There are a multitude of principles used in business, some are industry specific, others are functions of business.  But there is one that is a general principle that is used across the board in all areas of business.  It is called the ‘Substitution Principle’.  It works just like the substitution principle in math that we all learned about in algebra.  I can’t believe I’m saying this, but my ole adage in high school of ‘How is algebra going to help me as an adult in the real world?’ keeps coming back to haunt me.  This is a perfect example.

In algebra, the principle is straight forward – if two things are equal, it doesn’t matter which one we use.  Remember the algebra expression of 2x + 4?  Well if X = 4 then the expression via the substitution principle is 2(4) + 4 = 12.  Well in business it works the same way.  If I have a variable (remember the variable in the expression is X) and I substitute this with something different I should get a different result.

So, let’s use a simple example.  You own a retail store that sells pencils.  I didn’t know this, but there are over 150 pencil manufacturers.  So instead of purchasing your pencils from United for 3.3 cents each, you buy them from U.S. Pencil Co. for 3.28 cents each.  You literally buy 2 million pencils per month.  Let’s make some assumptions, first the quality of the pencils are the same.  Secondly, the length and lead duration is exactly the same.  The only difference is the purchase price.  So the question is, what is the price differential in cost savings by switching?

Answer – 2 million United Company pencils cost \$66,000, 2 million U.S. Pencil Co. pencils cost \$65,600.  The differential is a savings of \$400.

I know; you are saying to yourself, well, this is easy to understand, I get it; what is next?  Actually it is a bit more complicated than this.  You see, the problem is that many businessmen improperly use this substitution principle.  It is often misapplied or not fully determined because there are a lot of variables involved.  In my math equation above, it was straight forward 2x + 4.  In business you need to fully grasp the latitude in applying this principle to any given situation.  To do this properly, you must first consider all the variables.  Secondly, determine the single variable that has the greatest impact upon the result.  Finally, determine the gains and the losses and net them together.  The answer may surprise you.  The following sections educate you in how to exercise the substitution principle in business.

# Consider all the Variables

Hey, do you remember having a Coke back when they used pure cane sugar in the formula?  You know they use high fructose corn syrup today?  Why did they substitute cane sugar with corn syrup?  Well, simple economics is the answer.  By 1984, cane sugar had reached a price of 5 cents per pound.  High Fructose Corn Syrup was significantly less expensive and the food processors had generated a formula for use in making the soda syrup.  So both Coke and Pepsi switched over to high fructose corn syrup.  The cost savings were enormous and sales increased in the soda industry.

Well, I could taste the difference.  Now today, many consumers are concerned about the ability of the body to absorb high fructose corn syrup.  Different studies prove humans process sugar differently than high fructose corn syrup.  Actually, the human body does digest sugar and only partially digests high fructose corn syrup.  So getting back to my gains and losses analysis in evaluating the substitution principle; what were the gains and losses for Coke?

Well the gain was easy, lower costs and over large volumes of production huge savings were acquired.  The losses, well maybe some loyalty, some trust from the public, a lack of true leadership and so on.  But there is no doubt, the gains outweighed the losses.  In my research, I did discover that there is a Texas bottler that uses pure cane sugar.  Now I need to find me one of those bottles and get a throwback in time.

I would imagine at the time Coke was considering this change, several folks sat around the table and discussed these various issues.  The resounding economic gain was too much to ignore and thus the change.  Well, in the small business world, you have to do the exact same thing.  Look at all the variables.  Well, how do you do that?  Let’s take a look:

The best tool to use in identifying all the variables is brainstorming.  Get a group of employees together that are familiar with the particular item or subject and just sit down for a few minutes and identify all the different issues related to any substitution.  If the substitution is a product base as in the Coke example above, then everyone should be concerned about the consumer’s take on the change.  Does it affect quality, endurance, perception or trust?  If we are talking about process, does this affect the product?  Can it affect the employees in any way?  Does it change safety?  What about volume or do we need to change the storage facility because of more production.  Can it impact the raw resources in some way?

If you are talking about a change to the people aspect, well don’t involve them directly but confide in your human resources department and the professionals you work with.  Again, just as in the product issues and the process, can a substitution affect moral of the remaining staff?

Brainstorming is the best tool to use if you desire to grasp all of the variables.  There are others such as charting which is the process of laying out the variable and identifying the various connections to functions.  As an example, suppose you wanted to replace a particular position in the corporate structure.  First gain an understanding of the work environmentThen pull that position profile to see the respective duties and responsibilities.  Now create a chart the partitions these respective functions and list your possible variables.  Refine the list by identifying possible parallel duties from other staff members and narrow the list to those variables most likely impacted by this change.

