Evaluating Product Differentiation Strategies Via Multiple Product CVP
Analysis: A Graphical Approach
David Marcinko, Skidmore College
Saurav Dutta, University at Albany, SUNY
The Graphical Model
.
• Sales mix is a critical strategic variable.
Breakeven Achieved by Selling Only Product Y = Fixed Cost
CMY
A One Unit Reduction in Sales of Product Y
Causes Total Contribution Margin to Fall by $250
.
• Multiproduct CVP analysis becomes basic to strategy development
Challenges to Teaching Multiproduct CVP Analysis
0
Product X
Breakeven Can Be Maintained by Substituting Product X
for Product Y in the Proportions 2X – to – 1Y
The Set of Breakeven Points All Lie on a Line With Slope (– 1/2 )
(The Rate of Product Substitution = The Ratio of The Unit Contribution Margins)
This Line of Breakeven Points has the Equation
Y = (Fixed Cost ÷ Unit CMY) – (Unit CMX ÷ Unit CMY) X
Locus of All Breakeven Points
Product Y
0
An Illustrative Example
Product X
• The Sales Mix Can Be Added to the Model As a Ray From the Origin.
• The Slope of the Ray Reflects the Sales Mix
• If 2 Units of Y Are Sold to Each Unit of X, the Ray Will Have Slope = 2
• The Ray Has the Equation Y = kX, Where k = the Sales Mix Proportions
Line Reflecting Chosen Sales Mix
Locus of All Breakeven Points
0
0
Product X
X*
The (X*,Y*) coordinates of the solution may be found by
Solving the following two equation system:
Y = (Fixed Cost ÷ Unit CMY) – (Unit CMX ÷ Unit CMY) X
Y = kX
Using the parameters of the example, the equation system
becomes:
Y = 400 - 1/2X
Y = 2X
The solution (X = 160, Y = 320) is easily obtained through
successive substitution..
Sensitivity Analysis to a Change in Sales Mix
A firm sells two products, X and Y, under the following conditions
• Product X: Price = $225; Unit Variable Cost = $100; CMX = $125
• Product Y: Price = $550; Unit Variable Cost = $300; CMY = $250
• Fixed Cost = $100,000
• Sales Mix: 2 units of Product Y to each unit of Product X
Breakeven Solution
Locus of All Breakeven Points
Advantages of a Graphical Teaching Approach
• Nature of the problem can be more easily visualized.
• Underlying economic concepts are more evident.
• Analytical tools used are familiar to the student.
• Breakeven solutions can be obtained without resorting to the
use of a “weighted average contribution margin.”
• Sensitivity analysis is facilitated –students can more easily
experiment with strategic variations in sales mix.
Line Reflecting Chosen Sales Mix
Y*
The Lost Contribution Margin, and Breakeven Can
Be Restored by Selling Two Units of Product X
Each of Which Has a Contribution Margin of $125
Product Y
• Minimal text coverage.
• Strategic importance of sales mix is understated due to
computational difficulties.
• Solution algorithms feature cumbersome constructions such as
“weighted average contribution margin” or “product bundles.”
• These constructions offer little economic or strategic intuition.
• Sensitivity analysis to explore strategic options is hindered by
laborious computations.
Solving the Model for Breakeven Quantities
Product Y
Product Y
Business Strategy, Product Mix, and Multiproduct CVP Analysis
• A product differentiation strategy may require a diverse
mix of products and services. See: “Tiffany and Co.”,
Edward D. Hess, Darden Business Publishing.
Raef Lawson, Institute of Management Accountants
Product X
Should the desired sales mix change to Y = 3X, the new
breakeven solution can be obtained without resorting to
the cumbersome computation of a new “weighted average
contribution margin.” We simply solve the new system:
Y = 400 - 1/2X
Y = 3X
To obtain (X = 115, Y=343)*
*difference in sales mix due to rounding
Limitations
• Graphical analysis limited to two products.
• Generalization to n products requires background in basic linear
algebra.