Markup

The process of selling goods for a profit

Lesson Overview

Goals

Students will be able to calculate Markup when expressed in both amount , percentage of cost , and percentage of selling price.

Students will be able to calculate single step and multiple step Markdown problems.

DisplayTable[data_List,opts:OptionsPattern[]]:=Labeled[Grid[data,FilterRules[{opts},Options[Grid]],Frame->All,ItemSize->14,Alignment->Center,BaseStyle->{FontFamily->"Helvetica"},Background->LightYellow,Frame->All,Spacings->{2,0.62}],Style[OptionValue[TableLabel],FontFamily->"Times"]]

Instructor Presentation

Markup

Business expenses can be grouped into two categories: Those expenses related to the acquisition/manufacture of their products and those expenses not related to the acquisition of the products.  The cost of buying products to be resold is one example of the first type of expense.  Others expenses that fall into this category are:

costs of subparts, assembled into one sellable item.

labor used to combine subpart or complete the selling product.

Sales and Marketing expenses

electricity used to complete the selling product.

In order for a business to stay in business, they must cover all of these costs.  Since the costs associated with acquisition/manufacture of their products is a relatively easy amount to quantify, many industries use the simple concept of Markup to price their products to cover all costs and make a small profit.

Markup is calculated in several ways.   If the Markup is expressed as an amount, we use:

Cost (C) + Dollar amount of Markup (M) = Selling Price (S)

If the Markup is expressed as a percent of costs, we use:

( 1 + percentage of Markup ) x Cost (C) = Selling Price (S)

If the Markup is expressed as a percent of selling price, we use:

((Cost (C))/((1-percentage of Markup))) = Selling Price (S)

In business you will find all three of these techniques used, based on the situation being analyzed and the company preferences.

Graphically the relationship between Cost, Markup and Selling Price can be represented like:

cost=Graphics[{FaceForm[Pink],EdgeForm[Directive[Dashed,Thick,Blue]],Polygon[{{0,0},{0,2},{1,2},{1,0}}],Text["Cost",{.5,1}]}];
markup=Graphics[{FaceForm[LightBlue],EdgeForm[Directive[Dashed,Thick,Blue]],Polygon[{{0,2},{1,2},{1,3.5},{0,3.5}}],Text["Markup",{.5,2.75}]}];
sellingprice=Graphics[{FaceForm[Green],EdgeForm[Directive[Dashed,Thick,Blue]],Polygon[{{1.2,0},{2.2,0},{2.2,3.5},{1.2,3.5}}],Text["Selling Price",{1.7,1.75}]}];
Show[{cost,markup,sellingprice}]

Notes

Markup using a standard amount provides a simple model for covering selling expenses and ensuring some money remains for profit.  Markup using a standard amount can detrimental to sales when used with products with varying prices.  Products with lower prices get penalized with a proportionally larger markup fee.  In practice, Markup by Amount using a standard amount is usually adopted using multiple markup tiers based on the relative cost of the product.

Markup using a percentage of cost provides a pricing model for covering selling expenses is equitable across multiple price levels.  Markup using a percentage of cost is much harder to compute and manage. When using this method, forecasting of product mix sales levels become critical if a company is to cover their costs and create a profit.

Concept Exploration

Markup expressed in amount

When products are sold, they typically are sold in quantities of more than one unit.  In cases that sales are made in multiple quantities, the formula for calculating selling price is :

Quantity (Qty) * (Cost (C) + Dollar amount of Markup (M)) = Selling Price (S)

Demonstration 1: Move the sliders for Cost and Markup to see how they interact.

Manipulate[Plot[{x c,x (c+mu)},{x,0,100},AxesOrigin->{0,0},Filling->{1->{Bottom,{Yellow,Orange}}},Filling->{1->{{2},Yellow}},PlotRange->{0,3000},AxesLabel->{"Qty","$"}],{{c,5,"Cost ($ - in Orange)"},1,20},{{mu,3,"Markup ($ - in white)"},1,10}]

💡  Markup as a constant dollar amount is applied on top of any cost.  The purple line represents the selling price.

When moving the Cost and Markup sliders the plotted lines seem to pivot around the origin.  Why is this?

