6.S: Summary
- Page ID
- 22101
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Key Concepts Summary
6.1: Figuring Out the Cost: Discounts (How Much?)
- The relationship between distribution and pricing
- Some of the types of discounts available to businesses and consumers
- How to calculate the net price when only one discount is involved
- How to calculate the net price when multiple discounts are involved
- Converting multiple discounts into single discounts
6.2: Markup: Setting the Regular Price (Need to Stay in Business)
- The three components that compose a selling price
- Calculating the markup in dollars and the relationship to pricing components
- Calculating the markup as a percentage under two different approaches
- Determining the price point where all costs are paid but no profits are earned—the break-even point
6.3: Markdown: Setting the Sale Price (Everybody Loves a Sale)
- How to take a regular selling price and make it into a sale price by applying markdowns
- How to plan the merchandising of products that are always on sale
6.4: Merchandising (How Does It All Come Together?)
- Combining discounts, markup, and markdown into complete merchandising situations
- Calculating the maintained markup when a product was sold at both a regular selling price and a sale price
- How coupons and mail-in rebates impact product pricing
The Language of Business Mathematics
- cost
-
An outlay of money required to produce, acquire, or maintain a product, which includes both physical goods and services.
- coupon
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A promotion that entitles a consumer to receive certain benefits, usually in the form of a reduction of the selling price for a product.
- coupon handling expense
-
A handling charge that is paid to channel members for redeeming a coupon.
- coupon marketing expense
-
The expense associated with creating, distributing, and redeeming a coupon.
- coupon redemption expense
-
The face value price reduction offered by a coupon.
- discount
-
A reduction in the price of a product.
- expenses
-
A business’s financial outlays incurred in the selling of a product.
- list price
-
A price for a product that has been published or advertised in some way.
- loyalty discount
-
A discount given from a seller to a purchaser for repeat business.
- mail-in rebate
-
A refund that occurs after a product has been purchased.
- maintained markup
-
The average level of markup that is maintained across all units sold at various price levels including the selling price and the sale price(s).
- manufacturer's suggested retail price (MSRP)
-
A recommended product retail price that a manufacturer sets for a retailer based on market research.
- markdown
-
A reduction from the regular selling price of a product resulting in a new lower sale price.
- marketing price adjustment
-
Any marketing activity executed by a member of the distribution channel for the purposes of altering a product’s price.
- markup
-
The process of taking a product’s cost and increasing it by a certain amount to arrive at a selling price.
- markup amount
-
The dollar amount of the expenses and profit combined together into a single number; it represents the difference between the price and cost in dollars.
- markup on cost percentage
-
The markup dollars expressed as a rate using cost as the base.
- markup on selling price percentage
-
The markup dollars expressed as a rate using the regular selling price as the base.
- net price
-
The price of the product after a discount is removed from the list price.
- profit
-
The amount of money that remains after a business pays all of its costs and expenses.
- quantity discount
-
A discount for purchasing larger quantities of a certain product.
- rebate marketing expense
-
The expense associated with creating, distributing, and redeeming a rebate.
- rebate redemption expense
-
The face value amount that a consumer will receive as a refund if a submitted rebate fulfills all rebate conditions.
- sale discount
-
A temporary discount lowering the price from a product’s regular selling price.
- sale price
-
A price for a product after a markdown that is lower than its regular selling price.
- seasonal discount
-
A discount offered to consumers and businesses for purchasing products out of season.
- single equivalent discount
-
A single discount rate that is equal to a series of multiple rate discounts.
- trade discount
-
A discount offered to businesses only based on the type of business and its location in the distribution system.
The Formulas You Need to Know
Symbols Used
\(C\) = cost
\(d\) = discount rate or markdown rate
\(d_1, d_2, ... d_n\) = multiple discount rates, where the subscript represents each discount up to a count of n discounts
\(D\$\) = discount amount or markdown amount
\(E\) = expenses
\(L\) = list price
\(M\$\) = markup amount
\(MM\) = maintained markup
\(MoC\%\) = markup on cost percentage
\(MoS\%\) = markup on selling price percentage
\(n\) = number of pieces of data, which in this chapter is the level of output
\(N\) = net price
\(P\) = profit
\(P_{onsale}\) = planned profit amount when a product is sold at the sale price
\(S\) = regular selling price
\(S_{BE}\) = the selling price at the break-even point
\(S_{onsale}\) = sale price
Formulas Introduced
Formula 6.1 Single Discount: \(N=L \times(1-d)\)
Formula 6.2a Discount Amount: \(D\$=L \times d\)
Formula 6.2b Discount Amount: \(D\$=L-N\)
Formula 6.3 Multiple Discounts: \(N=L \times\left(1-d_{1}\right) \times\left(1-d_{2}\right) \times \ldots \times\left(1-d_{n}\right)\)
Formula 6.4 Single Equivalent Discount: \(d_{equiv}=1-\left(1-d_{1}\right) \times\left(1-d_{2}\right) \times \ldots \times\left(1-d_{n}\right)\)
Markup Formulas
Formula 6.5 The Selling Price of a Product: \(S=C+E+P\)
Formula 6.6 Markup Amount: \(M\$=E+P\)
Formula 6.7 The Selling Price of a Product Using the Markup Amount: \(S=C+M\$\)
Formula 6.8 Markup on Cost Percentage: \(MoC \%=\dfrac{M\$}{C} \times 100\)
Formula 6.9 Markup on Selling Price Percentage: \(MoS \%=\dfrac{M\$}{S} \times 100\)
Formula 6.13 Maintained Markup: \(MM=\dfrac{M\$\left(n_{1}\right)+(M\$-D \$)\left(n_{2}\right)}{n_{1}+n_{2}}\)
Markdown Formulas
Formula 6.10 The Sale Price of a Product: \(S_{onsale}=S \times(1-d)\)
Formula 6.11a Markdown Amount: \(D\$=S \times d\)
Formula 6.11b Markdown Amount: \(D\$=S-S_{onsale}\)
Formula 6.12 Markdown Percentage: \(d=\dfrac{D\$}{S} \times 100\)
Technology
Calculator
The following calculator functions were introduced in this chapter:
Markup on Selling Price Percentage
\(2^{nd}\) Profit to access this feature.
Enter two of the three variables by pressing Enter after each input and using and ¯ to scroll through the display. The variables are:
\(\mathrm{CST}= \text{ The cost of the item}\)
\(\mathrm{SEL}= \text{ The selling price of the item}\)
MAR = The markup on selling price percentage (in % format)
Press CPT on the unknown (when it is on the screen display) to compute.