4.8: Chapter 4 Summary
Formula & Symbol Hub Summary
For this chapter you used the following:
Symbols Used
- [latex]\times 100[/latex] = Percentage multiplier
- [latex]\%C[/latex] = Percent change
- [latex]C[/latex] = Cost
- [latex]CM[/latex] = Unit contribution margin
- [latex]CR[/latex] = Contribution rate
- [latex]d[/latex] = Discount rate or Cash discount rate
- [latex]D\$[/latex] = Discount amount
- [latex]d_1[/latex] = First discount
- [latex]d_2[/latex] = Second discount
- [latex]d_{equiv}[/latex] = Single equivalent discount rate
- [latex]d_n[/latex] = nth discount
- [latex]E[/latex] = Expenses
- [latex]L[/latex] = List price or Invoice amount
- [latex]M\$[/latex] = Markup amount
- [latex]MoC\%[/latex] = Markup on cost percentage
- [latex]MoS\%[/latex] = Markup on selling price Percentage
- [latex]n[/latex] = Level of output / break even output level
- [latex]N[/latex] = Net price or Net payment amount
- [latex]n(CM)[/latex] = Total contribution margin
- [latex]NI[/latex] = Net income
- [latex]n(S)[/latex] = Total revenue
- [latex]P[/latex] = Profit
- [latex]P_{onsale}[/latex] = Planned profit amount
- [latex]P_{red}[/latex] = Reduced profit
- [latex]S[/latex] = Selling price
- [latex]\text{SAvg}[/latex] = Simple Average
- [latex]S_{onsale}[/latex] = Sale price
- [latex]S_{red}[/latex] = Reduced sale price
- [latex]TR[/latex] = Total revenue
- [latex]TFC[/latex] = Total fixed costs
- [latex]TFC+n(VC)[/latex] = Total costs
- [latex]TR[/latex] = Total revenue at Break-even
- [latex]TVC[/latex] = Total variable cost
- [latex]VC[/latex] = Unit variable cost
- [latex]V_\textrm{i}[/latex] = Initial value
- [latex]V_\textrm{f}[/latex] = Final value
Formulas Used
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Formula 2.4a – Simple Average
[latex]\begin{align*}\text{SAvg}=\frac{\sum x}{n}\end{align*}[/latex]
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Formula 3.2a – Percent Change
[latex]\begin{align*}\%C=\frac{V_\textrm{f}-V_\textrm{i}}{V_\textrm{i}}\times 100\end{align*}[/latex]
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Formula 4.1a – Single Discount
[latex]\begin{eqnarray*}N\;=\;L\;\times\;(1\;-\;d)\end{eqnarray*}[/latex]
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Formula 4.1b – Discount Amount
[latex]\begin{eqnarray*}D\$=L\times d\end{eqnarray*}[/latex]
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Formula 4.1c – Discount Amount
[latex]\begin{eqnarray*}D\$=L-N\end{eqnarray*}[/latex]
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Formula 4.1d – Multiple Discounts
[latex]\begin{eqnarray*}N=L\times(1-d_1)\times(1-d_2)\times...\times(1-d_n)\end{eqnarray*}[/latex]
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Formula 4.1e – Single Equivalent Discount
[latex]\begin{eqnarray*}d_{equiv}=1-(1-d_1)\times(1-d_2)\times...\times(1-d_n)\end{eqnarray*}[/latex]
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Formula 4.2a – Single Discount Rearranged
[latex]\begin{eqnarray*}L=\frac{N}{(1-d)}\end{eqnarray*}[/latex]
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Formula 4.2b – Single Discount
[latex]\begin{eqnarray*}N=L\times (1-d)\end{eqnarray*}[/latex]
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Formula 4.3a – The Selling Price of a Product
[latex]\begin{eqnarray*}S=C+E+P\end{eqnarray*}[/latex]
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Formula 4.3b – Markup Amount
[latex]\begin{eqnarray*}M\$=E+P\end{eqnarray*}[/latex]
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Formula 4.3c – Selling Price Using Markup
[latex]\begin{eqnarray*}S=C+M\$\end{eqnarray*}[/latex]
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Formula 4.3d – Markup on Cost Percentage
[latex]\begin{eqnarray*}MoC\%=\frac{M\$}{C}\times 100\end{eqnarray*}[/latex]
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Formula 4.3e – Markup on Selling Price Percentage
[latex]\begin{eqnarray*}MoS\%=\frac{M\$}{S}\times 100\end{eqnarray*}[/latex]
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Formula 4.4a – The Sale Price of a Product
[latex]\begin{eqnarray*}S_{onsale}&=&S\times (1-d)\end{eqnarray*}[/latex]
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Formula 4.4b – Markdown Amount
[latex]\begin{eqnarray*}D\$&=&S\times d\end{eqnarray*}[/latex]
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Formula 4.4c – Markdown Amount
[latex]\begin{eqnarray*}D\$&=&S-S_{onsale}\end{eqnarray*}[/latex]
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Formula 4.4d – Markdown Percentage
[latex]\begin{eqnarray*}d&=&\frac{D\$}{S}\times 100\end{eqnarray*}[/latex]
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Formula 4.4e – The Selling Price of a Product Adapted
[latex]S_{onsale}=C+E+P_{onsale}[/latex]
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Formula 4.5a – Reduced Profit
