The Portable MBA in Finance and Accounting, 3rd Edition

Cost-Volume -Profit Analysis 119

For the example and data set in Exhibit 3.12, the steps would be as
follows:

1. High and low points=September sales or $23.75 million and July sales of
   $11.5 million.


2. Historical costs for each point=$25,000 (September) and $13,000 (July).


3. Slope=Rise/Run=($25,000−13,000)/($23,750−$11,500)=98%.


4. Fixed component: Total Cost=Variable Cost+Fixed Cost.
   For high data points:

For low data points:

This method has two weaknesses. First, the high and low data points chosen
are assumed to ref lect the pattern of all data points. Often, however, either or
both of these points may not be such, and the analysis is f lawed.^10 The second
weakness is an extension of the first. We had 12 data points but chose to ana-
lyze only two of them, ignoring the other 10. This method is data inefficient; if
you have 12 data points, all 12 should be considered for the analysis.
The third databased technique is called regression analysis.Here a func-
tion is fit through all data points in a manner that minimizes the total squared
error between each data point and the fitted line. The mathematics underlying
this technique are beyond the scope of this chapter, but the method is widely
used and preferred when the data set has problems such as a stepped fixed cost
or variable costs based on multiple factors. All spreadsheet software packages
have a function that performs simple regression analysis.^11 Exhibit 3.14 is an
example of what the output would look like for a least-squares regression analy-
sis using Excel. The estimate for the fixed cost is $2.73 million, and the vari-
able cost is 90% per sales dollar. The adjusted R^2 of 98% means that 98% of
the variance of the Total Cost data is explained by this equation. The drawback
of this analysis is that it is not intuitive. One must trust the output from the sta-
tistical package. If the user does not understand the statistical technique and
the assumptions of the software package, the output is often f lawed.^12 This ap-
proach needs a sound grounding in statistical analysis.
In summary, for the data set being analyzed, the three databased tech-
niques yield results that vary considerably (see Exhibit 3.15). The key to
correctly using databased techniques, however, is not choosing the right tech-
nique but beginning with a data set that truly ref lects the cost structure being

$, %($, )

$, %($, )

$.

13 000 98 11 500

13 000 98 11 500

1 725

=+

=−

=

Fixed Cost

Fixed Cost

million (rounded)

$, %($, )

$, %($, )

$.

25 000 98 23 750

25 000 98 23 750

1 725

=+

=−

=

Fixed Cost

Fixed Cost

million (rounded)