Department of Recreation, Park & Tourism Administration
Western Illinois University
RPTA 323 Administration of Leisure Services II
Analysis of Mixed (Semi-Variable) Costs
Mixed costs often need to be broken out into their respective fixed and variable components (e.g., for
forecasting, planning, or budgeting). This can be done using a cost-volume formula:
Y = a + bX
where
Y=
the mixed cost to be broken out
X=
any measure of activity such as direct labor hours, production
volume, etc.
a=
the fixed cost component
b=
the variable cost per unit of X
Two common methods of applying this principle are the (a) high-low-method and (b) regression analysis. We
will look at high-low analysis using the following table.
Table 1: Raw Data
vers. 2013/02
Month
Direct Labor Hours
(X)
Factory Overhead in $
(Y)
January
105
$2,510
February
100
$2,479
March
88
$2,080
April
116
$2,750
May
95
$2,330
June
107
$2,690
July
97
$2,480
August
110
$2,610
September
135
$2,920
October
115
$2,730
November
117
$2,760
December
96
$2,109
1
Hemingway
RPTA 323 Administration of Leisure Services II
Analysis of Mixed (Semi-Variable) Costs
1. Select the highest and the lowest pairs, based on activity level (X).
Table 2: Direct Labor Hours (X) for High and Low Months
Month
Direct Labor Hours
(X)
Factory Overhead in $
(Y)
High
September
135
$2,920
Low
March
88
$2,080
Source: Table 1
2. Compute the variable cost per unit of X, which is b in the cost-volume formula
Variable cost (b) = Difference in the mixed cost Y
_________________________
Difference in activity X
Table 3: Calculate Differences between X and Y for High and Low Months
X (Hours)
Y ($)
High (September)
135
$2,920
Low (March)
88
$2,080
Difference
47
$840
Source: Table 2
Variable cost (b) = 840 / 47 = $17.8723 per hour of direct labor
vers. 2013/02
2
Hemingway
RPTA 323 Administration of Leisure Services II
Analysis of Mixed (Semi-Variable) Costs
3. Compute the fixed cost portion of total mixed costs, which is a in the cost-volume formula
Fixed cost portion (a) = Total mixed cost (X) - Variable cost (b)
Table 4: Compute Fixed Cost Portion of Total Mixed Costs
High
Low
Factory overhead costs (Y)
$2,920.00
$2,080.00
Total variable costs (b)
$2,412.76
$1,572.76
Difference
$507.234
$507.234
Sources: Table 1 for Y, Table 4A for calculation of b
Table 4A: Compute Total Variable Expenses for X in High & Low Months
(b)·(X)
Variable Cost Per
Unit (b)
Hours of Direct
Labor (X)
Total
High
$17.8723
135
$2,412.76
Low
$17.8723
88
$1,572.76
Source: Table 3 for b per unit, Table 1 for X (direct labor hours)
Recall the cost-volume formula (on p. 1): Y = a + bX
Using the results above, our example cost-volume formula for breaking mixed costs into fixed and variable
components becomes:
Y = $507.234 + $17.8723X
where
Y = mixed costs to be broken out
X = total hours of direct labor
$507.234 = fixed cost component of Y
$17.8723 = variable cost per hour of direct labor
Note that the High-Low method of breaking out mixed costs is less accurate than using multiple regression
because it is more affected by extreme values. It is nonetheless useful when working with costs for relatively
short periods, e.g., a year or two.
vers. 2013/02
3