall cost per design will differ.

Knowing or estimating these project costs is essential to determine our yearly expense budgets. These budgets are tracked on a monthly basis and reported to management if we are over or under budget and how is the budget trending (up, down or neutral).

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Answer 1

Fixed Costs

A fixed cost remains unchanged in amount when the volume of activity varies from period to period within a relevant range. For example, $5,000 in monthly rent paid for a factory building remains the same whether the factory operates with a single eight-hour shift or around the clock with three shifts. This means that rent cost is the same each month at any level of output from zero to the plant’s full productive capacity. Notice that while total fixed cost does not change as the level of production changes, the fixed cost per unit of output decreases as volume increases. For instance, if 20 units are produced when monthly rent is $5,000, the average rent cost per unit is $250 (computed as $5,000/20 units). When production increases to 100 units per month, the average cost per unit decreases to $50 (computed as $5,000/100 units). The average cost decreases to $10 per unit if production increases to 500 units per month. Common examples of fixed costs include depreciation, property taxes, office salaries, and many service department costs. When production volume and costs are graphed, units of product are usually plotted on the horizontal axis and dollars of cost are plotted on the vertical axis. Fixed costs then are represented as a horizontal line because they remain constant at all levels of production. To illustrate, the graph in Exhibit 5.1 shows that fixed costs remain at $32,000 at all production levels up to the company’s monthly capacity of 2,000 units of output. The relevant range for fixed costs in Exhibit 5.1 is 0 to 2,000 units. If the relevant range changes (that is, production capacity extends beyond this range), the amount of fixed costs will likely change.

Variable Costs

A variable cost changes in proportion to changes in volume of activity. The direct materials cost of a product is one example of a variable cost. If one unit of product requires materials costing $20, total materials costs are $200 when 10 units of product are manufactured, $400 for 20 units, $600 for 30 units, and so on. Notice that variable cost per unit remains constant but the total amount of variable cost changes with the level of production. In addition to direct materials, common variable costs include direct labor (if employees are paid per unit), sales commissions, shipping costs, and some overhead costs. When variable costs are plotted on a graph of cost and volume, they appear as a straight line starting at the zero cost level. This straight line is upward (positive) sloping. The line rises as volume of activity increases.

Mixed costs

A mixed cost includes both fixed and variable cost components. For example, compensation for sales representatives often includes a fixed monthly salary and a variable commission based on sales. The total cost line in Exhibit 5.1 is a mixed cost. Like a fixed cost, it is greater than zero when volume is zero; but unlike a fixed cost, it increases steadily in proportion to increases in volume. The mixed cost line in Exhibit 5.1 starts on the vertical axis at the $32,000 fixed cost point. Thus, at the zero volume level, total cost equals the fixed costs. As the activity level increases, the mixed cost line increases at an amount equal to the variable cost per unit. This line is highest when volume of activity is at 2,000 units (the end point of the relevant range). In CVP analysis, mixed costs are often separated into fixed and variable components. The fixed component is added to other fixed costs, and the variable component is added to other variable costs.

Measuring Cost Behavior

Identifying and measuring cost behavior requires careful analysis and judgment. An important part of this process is to identify costs that can be classified as either fixed or variable, which often requires analysis of past cost behavior. Three methods are commonly used to analyze past costs: scatter diagrams, high-low method, and least-squares regression. High-low method is discussed in this section using the unit and cost data shown in the Exhibit below, which are taken from a start-up company that uses units produced as the activity base in estimating cost behavior.

High-Low Method

The high-low method is a way to estimate the cost equation by graphically connecting the two cost amounts at the highest and lowest unit volumes. In our case, the lowest number of units is 17,500, and the highest is 67,500. The costs corresponding to these unit volumes are $20,500 and $29,000, respectively (see the data in the above Exhibit ). The estimated line of cost behavior for the high-low method is then drawn by connecting these two points on the scatter diagram corresponding to the lowest and highest unit volumes as follows.

The variable cost per unit is determined as the change in cost divided by the change in units and uses the data from the high and low unit volumes. This results in a slope, or variable cost per unit, of $0.17 as computed in the Exhibit below:

To estimate the fixed cost for the high-low method, we use the knowledge that total cost equals fixed cost plus variable cost per unit times the number of units. Then we pick either the high or low point to determine the fixed cost. This computation is shown in Exhibit below—where we use the high point (67,500 units) in determining the fixed cost of $17,525. Use of the low point (17,500 units) yields the same fixed cost estimate: $20,500 [1] Fixed cost = ($0.17 per unit = 17,500), or Fixed cost [1] $17,525.

Thus, the cost equation used to estimate costs at different units is $17,525 plus $0.17 per unit. This cost equation differs slightly from that determined from the scatter diagram method. A deficiency of the high-low method is that it ignores all cost points except the highest and lowest. The result is less precision because the high-low method uses the most extreme points rather than the more usual conditions likely to recur.

We explained how managers classify costs by behavior. This often refers to classifying costs as being fixed or variable with respect to volume of activity. In manufacturing companies, volume of activity usually refers to the number of units produced. We then classify a cost as either fixed or variable, depending on whether total cost changes as the number of units produced changes. Once we separate costs by behavior, we can then compute a product’s contribution margin. Contribution margin per unit, or unit contribution margin, is the amount by which a product’s unit selling price exceeds its total unit variable cost. This excess amount contributes to covering fixed costs and generating profits on a per unit basis. Exhibit below shows the contribution margin per unit formula.

The contribution margin ratio, which is the percent of a unit’s selling price that exceeds total unit variable cost, is also useful for business decisions. It can be interpreted as the percent of each sales dollar that remains after deducting the total unit variable cost. Exhibit below shows the formula for the contribution margin ratio.

To illustrate the use of contribution margin, let’s consider company X, which sells footballs for $100 per unit and incurs variable costs of $70 per unit sold. Its fixed costs are $24,000 per month with monthly capacity of 1,800 units (footballs). X’s contribution margin per unit is $30, which is computed as follows.

Its contribution margin ratio is 30%, computed as $30/$100. This reveals that for each unit sold, X has $30 that contributes to covering fixed cost and profit. If we consider sales in dollars, a contribution margin of 30% implies that for each $1 in sales, X has $0.30 that contributes to fixed cost and profit

Briefly describing:

Cost behavior is described in terms of how its amount changes in relation to changes in volume of activity within a relevant range. Fixed costs remain constant to changes in volume. Total variable costs change in direct proportion to volume changes. Mixed costs display the effects of both fixed and variable components. Step-wise costs remain constant over a small volume range, then change by a lump sum and remain constant over another volume range, and so on. Curvilinear costs change in a nonlinear relation to volume changes.

Conventional cost-volume-profit analysis is based on assumptions that the product’s selling price remains constant and that variable and fixed costs behave in a manner consistent with their variable and fixed classifications.