Examples

Example 1:  Applying markup when expressed as a fixed amount

Cost (C) + Dollar amount of Markup (M) = Selling Price (S)

Complete the following table:

markup={{$2450,$800,\[Placeholder]},{"$1.57","$0.50",\[Placeholder]},{$100,\[Placeholder],$170},{\[Placeholder],$200,$500}};
fulldata=Prepend[markup,{"Cost","Markup(M)","Selling Price"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Example 2

Often products are sold through multiple sales channels with each sale agent adding a markup.  A good example would be Cola.  The Cola company sells its product to a distributor (who buys in LARGE quantities).  In turn the distributor sells is to the local grocery store (who buys in smaller quantities). Each company in the sale channel needs to cover their expenses, so they add a markup.The formula for this type of channel is:

Cost (C) + (Subscript[Markup, 1]) ((Subscript[M, 1])) +  (Subscript[Markup, 2]) ((Subscript[M, 2])) = Selling Price (S)

Complete the following table:

markup={{"$50","$20","$30",\[Placeholder]},{"$1.57","$0.50","$0.75",\[Placeholder]},{"$100",\[Placeholder],"$50","$270"},{\[Placeholder],"$200","$100","$700"}};
fulldata=Prepend[markup,{"Cost","(Subscript[Markup, 1])((Subscript[M, 1]))","(Subscript[Markup, 2])((Subscript[M, 2]))","Selling Price"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Concept Exploration

Markup expressed as Percent Markup on Cost

When markup is figured as a percent of cost, the rate of markup is called the Percent Markup On Cost.  This is by far the most common method of calculating Markup.

When we are given the Cost and the Percent Markup On Cost (% Markup On Cost), the computation is very straightforward.

Cost (C) + ( Cost (C) * Percent Markup On Cost (M) )  = Selling Price (S)

Lets look at a quick example:

If a National Electronics Store purchases television sets for $250 each and has a markup policy of 40 % Markup On Cost.  What will the television set be listed for sale at?

According to the formula provided, the Selling Price is equal to the Cost + (Cost * Percent Markup On Cost).  We know from above the Cost is $250 and we are also given that the Percent Markup On Cost is .40.   Simple Algebra helps solve this.

Cost (C) + ( Cost (C) * Percent Markup On Cost (M) )  = Selling Price (S) 
250 + ( 250 * .40) = Selling Price (S)
250 + 100 = Selling Price (S)
350 = Selling Price

Remembering our units are  $.  The Selling Price (S) is $350 for each television set.

Concept Exploration (cont)

Markup expressed as Percent Markup on Cost

Let's look at the formula again:

Cost (C) + ( Cost (C) * Percent Markup On Cost (M) )  = Selling Price (S)

So exploring this and introducing the concept of quantity (qty), we find the following:

Quantity (Qty) * (Cost (C) + ( Cost (C) * Percent Markup On Cost (M) )) = Selling Price (S)

Demonstration 2: Move the sliders for Cost and Markup to see how they interact.

Manipulate[Plot[{x c,(x (c mu)+x c)},{x,0,100},AxesOrigin->{0,0},Filling->{1->{Bottom,{Yellow,Red}}},Filling->{1->{{2},Yellow}},PlotRange->{0,3000},AxesLabel->{"Qty","$"}],{{c,5,"Cost ($ - in Red)"},1,20},{{mu,.4,"Markup (as % - in white)"},.1,.7}]

💡  Percent Markup On Cost is advantageous for pricing products that vary greatly in their cost.  Due to using a percent of cost for the markup, the selling price for small cost items and larger cost items are in relative proportion to their costs.  This is not the case with when Markup as a fixed amount is used.

Examples

Example 3:  Applying markup when expressed as a Percent Markup On Cost

Cost (C) + ( Cost (C) * Percent Markup On Cost (M) )  = Selling Price (S) 
or
((Selling Price (S))/(1+Percent Markup On Cost (M)))  =  Cost (C)

Complete the following table:

markup={{"$2,450","30%",\[Placeholder]},{"$1.57","55%",\[Placeholder]},{"$100",\[Placeholder],"$170"},{\[Placeholder],"66.66%","$500"}};
fulldata=Prepend[markup,{"Cost","Markup(%)","Selling Price"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Example 4:

Often products are sold through multiple sales channels with each sale agent adding a markup.  A good example would be Pepsi.  PepsiCo sells its product to a distributor (who buys in LARGE quantities).  In turn the distributor sells is to the local grocery store (who buys in smaller quantities). Each person in the sale channel need to cover expenses, so they add a markup.  The formula for this type of channel when using Percent Markup On Cost is:

