### Valuation Tutor Lesson: Cost Volume Profit (CVP) Analysis

Overview

Cost Volume Profit is an important managerial and financial analyst tool for understanding the operating risk faced by a firm.  Suppose management and analysts want to answer the following types of questions:

How much does each \$ of sales revenue contribute to the bottom line on average?

How sensitive is the bottom line (i.e., corporate P&L) to a downturn in sales from recession?

How can management and analysts assess the expected return from a company’s sales and marketing investing strategy?

You can answer these types of questions and more, from a Cost Volume Profit analysis.

The starting point is to first evaluate cost behavior in terms of the following simple equation:

Total Cost (TC) = Variable Cost per Unit of Activity (VC) * Activity + Fixed Costs (FC)   1)

The above is useful for both assessing profitability as well as assessing risk.  For example, this linear function underlies standard activity analysis where profit and loss is projected for different levels of activity.  For example, an analyst needs to forecast future earnings and can approach this problem by applying standard CVP analysis or as it is also referred to “Activity Analysis.”  This is because from an outsider’s perspective the natural choice of “activity” is Sales Revenue.  Furthermore, if sales revenue growth can be predicted and cost behavior can be estimated, an analyst can forecast earnings.  Given the increased importance of “Earnings Season” in the capital markets this tool assumes additional importance.

Important Aside

The above equation assumes that the scale of operations remain unchanged which is usually not the case for a growing firm as revealed from their investing activities (measured in the cash flow statement).  When this is the case then an additional adjustment is required to “FC” in equation 1) to account for the increased level of investing activities resulting in increased Fixed Costs (FC) when projecting future earnings.

Implementing Cost Volume Profit Analysis

For CVP analysis we need to estimate the % of each cost category that is variable.  That is, if \$100 is COGS what is the % variable and what is the % fixed?

Equation 1) does not answer this second question.  Assuming the unit of activity is \$ sales revenue then VC is a % of Sales Revenue but not a % of the cost category.  To compute the % of the cost category we apply the following transformation:

% Variable Cost for a specific Category = (VC*Sales/Cost Category)*100                2)

Applying CVP Analysis

In this lesson we will assume that Sales Revenue is the unit of activity.

Step 1:  Estimating the Variable Cost per \$ of Sales Revenue

There are three main approaches to assessing cost behavior.  These approaches are:

Account Analysis and Professional Judgment

High-Low Cost Method

Regression Analysis

In practice an analyst will employ all three techniques.

Step 2:  Transform the estimate into a relative % for each cost category.

Account Analysis and Professional Judgment

First, Account Analysis is always the starting place.  Here understanding the business model and the relative makeup f the balance sheet is important.  For example, COGS for a retailer is going to have a large variable proportion to it even if you know some fixed costs are allocated to COGS.  The simple reason being the higher the turnover the larger the dominance the variable cost drivers will be in COGS.  As a result, for a retailer it is not unusual to assume between 90-100% variable.  Similarly, for business that does not have a large amount of fixed assets on their balance sheet.

For example, contrast the latest Balance Sheets for Microsoft and Intel (using Valuation Tutor’s data collector and plotting abilities):

It is immediately clear that Property Plant and Equipment is of far more importance to Intel’s business model than it is to Microsoft.
As a result, estimating the % of cost of goods sold that is variable usually require going beyond the professional judgment approach.
Estimating Cost Behavior Relative to Sales for COGS
The easiest technique to apply is the High/Low method.  This will give a reasonable estimate.  For the case of Intel, by examining two recent 10-K’s and using the data collector, we can collect four or five past observations:

In the above example, we have collected all cost categories down to Operating Income for Intel from their 2012 10-K and their 2010 10-K.

Note: for some firms you may need to work with their 10-Q’s.

By double clicking on any line item in the LHS of the screen automatically transmits to the RHS so it is easy to work across statements.  When done click on Copy All (Button RHS of screen), Paste into Excel and Clean Up to get:

Operating expenses is the sum of Research and development, Marketing, general and administration, Restructuring and Amortizations.

Hi Lo Method

This method uses observations on two dates to estimate fixed costs and the variable cost per dollar of sales revenue.  The Y-Axis variable is the aggregate cost category and the X-axis variable is the volume of activity (sales revenue for a financial analyst).

Variable Cost Per \$ Sales Revenue   = (Total Costs High Sales Revenue – Total Costs Low Sales Revenue)/(Sales Revenue High – Sales Revenue Low)

Working with the above Intel Data the Hi/Lo method reveals:

That is, the Variable Cost per \$ of Sales for Intel’s Cost of Sales equals 0.1157.

Question:  What is the cost behavior equation?

The beauty of the hi/lo technique is that you can solve for FC from by substituting in one of the two points:

Total Cost (TC) = Variable Cost per Unit of Activity (VC) * Activity + Fixed Costs (FC)

53,999 = 0.1157*20,242 + FC => FC = 13,994.

Regression Analysis:

One advantage of running a simple regression is that we now use all observations not just the high and the low.  Running regression we get a little higher estimate for the Variable Cost per Dollar of Sales at: 0.185 and a lower fixed cost estimate of \$9496.

In both cases this is well below the case for a retailer or a software company.

Working with the regression analysis then the % variable costs for COGS is 18.5% and 81.5% fixed.

Results from Cost Behavior Analysis:

Columns 2 and 3 contain the results from Hi/Lo for all cost categories and columns 4 and 5 the regression analysis.  Columns 2 and 4 contain the estimate of the variable cost per dollar of sales and columns 3 and 5 the implied Fixed Costs from the analysis.

