COST BEHAVIOR: ANALYSIS AND USE

COST BEHAVIOR: ANALYSIS AND USE

I. Variations of Cost Behavior Patterns

A. Variable costs can be broken down into those that are:

1. Engineered--are those costs observed when an optimum relationship exists between inputs (costs) and outputs (activity). This relationship has been carefully determined by using work measurement techniques. Examples include wages/time, material/usage.

2. Discretionary--are those costs which fluctuate with activity simply because management has made a decision which in effect permits them to vary. For example: percentage of each sales dollar spent for advertising, units of performance method of depreciation.


B. Fixed costs can be subdivided as:

1. Discretionary--costs arising where management policies are established concerning maximum amounts to be incurred and which have no observable optimum relationship. Examples include: advertising, research and development and company picnic expenditures.

2. Committed--costs arising from the use of plant, equipment and maintaining an organization. Examples include rent, property taxes, straight-line depreciation and salaries of key executives.


There are several methods that can be used to simplify a cost function (behavior pattern):

1. experience, intuition, account analysis.
2. high-low method.
3. scattergraph.
4. engineering method.
5. simple and multiple regression.


Example: A firm observed the following energy costs at various levels of activity over the past 15 months.

Month	Units produced	Energy cost ($)
1	4,500	38,000
2	11,000	52,000
3	12,000	56,000
4	5,500	40,000
5	9,000	47,000
6	10,500	52,000
7	7,500	44,000
8	5,000	41,000
9	11,500	52,000
10	6,000	43,000
11	8,500	48,000
12	10,000	50,000
13	6,500	44,000
14	9,500	48,000
15	8,000	46,000

What is the approximate monthly fixed cost?
What is approximate variable cost per unit?

HIGH-LOW METHOD

VC rate = change in cost / change in activity

VC rate = $18,000 / 7,500

VC rate = $2.40/unit

FC = Total cost - variable cost

FC = $56,000 - (12,000 * $2.40)

FC = $27,200

or

FC = $38,000 - (4,500 * $2.40)

FC = $27,200

TC = VC + FC

High activity: $56,000 = (12,000 * $2.40) + 27,200

Low activity: $38,000 = (4,500 * $2.40) + 27,200

Cost formula: TC = $2.40X + $27,200/month

SCATTERGRAPH

Draw a regression line from the points plotted on the graph—using an observed activity and corresponding cost--10,000 units with a total cost of $50,000.

TC = FC + VC

$50,000 = $30,000 + VC

VC = TC - FC

VC = $50,000 - $30,000

VC = $20,000

VC rate = VC/observed activity

VC rate = $20,000 / 10,000 units

VC rate = $2.00 /unit

Estimated cost at 11,000 units

TC = FC + VC

TC = $30,000 + (11,000 * $2.00)

TC = $30,000 + $22,000

TC = $52,000

Cost formula: TC = $2.00/unit + $30,000/month

LINEAR REGRESSION ANALYSIS

This technique overcomes the subjectivity inherent in the scattergraph by calculating a precise placement for the estimated total cost line; by using a number of past values, it also addresses the 'two-value' weakness of high-low analysis. Regression analysis operates by obtaining the values for fixed cost and variable cost per unit in a math­ematical formula for total cost:

y=a+bx

where	y represents total cost
	a is the fixed element of total cost
	b is the variable cost per unit
	X is the volume of activity.

You should note that `y = a + bx' is the standard mathematical equation for a straight line, with a representing the vertical intercept and b the slope of the line. Based on a number of past total costs (y) and their related volume levels (x), values for the variable cost per unit (b) and fixed cost (a) can be calculated using the following formulae:

b=	nΣxy-ΣxΣy	and	a=	Σy	-	bΣx
	nΣx²-(Σx)²			n		n

n representing the number of past observations being used and I being the mathemat­ical symbol for `sum of'. For convenience, Exhibit 3.3 presents again the previous six years' total production overhead and associated output volumes for KTI Ltd.

KTI Ltd: Production Overhead
KTI Ltd, which produces and sells cheese, has recorded the following production overhead costs and associated volumes of output over the last six years:
	Year	Production overhead (£)	Volume of output (kg)
	19X1	820 000	360 000
	19X2	1 040 000	510 000
	.19X3	720 000	310 000
	19X4	920 000	390 000
	19X5	1 060 000	470 000
	19X6	1 220 000	560 000
In 19X7, it is anticipated that output will be 500 000 kg. It is known that some of the pro­duction overhead costs vary according to the number of kilograms produced, while some (like depreciation of production equipment) are incurred at a fixed amount per annum.
Exhibit 3.3 KTI Ltd production overhead

There are six past costs and volume levels, so here, n= 6. Although the formulae above appear very daunting, a simple tabulation will provide us with the other values we need to enable us to obtain values for a (fixed cost) and b (variable cost per kg). For ease of calculation, all the values for x (output) and y (total production overhead) in the table which follows have been stated in thousands (kg and £).

n		X		y		xy		X2
1		360		820		295,200		129,600
2		510		1,040		530,400		260,100
3		310		720		223,200		96,100
4		390		920		358,800		152,100
5		470		1,060		498,200		220,900
6		560		1,220		683,200		313,600
	Σ	2,600		5,780		2,589,000		1,172,400

Inserting the appropriate values into the formula for b gives:

b	=	nΣxy-ΣxEy
		nΣx²-(Σx)²

	=	6(2589000)-(2600x5780)
		6(1172400)-(2600) ²

	=	15,534,000 – 15,028,000
		7,034,400 – 6,760,000

	=	506 000	1.84 (rounded)
		274 400

In other words, our estimate of the variable overhead per kg is £1.84. This value can now be used to obtain a value for a (the fixed cost):

a	=	Σy	-	bΣx
		N		n

	=	5780	-	(1.84 x2,600)
		6		6

=

963.33

-

797.33

=

166.00

Bearing in mind that the figures for x and y are stated in thousands, our estimate of the fixed production overhead is £166 000. Estimated total production overhead for 19X7 will be:

	£
Fixed element	166 000
Variable element (500 000 kg @£1.84)	920 000
Total cost	1 086 000