# Identify the Most Critical Variable

Here, the goal is to isolate the most critical variable.  Just as in brainstorming or charting, take one variable at a time and identify possible issues and subjective outcomes related to a change in that variable.  Allow me to illustrate using a personnel issue.

The Perfect Employee

In a small grocery store operation, the manager has an employee that is perfect.  Never talks back, always on time, appearance is immaculate and this employee is versatile.  The employee can manage the customer service counter, has the highest volume per hour at the cash register, receives several complimentary comments from customers per day, can stock more cases per hour than any other employee and even knows how to fix the forklift in the warehouse.  The manager wishes he had 20 of these employees; he would have the perfect store.

So the manager decides to apply the substitution principle to maximize the value of this single employee.  To do this, he has identified three distinct variables related to this employee.  They are: customer service, cashiering and stocking shelves.  The forklift issue is just a once in a while function and it will not matter how he utilizes this employee; he’ll still be able to fix the forklift.  So to determine the maximum value attributable to this employee, the manager decides to isolate each variable one at time.  So here is the process:

Stocking Shelves – a good employee can stock around 28 cases of items per hour of work. In a typical 8 hour shift the store needs an employee to handle at least 200 cases of food, get them unboxed and placed on the shelf oriented correctly.  This particular employee is able to handle 265 cases in a typical eight hour shift.  Therefore the employee is worth 1.325 standard employees.  Effectively, the employee is saving around one full employee per three days of work.  However, the manager pays this particular employee about 10% more than other stock clerks.  Therefore, this employee is really worth close to one employee day per week related to stocking shelves.

Cashiering – In general, the employee is only used as a cashier whenever the store’s customer volume peaks and the manager opens up more registers to reduce the wait time. This employee is able to process customers through the register at a rate this is about 25% greater than the average cashier.  But at the same time, he is paying this employee about 20% more than what is paid to other cashiers.  So the overall value is not as great as initially evaluated.

Customer Service – this is the one area of any grocery or department store environment that makes or breaks your business. Typically, customers are returning unused items or the item is damaged.  The customer service representative has to address several issues; in this store the customer service counter does the following:

• Returns
• Complaints
• Manages the Cigarettes
• Takes Payments for Utilities (Verizon & Local Power Company)
• Issues Money Orders

This particular employee has a knack for dealing with complex issues and can easily use the technology available to expedite the customer encounter.  There are only about three employees in the store that have these skills and this employee is only used as a backup for this aspect of operations.

From reading the variable breakouts above, the answer is quite obvious.  This particular employee is best utilized in the customer service department.  The other areas can be easily substituted with new employees but the customer service counter is clearly much more difficult and requires an attentive employee to maximize the value to the store.

Although the above example illustrated a subjective outcome that was relatively easy to discern, most of the time the critical variable will require some mathematical equation to determine the answer.  In business, you have to not only look at the gain from the change, but also the loss associated with the change.  In the above example, sure it would be nice to have the employee stocking shelves but the reality is value.  As a customer service representative, this employee can easily cover associated wages just in processing returns correctly.  Overall, the losses are in the stocking function and in cashiering, but the gains in customer service well offset the losses.

Not all substitutions will be this easy to evaluate, some can get a little bit more frustrating.

# Calculate the Gains and Losses

This is the third step in determining the outcome associated with substitution.  In the first two steps, the goal is to identify the most critical variable and by substituting determine the overall value change.  I’m sure most of you are wondering what I mean when I refer to the losses element.  I always like to refer to sports to illustrate the gains and losses associated with substitution.  So I’ll use two different sports so I can cover as many folks as possible:

Baseball – In the American League, the manager is allowed to substitute the pitching on the offensive side of the game.  Typically, most pitchers, actually pretty much all pitchers are horrible in the box when it is time to bat.  Most can barely manage batting over .100 as an average, so most teams find a really great hitter to substitute for the pitcher.  With this pitcher in the line-up, the team’s batting average is .260.  If the team drops him out and substitutes with a .320 hitter, what is the new team batting average?  Simple, first let’s figure out the team’s new average by first calculating the loss associated with the elimination of the pitcher’s average.  For the sake of this situation, I’m going to assume that everybody in the 9 man line-up bats the same number of times.  This means that the other eight players if they have the same batting average bat around .280.  To get the overall average, we take the eight players times .280 and then add .100 and divide this total by nine.  The group of eight at .280 times 8 equals 2.24.  Now let’s add in the pitcher’s average of .100.  So now the nine players total 2.34.  Let’s divide that 2.34 by 9 and we get an average of .260.  So the loss to the team is actually 2.24 divide by 9 players as now our pitcher can no longer bat but his slot is still open and he is automatic out as if he batted zero.  Now the new average is .2489 (2.24 total divided by 9).  So the loss is .0111 (.260 average before and .2489 after setting the pitcher to zero).

