MAS 3 Cost Behavior and Relevant Range PDF

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Cost Behavior and Relevant Range Relevant Range defines the limits within which per-unit variable costs remain constant and fixed costs are not changeable. It is synonymous with the short run. It is established by the efficiency of a company’s current manufacturing plant, its agreements with labor unions and suppliers, etc.

Variable Costs Variable Costs are a direct function of production volume. They increase when production grows and decrease when production shrinks. Raw materials and labor directly involved with production shrinks are common variable costs. Variable Costs Per Unit remains constant in the short run regardless of the level of production.

Variable Costs in Total, on the other hand, vary directly and proportionally with changes in volume.

Variable cost behavior can be summarized as follows:

Fixed Costs Fixed Costs remain constant regardless of production. Examples of fixed costs include rent, interest, insurance, and lease payments.

Fixed Costs in total remain unchanged in the short run regardless of production level, e.g., the amount paid for an assembly line is the same even if production is halted entirely.

Fixed cost per unit, on the other hand, varies indirectly with the activity level.

EXAMPLE: Payon Company manufactures umbrellas. Each umbrella requires a canopy that costs ₱10. Payon Company also pays ₱75,000 per month to rent its small workstation at Net Park, BGC. The capacity of the workstation is 1,500 umbrellas per month. The total cost of canopies and cost per unit of rent at various levels of activity would be:

Payon Company’s Total Variable and Fixed Cost in the graph

Payon Company’s Variable and Fixed Cost per Unit in the graph

Mixed (Semivariable) Costs Mixed (semivariable) costs combine fixed and variable elements, e.g., rental expense on a car that carriers a flat fee per month plus an additional fee for each mile driven.

EXAMPLE: The Mercenary Guild rents a piece of machinery to make it guild system more efficient. The rental is ₱150,000 per year plus ₱10 for every unit produced.

The Analysis of Mixed Costs Account Analysis and Engineering Approach 1. Account Analysis. Each account under consideration is classified as variable or fixed based on the analyst’s prior knowledge about how costs behave. This approach is limited in value in the sense that it glosses over the fact that some accounts may have both fixed and variable components. 2. The engineering approach classifies costs based upon an industrial engineer’s evaluation of production methods, material specifications, labor requirements, equipment usage, power consumption, and so on. This approach is particularly useful when no past experience is available concerning activity and costs. Scattergraph Method As the first step in the analysis of a mixed cost, cost and activity should be plotted on a scattergraph. This helps to quickly diagnose the nature of the relation between cost and activity. EXAMPLE: New Eden Garden Florists has maintained records of the number of orders and billing costs in each quarter over the past several years.

The relation between the number of orders and the billing cost is approximately linear. (A straight line that seems to reflect this basic relation was drawn with a ruler on the scattergraph.) Because a straight line seems to be a reasonable fit to the data, we can proceed to estimate the variable and fixed elements of the cost using one of the following methods. 1. The quick-and-dirty method based on the line in the scattergraph. 2. High-low method. 3. Least-squares regression method. The Quick-and-Dirty Method (The Scattergraph Plot) The straight line drawn on the scattergraph can be used to make a quick-and-dirty estimate of the fixed and variable elements of billing costs. Recall that we are trying to estimate the fixed cost, a, and the variable cost per unit, b, in the linear equation Y= a + bX. The vertical intercept, approximately ₱30,000 in this case, is a rough estimate of the fixed cost. The slope of the straight line is an estimate of the variable cost per unit. Select a point falling on the line (in this case 2,000 orders):

Variable cost per unit = ₱18,000 ÷ 2,000 orders = ₱9 per order. Therefore, the cost formula for billing costs is ₱30,000 per quarter plus ₱9 per order or:

Y = 30,000 + 9X, where X is the number of orders. This method of estimating fixed and variable costs is seldom used in practice because of its imprecision. Nevertheless, it is always a good idea to plot the data on a scattergraph before using the more precise high-low or least-squares regression methods. High-Low Method This method can be used to analyze mixed costs if a scattergraph plot reveals a linear relationship between the X and Y variables. The first step in applying the high-low method is to isolate the variable portion of the cost. Variable portion is computed using the difference in cost between the highest and lowest level of activity for a group of periods is divided by the difference in the cost drivers (activity level) at the two levels.

The fixed portion can now be calculated by inserting the appropriate values for either the high or low period in the portion Fixed portion = Total cost - variable portion Fixed portion = Total cost - (Highest or lowest activity level x computed variable cost per unit) EXAMPLE: Novigrad Company has incurred the following shipping costs over the past eight months:

The cost formula for shipping cost is: Y = 40,000 + 5X

The high-low method suffers from two major defects: 1. It throws away all but two data points. 2. The periods with the highest and lowest volumes are often unusual. Least-Squares Regression Method This method can be used to analyze mixed costs if a scattergraph plot reveals an approximately linear relationship between the X and Y variables. This method uses all of the data points to estimate the fixed and variable cost components of a mixed cost. This method is superior to the scattergraph plot method that relies upon only one data point and the high-low method that uses only two data points to estimate the fixed and variable cost components of a mixed cost.

The basic goal of this method is to fit a straight line to the data that minimizes the sum of the squared errors. The regression errors are the vertical deviations from the data points to the regression line. The least-squares regression method for analyzing mixed costs uses mathematical formulas to determine the regression line that minimizes the sum of the squared “errors.”

Least Square Regression Formula Y = a + bX

Where: X=T  he level of activity (independent variable) Y = The total mixed cost (dependent variable) a= T  he total fixed cost (the vertical intercept of the line) b= T  he variable cost per unit of activity (the slope of the line) n= N  umber of observations ∑=S  um across all n o  bservations

EXAMPLE: Fenrir Hospital operates a cafeteria for employees. Management would like to know how cafeteria costs are affected by the number of meals served.

Statistical software or a spreadsheet program can do the computations required by the least-squares method. The results in this case are:

The fixed cost is therefore ₱2,433 per month and the variable cost is ₱1.68 per meal served, or: Y = ₱2,433 + ₱1.68X, where X is meals served. R2 is a measure of the goodness of fit of the regression line. In this case, it indicates that 99% of the variation in cafeteria costs is due to the number of meals served. This suggests an excellent fit. The R2 (Coefficient of determination) quantifies the percentage of the variation in the dependent variable that is explained by variation in the independent variable. The R2 varies from 0% to 100%, and the higher the percentage the better.

Nonlinear Cost Functions Fixed cost per unit is an example of a nonlinear-cost function. Note that fixed cost per unit has an asymptotic character with respect to the x-axis, approaching it closely while never intersecting it (it does intersect the y-axis at the zero level of activity). The function shows a high degree of variability over its range taken as a whole. Another type of nonlinear-cost function is a step-cost function, one that is constant over small ranges of output but increases by steps (discrete amounts) as level of activity increases.

Both fixed and variable costs can display step-cost characteristics. If the steps are relatively narrow, these costs are usually treated as variable. If the steps are wide, they are more akin to fixed costs. An example of a step cost would be the salary of production foreman. Operating at one shift per day might require one foreman, while two shifts would require two foremen....