[ Cost (C) * ( 1 +  Percent Markup On Cost ((Subscript[%, 1])) ) ] * ( 1+Percent Markup On Cost ((Subscript[%, 2]))  )  = Selling Price (S)
or
((Selling Price (S))/(( 1 + Percent Markup On Cost ((Subscript[M, 1])) ) * ( 1 + Percent Markup On Cost ((Subscript[M, 2])) )))  =  Cost (C)

Complete the following table:

markup={{"$50","20","30",\[Placeholder]},{"$1.57","50","75",\[Placeholder]},{"$100","40",\[Placeholder],"$270"},{\[Placeholder],"50","100","$700"}};
fulldata=Prepend[markup,{"Cost","(Subscript[Markup, 1])((Subscript[%, 1]))","(Subscript[Markup, 2])((Subscript[%, 2]))","Selling Price"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Concept Exploration

Markup expressed as Percent Markup On Selling Price

When markup is figured as a percent of Selling Price, the rate of markup is called the Percent Markup On Selling Price.

In real world situations, often a company knows what price their competitors are selling a product for (Selling Price).  Since competition establishes Selling Price, the company's principle activity is to determine whether they can get the product at a low enough price to cover their costs (and make a bit of profit).  The Percent Markup On Selling Price is used to establish this threshold .

Cost (C) + ( Percent Markup On Selling Price(M) * Selling Price (S) )  =  Selling Price (S) 
or
 Selling Price (S) - ( Percent Markup On Selling Price(M) * Selling Price (S) ) = Cost (C)

But first, lets look at an example:

All over town, IPODs are selling for $150.  In order to attract a younger crowd, Jerry's Novelty is thinking of adding the IPOD to their sales inventory.   Jerry's needs to have a 50% Markup On Selling Price to break even.  What is the most that Jerry's should buy IPOD's for?  If Jerry's cost for an IPOD is $89, should he offer IPODs for sale?

According to the formula provided, the 
Cost (C) must be less than or equal to the Selling Price (S) - ( Percent Markup On Selling Price(M) * Selling Price (S) ).  
We know from above the Selling Price (S) is $150 and we are also given that the Percent Markup On Selling Price is .50.   Simple Algebra helps solve this.

Selling Price (S) - ( Percent Markup On Selling Price(M) * Selling Price (S) ) ≥ Cost (C)  
150 - ( 150 * .50) ≥ Cost (C)
150 - 75 ≥ Cost (C)
75 ≥ Cost (C)

Remembering our units are  $.  The Cost (C) must be no more than $ 75  per IPOD.

Should Jerry sell IPODs if his cost is $ 89?

Concept Exploration (cont'd)

Markup expressed as percent of Selling Price

Lets look at the formula again:

Selling Price (S) - ( Percent Markup On Selling Price(M) * Selling Price (S) ) = Cost (C)

So exploring this and introducing the concept of quantity (qty), we find the following:

Quantity (Qty) * ( Selling Price (S) - ( Percent Markup On Selling Price(M) * Selling Price (S) )) = Cost (C)

Demonstration 3: Move the sliders for Cost and Markup to see how they interact.

Manipulate[Plot[{x s,(x (s-(s mu)))},{x,0,100},AxesOrigin->{0,0},Filling->{2->{Bottom,{Yellow,Green}}},Filling->{1->{{2},Yellow}},PlotRange->{0,3000},AxesLabel->{"Qty","$"}],{{s,15,"Selling Price ($ - Purple Line)"},5,30},{{mu,.4,"Markup (as % of Selling Price - in white)"},.1,.7}]

💡  In the above interactive demonstration, the cost of the product is found as the hypotenuse of the green triangle .  Therefore, if one is looking to decide to purchase a product for resale, the cost must be found within the green triangle in order for the reseller to make any money.

Examples

Example 5:  Applying markup when expressed as a Percent Markup On Selling Price

Selling Price(S) - ( Percent Markup On Selling Price(M) * Selling Price (S) ) = Cost (C) 
or
Selling Price(S)  = ((Cost (C))/((1-Percent Markup On Selling Price (M))))

Complete the following table:

markup={{"$2,450","30%",\[Placeholder]},{"$1.57","55%",\[Placeholder]},{"$170",\[Placeholder],"$100"},{\[Placeholder],"66.66%","$500"}};
fulldata=Prepend[markup,{"Selling Price","Markup(M)","Cost"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Example 6:  Take a look at Demonstrations 1, 2 & 3.  Outside of the colors, why do these demonstrations look so similar?

