A price change results in a markup change. Whenever a selling price is reduced to a sale price, it has been demonstrated that the amount of the markup decreases (from to ) by the amount of the discount (). This means that some of the products are sold at full markup and some at a partial markup. For businesses, the strategic marking up of a product must factor in the reality that they do not sell every product at the same level of markup. Therefore, if a business must achieve a specified level of markup on its products, it must set its price such that the average of all markups realized equals its markup objective. The average markup that is realized in selling a product at different price points is known as the maintained markup.
To understand the formula, assume a company has 100 units for sale. From past experience, it knows that 90% of the products sell for full price and 10% sell at a sale price because of discounts, damaged goods, and so on. At full price, the product has a markup of $10, and 90 units are sold at this level, equalling a total markup of $900. On sale, the product is discounted $5, resulting in a markup of $5 with 10 units sold, equalling a total markup of $50. The combined total markup is $950. Therefore, the maintained markup is $950 ÷ 100 = $9.50 per unit. If the company’s goal is to achieve a $10 maintained markup, this pricing structure will not accomplish that goal. Formula 1.13 summarizes the calculations involved with maintained markup.
is Maintained Markup: The maintained markup is the average markup in dollars that is realized after factoring in the quantity of units sold and differing levels of markup. In its simplest form, this formula is an applied version of Formula 2.4 on weighted average discussed in Chapter 2.
is Markup Amount: The markup amount represents the amount of markup realized at the regular selling price for the product. If you do not know this amount directly, calculate it using any of the markup formula (Formulas 1.6 through 1.9).
is Full Markup Output: This variable represents the number of units sold at full markup (the regular selling price). It could be an actual or forecasted number of units sold. This variable acts as a weight: If you do not know actual unit information, then you can instead assign a forecasted weight or percentage.
is Partial Markup Output: This variable represents the number of units sold at the reduced markup (the sale price). If you do not know unit information, use a forecasted weight or percentage instead.
is Markdown Amount: The markdown amount represents the amount by which the regular selling price has been reduced to arrive at the sale price. If you do not know this amount directly, calculate it using any of the markdown formulas (Formulas 1.11a, 1.11b, or 1.12).
Formula 1.13 assumes that only one price reduction applies, implying that there is only one regular price and one sale price. In the event that a product has more than one sale price, you can expand the formula to include more terms in the numerator. To expand the formula for each additional sale price required:
- Extend the numerator by adding another , where the always represents the total difference between the selling price and the corresponding sale price and is the quantity of units sold at that level of markup.
- Extend the denominator by adding another as needed.
For example, if you had the regular selling price and two different sale prices, Formula 1.13 appears as:
How It Works
Follow these steps to calculate the maintained markup:
Step 1: Identify information about the merchandising scenario. You must either know markup dollars at each pricing level or identify all merchandising information such as costs, expenses, profits, and markdown information. Additionally, you must know the number of units sold at each price level. If unit information is not available, you will identify a weighting based on percentages.
Step 2: If step 1 already identifies the markup dollars and discount dollars, skip this step. Otherwise, you must use any combination of merchandising formulas (Formulas 1.1 to 1.12) to calculate markup dollars and discount dollars.
Step 3: Calculate maintained markup by applying Formula 1.13.
1. A company’s pricing objective is to maintain a markup of $5. It knows that some of the products sell at regular price and some of the products sell at a sale price. When setting the regular selling price, will the markup amount be more than, equal to, or less than $5?
A grocery store purchases a 10 kg bag of flour for $3.99 and resells it for $8.99. Occasionally the bag of flour is on sale for $6.99. For every 1,000 units sold, 850 are estimated to sell at the regular price and 150 at the sale price. What is the maintained markup on the flour?
You are looking to calculate the maintained markup ().
Step 1: The cost, selling price, and sale price information along with the units sold at each price are known:
Step 2: To calculate markup dollars, apply Formula 1.7, rearranging for . To calculate markdown dollars, apply Formula 1.11b.
Step 3: Calculate maintained markup by applying Formula 1.13.
On average, the grocery store will maintain a $4.70 markup on the flour.
Maplewood Golf Club has set a pricing objective to maintain a markup of $41.50 on all 18-hole golf and cart rentals. The cost of providing the golf and rental is $10. Every day, golfers before 3 p.m. pay full price while “twilight” golfers after 3 p.m. receive a discounted price equalling $30 off. Typically, 25% of the club’s golfers are “twilight” golfers. What regular price and sale price should the club set to meet its pricing objective?
The golf club needs to calculate the regular selling price () and the sale price ().
Step 1: The cost information along with the maintained markup, markdown amount, and weighting of customers in each price category are known:
Reverse steps 2 and 3 since you must solve Formula 1.13 first and use this information to calculate the selling price and sale price.
Step 3: Apply Formula 1.13, rearranging for .
Step 2: Calculate the selling price by applying Formula 1.7.
Calculate the sale price by applying Formula 1.11b, rearranging for .
In order to achieve its pricing objective, Maplewood Golf Club should set a regular price of $59 and a “twilight” sale price of $29.
The section is reproduced from Chapter 4.4 in Fundamentals of Business Mathematics by OER Lab licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License