[latex]\begin{eqnarray*}P_{red}=S_{red}–C-E\end{eqnarray*}[/latex]
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Formula 4.5b – Reduced Profit
[latex]\begin{eqnarray*}P_{red}=P-E\end{eqnarray*}[/latex]
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Formula 4.6a – Unit Variable Cost:
[latex]\begin{eqnarray*}VC=\frac{TVC}{n}\end{eqnarray*}[/latex]
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Formula 4.6b – Net Income Using a Total Revenue and Cost Approach
[latex]\begin{eqnarray*}NI&=&n(S)-(TFC+n(VC))\end{eqnarray*}[/latex]
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Formula 4.6c – Unit Contribution Formula
[latex]\begin{eqnarray*}CM&=&S-VC\end{eqnarray*}[/latex]
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Formula 4.6d – Net Income Using Total Contribution Margin Approach Formula
[latex]\begin{eqnarray*}NI&=&n(CM)-TFC\end{eqnarray*}[/latex]
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Formula 4.6e – Contribution Rates Formula
[latex]\text{Contribution Rate if Unit Information Is Known:}[/latex]
[latex]\begin{eqnarray*}CR&=&\frac{CM}{S}\times 100\end{eqnarray*}[/latex]
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Formula 4.6f – Contribution Rate if Aggregate Information Is Known
[latex]\begin{eqnarray*}CR&=&\frac{TR-TVC}{TR}\times 100\end{eqnarray*}[/latex]
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Formula 4.7a – Unit Break-Even
[latex]\begin{eqnarray*}n&=&\frac{TFC}{CM}\end{eqnarray*}[/latex]
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Formula 4.7b – Dollar Break-Even
[latex]\begin{eqnarray*}TR&=&\frac{TFC}{CR}\end{eqnarray*}[/latex]
Key Concepts Summary
Section 4.1: 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
Section 4.2: Invoicing: Terms of Payment and Cash Discounts (Make Sure You Bill Them)
- How invoicing works: understanding invoice terms and invoice dating
- The calculations involved when a full payment amount is made
- The calculations involved when a partial payment amount is made
- The calculations involved when a late payment amount is made
Section 4.3: 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
Section 4.4: 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
Section 4.5: 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
Section 4.6: Cost-Revenue-Net Income Analysis (Need to Be in the Know)
- The three different types of costs
- How to determine the unit variable cost
- Calculating net income when you know total revenue and total cost
- Calculating net income when you know the contribution margin
- Comparing varying contribution margins by calculating a contribution rate
- Integrating all of the concepts together
Section 4.7: Break-Even Analysis (Sink or Swim)
- Explanation of break-even analysis
- How to calculate the break-even point expressed in the level of output
- How to calculate the break-even point expressed in total revenue dollars
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 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.
credit period The number of interest-free days from the date of commencement before full payment of the invoice is required.
date of commencement The first day from which the invoice terms extend forward in time and from which all due dates are established.
discount A reduction in the price of a product.
discount period The number of days from the date of commencement for which a cash discount is offered.
end-of-month invoice dating A term of payment where the date of commencement is the last day of the same month as indicated by the invoice date.
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.
ordinary invoice dating A term of payment where the date of commencement is the same date as the invoice date.
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.
receipt-of-goods invoice dating A term of payment where the date of commencement is the day on which the customer physically receives the goods.
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.
Technology
Calculator
The following calculator functions were introduced in this chapter:
Markup on Selling Price Percentage
[latex]2^{\text{nd}}\;\text{Profit}[/latex] 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:
[latex]\text{CST}[/latex] = The cost of the item
[latex]\text{SEL}[/latex] = The selling price of the item
[latex]\text{MAR}[/latex] = The markup on selling price percentage (in [latex]\%[/latex] format)
Press [latex]\text{CPT}[/latex] on the unknown (when it is on the screen display) to compute.
Attribution
“Chapter 5, 6 & 7 Summary” from Business Math: A Step-by-Step Handbook (2021B) by J. Olivier and Lyryx Learning Inc. through a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License unless otherwise noted.