Examples Answer Key

Example 1

Cost (C) + Dollar amount of Markup (M) = Selling Price (S)

markup={{"$2,450","$800","$3,240"},{"$1.57","$0.50","$2.07"},{"$100","$70","$170"},{"$300","$200","$500"}};
fulldata=Prepend[markup,{"Cost","Markup($)","Selling Price"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Example 2

Cost (C) + (Subscript[Markup, 1]) ((Subscript[M, 1])) +  (Subscript[Markup, 2]) ((Subscript[M, 2])) = Selling Price (S)

markup={{"$50","$20","$30","$100"},{"$1.57","$0.50","$0.75","$2.83"},{"$100","$120","$50","$270"},{"$400","$200","$100","$700"}};
fulldata=Prepend[markup,{"Cost","(Subscript[Markup, 1])((Subscript[M, 1]))","(Subscript[Markup, 2])((Subscript[M, 2]))","Selling Price"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Examples Answer Key

Example 3:  Applying markup when expressed as a Percent Markup On Cost

Cost (C) + ( Cost (C) * Percent Markup On Cost (M) )  = Selling Price (S) 
or
((Selling Price (S))/(1+Percent Markup On Cost (M)))  =  Cost (C)

Complete the following table:

markup={{"$2,450","30%","$3,185"},{"$1.57","55%","$2.43"},{"$100","70%","$170"},{"$300","66.66%","$500"}};
fulldata=Prepend[markup,{"Cost","Markup(%)","Selling Price"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Example 4:

Often products are sold through multiple sales channels with each sale agent adding a markup.  A good example would be Pepsi.  PepsiCo sells its product to a distributor (who buys in LARGE quantities).  In turn the distributor sells is to the local grocery store (who buys in smaller quantities). Each person in the sale channel need to cover expenses, so they add a markup.  The formula for this type of channel when using Percent Markup On Cost is:

[ Cost (C) * ( 1 +  Percent Markup On Cost ((Subscript[%, 1])) ) ] * ( 1+Percent Markup On Cost ((Subscript[%, 2]))  )  = Selling Price (S)
or
((Selling Price (S))/(( 1 + Percent Markup On Cost ((Subscript[M, 1])) ) * ( 1 + Percent Markup On Cost ((Subscript[M, 2])) )))  =  Cost (C)

Complete the following table:

markup={{"$50","20","30","$78"},{"$1.57","50","75","$4.12"},{"$100","40","93","$270"},{"$233.33","50","100","$700"}};
fulldata=Prepend[markup,{"Cost","(Subscript[Markup, 1])((Subscript[%, 1]))","(Subscript[Markup, 2])((Subscript[%, 2]))","Selling Price"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amounts",ItemSize->13]

Examples Answer Key

Example 5:  Applying markup when expressed as a Percent Markup of Selling Price

Selling Price(S) - ( Percent Markup On Selling Price(M) * Selling Price (S) ) = Cost (C) 
or
Selling Price(S)  = ((Cost (C))/((1-Percent Markup On Selling Price (M))))

Complete the following table:

markup={{"$2,450","30%","$1,715"},{"$1.57","55%","$0.71"},{"$170","58.8%","$100"},{"$1,499.70","66.66%","$500"}};
fulldata=Prepend[markup,{"Selling Price","Markup(M)","Cost"}];
DisplayTable[fulldata,TableLabel->"Fill in the Missing Amount",ItemSize->13]

Example 6:  Take a look at Demonstrations 1, 2 & 3.  Outside of the colors, why do these demonstrations look so similar?

No matter what technique is used to calculate the appropriate amount of Markup, there will always be an amount of Markup that is added to the Cost to equal the Selling Price, as depicted in the graphic below.

cost=Graphics[{FaceForm[Pink],EdgeForm[Directive[Dashed,Thick,Blue]],Polygon[{{0,0},{0,2},{1,2},{1,0}}],Text["Cost",{.5,1}]}];
markup=Graphics[{FaceForm[LightBlue],EdgeForm[Directive[Dashed,Thick,Blue]],Polygon[{{0,2},{1,2},{1,3.5},{0,3.5}}],Text["Markup",{.5,2.75}]}];
sellingprice=Graphics[{FaceForm[Green],EdgeForm[Directive[Dashed,Thick,Blue]],Polygon[{{1.2,0},{2.2,0},{2.2,3.5},{1.2,3.5}}],Text["Selling Price",{1.7,1.75}]}];
Show[{cost,markup,sellingprice}]