Learning Outcomes

  • Understand how constraints affect product mix

Here again, are five basic questions to address as you contemplate segments with regard to the sales mix:

  1. Does the segment have a positive contribution margin?
  2. What happens to fixed costs if we eliminate a segment?
  3. How will dropping a product or segment affect other areas of the business?
  4. What can the company do with freed-up capacity?
  5. What are the qualitative (non-financial) considerations?

The final three questions could be framed in terms of constraints. In other words, other than direct financial considerations, what are the other factors that limit our ability to produce or otherwise affect our sales mix?

The theory of constraints is based on the idea that production or sales of products are limited in some way. There may be a bottleneck in the production process or simply a surplus of products in the market that limits the number of new products a firm can sell.

Constraints can be classified in many ways, but for our purpose here, we’ll group them into the following categories: market, capacity, political, and behavioral.

  • Market constraints generally arise from the laws of supply and demand. The main strategy for eliminating the market constraint to increase demand. This is largely a marketing function, although reducing production costs can also result in some competitive advantage.
  • Capacity constraints occur as a result of insufficient resources to meet the demand of the market. This could be a lack of raw materials, labor, or physical space, but it could also result from logistical problems such as distribution and marketing. In our 3Yachts, Inc. example, the 10,000-foot production facility is a physical constraint. As with most constraints, we can address it by renting a larger facility or outsourcing some of the work.
  • Political constraints generally occur internally, often in marketing, accounting, and/or finance departments, but they can also be higher level. For instance, in our 3Yachts example, the owners may be emotionally attached to the HighLine boats because they are classier and show better than the more basic MidLine and LowLine models.
  • Behavioral constraints are difficult to identify and eliminate but include things like poor management as well as negative decisions of the managers, possibly due to bias or lack of accurate information. For instance, Ford has a long history of making bad marketing decisions. The Ford Mustang was a best-seller in the 60s and 70s but lost favor in the 80s when Ford redesigned it to become the Mustang II. Its current iteration is much more in line with the Mustang of the 70s and is popular enough to be one of the last two autos that Ford is producing. Companies like Harley-Davidson may find that stepping into new territory, as Harley is doing by dropping the Sportster and adding the LiveWire and the Pan America lines, may not pay off as planned unless those decisions were well supported by cost and market analysis.

As you can imagine, the field of constraints is wide and varied, but let’s take a simple example to illustrate how a managerial accountant might adjust the CVP model to accommodate constraints.

Based on contribution margin, the company would prefer to sell more MidLine models, but let’s say there is a market constraint—they are already selling as many of those models as they can. However, in this case, there is excess capacity once the HighLine segment is eliminated.

Let’s go back to our original CVP analysis based on actual results for a prototypical month.

3Yachts, Inc.
Product Mix
CVP Analysis (month)
MidLine HighLine LowLine Total
Subcategory, Assumptions
Sales price per unit $6,500 $11,000 $4,000
Variable cost per unit $4,695 $12,050 $3,180
CM per unit Single Line$1,805Double line Single Line($1,050)Double line Single Line$820Double line
Fixed costs per month $71,667 $15,111 $23,222 $110,000
Sales volume 60 10 20
Subcategory, CVP Model Results MidLine HighLine LowLine Total
Sales $  390,000 $  110,000 $   80,000 $  580,000
Variable costs 281,700 120,500 63,600 465,800
Contribution margin Single Line108,300 Single Line(10,500) Single Line</span”>16,400 Single Line114,200
Fixed costs 71,667 15,111 23,222 110,000
Operating income Single Line$   36,633Double line Single Line$ (25,611)Double line Single Line$  (6,822)Double line Single Line$    4,200Double line


We still want to get rid of the HighLine model, even though the owners might like having it in the lineup (a behavioral constraint). But let’s see what happens if we discover that we can shift production to LowLine and sell a lot more of those. We were producing and selling 20 LowLines per month using 1,000 square feet of space. Once we eliminate the HighLine, we have an additional 4,000 square feet of space we could retool for LowLine production, meaning we could now produce another 80 per month. Let’s say that although we are selling as many MidLines as the market will bear, there is a large, untapped market for more affordable base models, and we can now produce and sell 100 LowLines per month. We keep our sales staff and marketing budget at current levels, so fixed costs do not go down or up. Our new fixed cost allocations look like this:

Production facility usage MidLine HighLine LowLine Total
Square feet       5,000               –       5,000     10,000
Allocation rate 50.00% 0.00% 50.00% 100.00%