Now for the gain, let’s substitute in our .320 hitter into the lineup to fill the void left by the pitcher.  The new batting average is the original 2.24 for the eight players plus the .360 for a team total of 2.60.  Then divide this by 9 players at the plate.  So now the new team batting average is .2889.  To determine the gain, this batter’s average of .360 is divided by 9 (for the nine spots at the plate) for a gain of .04.  Our total gain is .04, our total loss is .0111 and when we add these together we get .0289 (.04-.0111).  Now we take the net gain and add this to the team average of .260 and we get a new team batting average of .2889 (.260 plus .0289).

This is exactly how professional teams address substitution in team play.  Just to give you an idea, this marginal increase in batting average means about 1 more hit per nine inning game.  In baseball, this is pretty significant in getting a win.

Racing – In NASCAR the key to victory is power.  Most of the time, these cars have more than 600 horsepower under the hood.  Imagine the value of an additional two or three horsepower (substituting a larger fuel injector over the existing fuel injector).  The cost associated with this increase is always additional fuel consumption.   Each car has the exact same size fuel cell (tank).  In this sport, the gain is the additional marginal speed; the loss is more fuel consumption.  Fuel consumption means having to possible pit one more time in a race to have enough fuel to make it to the end.  Racing is all about the amount of time it takes to accumulate the 500 miles for the race.  So the formula is gain of time saved to race 500 miles with additional speed less the cost in time to pit for the additional fuel.

Now it is actually a lot more complicated than this due to the normal process of having free opportunities to pit associated with wrecks and debris on the track (yellow flag conditions).  So often the cost to pit one additional time is moot.  Usually the engineers concern themselves with issues such as additional heat or force on the tires associated with the additional horsepower.  But the idea is to illustrate to you the give and take associated with substitution.

Both of these examples are economic application of this substitution principle.  As an owner of a business, you have to do the exact same thing when using the substitution principle in your daily work.  In the three areas of business, people, processes and product you have to look at the different types of gains and losses.

People – the most common substitution application I’ve seen is the application of the value associated with management.  Typically this is done with business valuations and the substituting of an owner manager situation.  Usually owners pay themselves more than the typically manager doing the same job.  It is absolutely normal.  There is nothing illegal or immoral about this.  In retail the owner manages the store while also running the business.  He typically pays himself significantly more compensation in order to account for these other responsibilities.  In exercising the formula, the owner simply substitutes the value for the position and calculates the savings to the bottom line.  As an example, I had an owner/manager that was paying herself \$83,000 per year for a job that she knew she could hire a qualified individual to do the exact same service for \$58,000 per year.  The netted value is \$25,000 plus the tax and insurance savings.  The final value change was actually \$27,085 (matching Social Security taxes, matching Medicare taxes, savings in worker’s compensation insurance).  So when it came to time to evaluate the business for a possible sale, the analysis used the substitution principle and the \$27,085 was added to the bottom line for the(business valuation formula).

Processes – in analyzing processes, the most common factors to evaluate are changes in time or in unit count per unit of measurement (typically time).  A good example is running a fast food restaurant and throughput is the primary focus.  If you exercise the substitution principle, can you achieve higher volume with the same personnel or do you have to increase the personnel side which means additional costs (losses).  Sometimes it is this simple.  You can increase the volume of served customers but at a higher cost of wages.  So the question becomes, does the contribution margin associated with additional volume offset the additional labor costs?

Product – with product based substitution, the key is typically the increase in sales or the decrease in costs.  In almost all cases, it is both combined.  The gain is usually sales driven and the cost is material changes and both are netted to the gross margin. Most of the time, the substitution principle is applied against a raw material change such changing the quality of the ingredients in the food industry or substituting a lower grade material for parts of an item.

Always ask yourself, what are the losses associated with the substitution and then what are the gains?  Please be sure to evaluate both perspectives as sometimes the losses far outweigh the value change associated with the gains.

# Summary – Substitution Principle in Business

The substitution principle is used frequently in business for a multitude of applications.  The primary reason for its application is to continuously improve the business.  It is one of the more generic principles used just about everywhere.  The key is to identify all the variables related to the substitution, define the most critical variable and then calculate both gains and losses associated with the change in value.  The principle is applied in areas of personnel, production and with the core product or service provided to the customer.  Remember, the substitution principle is simply the substitution of one variable to determine the value change.  The most common result is a financial measurement via the financial statements.  Act on Knowledge.

If you have any comments or questions, e-mail me at dave (insert the usual ‘at’ symbol) businessecon.org.  I would love to hear from you.   If interested in my help as an accountant or consultant, contact me through the ‘My Services’ page in the footer.