Observation 1:  When the implied fixed costs are negative this is consistent with the model being miss-specified and so it is clear that this happens less with the regression analysis versus the Hi/Lo the former which processes more information to arrive at the estimate.  In practice an analyst will combine their professional judgment with statistical techniques such as regression analysis to arrive at their final estimates for cost behavior.

A second important point, especially when working across firms, is to impose some standard cost categories upon the analysis.  In Valuation Tutor these cost categories are:  COGS, Sales, Marketing and Administration and Other.  So for Intel our estimates for these three categories are:

Other is based upon on Research and Development which dominates this category for Intel.  Given the projected proportion is greater than one we will apply this as 100% variable and 0% fixed.  This is consistent with the fact that Research and Development is budgeted as a percent of sales.

The relationship between the 2nd and 3rd columns above is that column 2 comes directly from the Total Cost Equation that can be estimated from regression analysis or applying the hi/low method to estimate the straight line.  That is, column 2 is expressed relative to the level of activity (i.e., % of sales).  Column 3 is the coefficient transformed to re-express the variable cost component relative to the cost category directly as opposed to being a % of Sales.  The relationship between the two columns are:

Variable/Total Costs = Proportion of the costs relative to \$1 Revenue * (Sales Revenue/Total Costs for the Cost Category (e.g., COGS)).

0.4939 = 0.1851*(53,999/20,242)

In other words, the proportion of variable costs to the total cost category will be higher than variable cost per \$ of sales estimated from a traditional regression analysis.

It is noted that the inputs into Valuation Tutor are in the form of the third column, the proportion of variable to the total costs in each category.  This is because although a user may estimate this from a regression it is also common to do this by employing account identification/professional judgment.

Working with the Above Assessments:  Variable versus Full Costing Income Statements

In the screen shot below the Valuation Tutor calculator is provided for Intel.  Two income statement formats are provided.

The two formats differ as follows, in relation to Net Income from Operations (Illustrated for INTC in millions for year ending Dec 31, 2011):

Absorption Costing:
Sales (53,999)
Less COGS (20,242)
Gross Margin (33,757)
Less Other (8610)
Net Income from Operations (17,477)

Now given our earlier estimates for the proportion of variable costs for each expense line item provided earlier:
Other is based upon on Research and Development which dominates this category for Intel.  Given the projected proportion is greater than one we will apply this as 100% variable and 0% fixed.  This is consistent with the fact that Research and Development is budgeted as a percent of sales.
The relationship between the 2nd and 3rd columns above is that column 2 comes directly from the Total Cost Equation that can be estimated from regression analysis or applying the hi/low method to estimate the straight line.  That is, column 2 is expressed relative to the level of activity (i.e., % of sales).  Column 3 is the coefficient transformed to re-express the variable cost component relative to the cost category directly as opposed to being a % of Sales.  The relationship between the two columns are:
Variable/Total Costs = Proportion of the costs relative to \$1 Revenue * (Sales Revenue/Total Costs for the Cost Category (e.g., COGS)).
0.4939 = 0.1851*(53,999/20,242)
In other words, the proportion of variable costs to the total cost category will be higher than variable cost per \$ of sales estimated from a traditional regression analysis.
It is noted that the inputs into Valuation Tutor are in the form of the third column, the proportion of variable to the total costs in each category.  This is because although a user may estimate this from a regression it is also common to do this by employing account identification/professional judgment.
Working with the Above Assessments:  Variable versus Full Costing Income Statements
In the screen shot below the Valuation Tutor calculator is provided for Intel.  Two income statement formats are provided.
The two formats differ as follows, in relation to Net Income from Operations (Illustrated for INTC in millions for year ending Dec 31, 2011):
Absorption Costing:
Sales (53,999)
Less COGS (20,242)
Gross Margin (33,757)
Less Other (8610)
Net Income from Operations (17,477)
Now given our earlier estimates for the proportion of variable costs for each expense line item provided earlier:

What are the immediate advantages from recasting the above in this way?

The immediate answers to this are summarized as follows.  A user can immediately pull off the following set of performance measures:

Contribution Margin Ratio = Contribution Margin/Sales Revenue
Contribution Margin Ratio = (Sales Revenue – Total Variable Costs)/Sales Revenue
Break Even (B/E) Analysis (\$Sales Revenue)  = Total Fixed Costs/(Contribution Margin Ratio)
Break Even (B/E) Margin = B/E \$Sales Revenue/\$Sales Revenue

For Intel these are:

In a later lesson you will learn how to apply this type of analysis to perform a full activity analysis on Intel.
Conclusions
Cost Volume Profit is an important managerial and financial analyst tool for understanding the operating risk faced by a firm.  Some of the important questions answered from this analysis are:
How much does each \$ of sales revenue contribute to the bottom line on average?
How sensitive is the bottom line (i.e., corporate P&L) to a downturn in sales from recession?
Alternatively,
What is the current Margin of Safety?  Is this improving or deteriorating?
When we connected the dots across financial statements in an earlier lesson the potential importance of investing in sales and marketing became apparent.
How can management and analysts assess a company’s sales and marketing investing strategy?
Here again CVP analysis provides powerful insights to be gained into these types of questions.  For example, if the company spends \$x on a marketing campaign that is expected to increase sales revenue by y% what type of return is this likely to generate and does this return cover the initial investment cost of the marketing campaign?
The answer to this question requires performing a cost versus benefit analysis where the expected benefit is measured from the contribution margin associated with the projected increase in sales.