SG&A and sales salaries MidLine HighLine LowLine Total
Unit sold             60               –           100           160
Allocation rate 37.50% 0.00% 62.50% 100.00%


Making our fixed cost allocation look like this:

Fixed costs per month MidLine HighLine LowLine Total
Sales Salary $  3,750 $0 $  6,250 $ 10,000
Selling, General, and Administrative 33,750 $0 56,250 90,000
Production Facility Rent 5,000 $0 5,000 10,000
Single Line$ 42,500Double line Single Line$0Double line Single Line$ 67,500Double line Single Line$110,000Double line


And the resulting CVP analysis shows an increased profit:

3Yachts, Inc.
Product Mix
CVP Analysis (month)
MidLine HighLine LowLine Total
Subcategory, Assumptions
Sales price per unit $6,500 $11,000 $4,000
Variable cost per unit $4,695 $12,050 $3,180
CM per unit Single Line$1,805Double line Single Line($1,050)Double line Single Line$820Double line
Fixed costs per month $42,500 $0 $67,500 $110,000
Sales volume 60 100
Subcategory, CVP Model Results
Sales $  390,000 $ 400,000 $  790,000
Variable costs 281,700 318,000 599,700
Contribution margin Single Line108,300 Single Line Single Line</span”>82,000 Single Line190,300
Fixed costs 42,500 67,500 110,000
Operating income Single Line$   65,800Double line Single LineDouble line Single Line$  14,500Double line Single Line$   80,300Double line


We can also demonstrate this using differential analysis, although, for a presentation to the owners and upper management, we might want to use the CVP analysis.

Description Amount Total
Expected decrease in revenue due to elimination of HL $   (110,000)
Expected increase in revenue due to additional sales of LL 320,000
Expected increase in total revenue Single Line $  210,000
Expected decrease in total variable costs due to elimination of HL $     120,500
Expected increase in total variable costs due to additional sales of LL (254,400)
Expected increase in total costs Single Line (133,900)
Expected increase/(decrease) in operating income Single Line$   76,100Double line
Current operating income $    4,200
Expected increase/(decrease) in operating income 76,100
Projected operating income Single Line$   80,300Double line


In terms of constraints, this strategy could signal a dramatic shift in the way the business is viewed by outsiders since the flagship model is being discontinued, and the product line will now be dominated by a low-cost, stripped-down model. A proposal like this could also run afoul of the emotions and beliefs of some owners, who may have invested in this business because of the HighLine model and may not want to be associated with a company that makes cheap boats. In addition, there could be all kinds of unforeseen ramifications of changing the product mix that could affect the bottom line. The numbers won’t tell the whole story, and much of marketing is trial and error supported by good information.

Here is another example of how constraints can be analyzed in making product decisions:

You can view the transcript for “Managerial Accounting 6.5: Using a CM When Faced with Resource Constraints” here (opens in new window).

Applying this method to our original data, we find the following.

Assuming the major constraint is production area:

(1) We divide the units we produce by the square footage used to produce that model and come up with the number of units we are producing a month per square foot.

(2) Units per square foot times the contribution margin per unit gives us a metric called contribution margin of the constraint, which in this case is the contribution margin per square foot of production space.

(3) Contribution margin per square foot for each product line times our total constraint of 10,000 square feet gives us the contribution margin we would realize if we dedicated our entire space to that one line.

MidLine HighLine LowLine
Units produced             60             10             20
Divided by square feet of space       5,000       4,000       1,000
Equals units produced per SF (1)     0.0120     0.0025     0.0200
Times contribution margin/unit $1,805 ($1,050) $820
Equals contribution margin/SF (2) Single Line$    21.66 Single Line$   (2.63) Single Line$    16.40
Times total capacity     10,000     10,000     10,000
Total CM at Capacity (3) Single Line$  216,660Double line Single Line$ (26,300)Double line Single Line$  164,000Double line


This shows us what we had already surmised, that the MidLine product is our most profitable, but we have the market constraint that limits our sales to 60 per month. If we dedicated the entire facility to Midline, we could produce 120 units, which, if we could sell them at $6,500 each, would in fact give us $216,660 in contribution margin and $106,600 in operating income. However, under the scenario we have created, the market can’t absorb another 60 boats per month, and a surplus in the market would drive the price down according to the law of supply and demand.

Thus, as managerial accountants, we have to be able to see both the forest and the trees and to understand the relationships between marketing, economics, accounting, and management.

Now, check your understanding of how constraints can affect the product mix.

Practice Question