Basic Quantitative Questions on Setting and Changing Prices
Ted Mitchell Jan. 2013
There are three basic approaches to calculating a selling price:
1. Cost-Based Pricing
2. Competitive-Based Pricing
3. Customer Demand-Based Pricing
The introductory marketing class must ensure that students know the most basic of the equations for each of the three approaches. The following questions assume that the students have high school algebra. Students will have been exposed to the following definitions in lectures and chapter leading up to Pricing chapters. Students need to know the following definitions (D1-D11) before they can do the pricing questions that follow:
D1) Revenue, R, is equal to Price per unit, P, times Quantity sold, R = PQ.
D2) Cost of Goods Sold, COGS, is equal to the variable cost per unit sold, V, times the quantity of units sold, Q, COGS = VQ.
D3) Gross profit, G, equals the total sales revenue, R = PQ, minus the total cost of goods sold, COGS = VQ,
G = R – COGS
G = PQ - VQ
D4) Profit per unit sold, (P-V), is the difference between the selling price per unit, P, and the variable cost per unit sold, V.
D5) Net profit, Z, equals the Revenue, R, minus the cost of goods sold, COGS, minus the fixed costs, F, for the period,
Z = R – COGS – F
D6 The basic profit equation is
Z = Revenue – Cost of Goods Sold – Fixed Costs
Z = PQ – VQ – F
Z = PQ – VQ – AD – CP – SF -DP
where
Z = Profit and Breakeven Profit is Z = 0
P = Selling price per unit
Q = Quantity of Units Sold
V = Variable cost per unit
F = Fixed cost per period = (AD + CP + SF + DP)
AD = Advertising Expense for the period
CP = Consumer Promotion Expense for the period
SF = Sales Force Expense for the period
DP = Dealer Promotion Expense for the period
The basic profit equation is crucial to the interpretation of the operating statement and making decisions in the simulation game.
D6) The definition of the Gross Return on Sales, GROS, is the ratio equal to the gross profit, G, divided by the sales revenue, R, such that
GROS = G/R.
The GROS percentage is often held to be a measure of the firm’s efficiency at converting sales revenue into gross profits.
D7) The functional form of the gross return on sales is
Gross profit = GROS x (Revenue)
It reminds us that both amount of revenue generated and the GROS determine the amount of gross profit earned in a period.
D8) The definition of markup on price, Mp, is a simplified version of the gross return on sales. Markup on price is the ratio of the profit per unit sold, (P-V), divided by the selling price per unit, P.
Mp = (P-V)/P
The Markup on Price percentage is often held as measure of the firm’s efficiency at converting the revenue per unit, P, into profit per unit, P-V.
D9) The functional form of the markup on price ratio is
(P-V) = Mp x Price
It reminds us that the amount of profit per unit generated is dependent on both the markup percentage and the selling price.
D10) The definition of Net Return on Sales, ROS, is the ratio of the net profit, Z, divided by the sales revenue, R, such that
ROS = Z/R
The Return on Sales percentage is often held as the firm’s efficiency at converting sales revenues into net profits.
D11) The functional form of the net return on sales is
Z = ROS x (Revenue)
and reminds us that amount of net profit generated is determined by both the firm’s conversion efficiency and the amount of revenue earned in a period.
Basic Price Setting Calculations
In the Principles of Marketing course, there are no cheat sheets, help notes or formula lists allowed into the examination room. Students must know the following formulae or how to derive them.
1) Cost-based Pricing: Determining the Breakeven Price, BEP.
Your sales of Q = 200,00 units in the Home Market has the following costs:
Advertising AD = $1,500,000
Consumer Promotion CP = $600,000
Sales Force SF = $320,000
Dealer Promotion DP = $180,000
Variable Cost per Unit V = $30
What is the selling price per unit , BEP, that is necessary to breakeven on the sale of 200,000 units?
Answer:
Set the selling price at $43 per unit to breakeven
Derived from the basic profit equation
Z = PQ – VQ – AD – CP – SF –DP
Where Z = O and the price, P, equal the breakeven price, BEP
Calculated as
BEP = V + (AD+CP+SF+DP)/Q
BEP = 30 + (1,500,000+600,000+320,000+180,000)/200,000
BEP = 30 + 2,600,000/200,000
BEP = $30 + $13 = $43 per unit
Students must know the definition of profit, revenue, variable cost per unit, and fixed cost in order to calculate the average cost per unit. They must know that the breakeven price is the average cost per unit and if they set the selling price to the BEP, then they will earn zero profit in the market.
2) Cost-Based Pricing: Choosing a Price to Achieve a Target Net Profit.
Your sales of Q = 200,00 units in the Home Market has the following costs:
Advertising AD = $1,500,000
Consumer Promotion CP = $600,000
Sales Force SF = $320,000
Dealer Promotion DP = $180,000
Variable Cost per Unit V = $30
What is the selling price per unit , P, that is necessary to achieve a net profit of
Z = $400,000 on the sale of 200,000 units?
Answer:
Set the selling price equal to $45 per unit
Derived from the basic profit equation
Z = PQ – VQ – AD – CP – SF –DP
Where Z is the target net profit of $400,000 and the price, P, needs to calculated.
Calculated as
P = V + (AD+CP+SF+DP)/Q + Z/Q
P = 30+(1,500,000+600,000+320,000+180,000)/200,000 +400,000/200,000
P = 30 + 2,600,000/200,000 + 400,000/200,000
P = $30 + $13 + $2 = $45 per unit
If students do not know the specific formula, then they are expected to be able to derive it from the basic profit equation.
3) Cost-Based pricing: Choosing a Price to Achieve a Target ROS
Your sales of Q = 200,00 units in the Home Market has the following costs:
Advertising AD = $1,500,000
Consumer Promotion CP = $600,000
Sales Force SF = $320,000
Dealer Promotion DP = $180,000
Variable Cost per Unit V = $30
What is the selling price per unit, P, that is necessary to achieve a profit equal to the normal 40% net return on sales, Z = 40% ROS on the sale of 200,000 units?
Answer:
Set the Selling Price equal to $77.67 to achieve a 40% Net Return on Sales
Derived from the basic profit equation
Z = PQ – VQ – AD – CP – SF –DP
Where the target profit, Z, is replaced with the functional form of
Z = ROS x R
Z = ROS x P x Q
ROS(P) = P – V – F/Q
P – ROS(P) = V + F/Q
P (1-ROS) = BEP
P = BEP/(1-ROS)
Calculated as
Price = (Breakeven price)/(1- ROS)
P = (V + (AD+CP+SF+DP)/Q) / (1-ROS)
P = (30+(1,500,000+600,000+320,000+180,000)/200,000) / (1-0.40)
P = (30 + 2,600,000/200,000)/0.6
P = ($30 + $13) = $43/0.6 = $71.67 per unit
Most students will know the ROS pricing formula from frequent use in the simulation game.
4) Cost –Based Pricing: Using a Target Gross Profit for Setting A Price
Your sales of Q = 200,000 units in the Home Market have the following costs:
Variable Cost per Unit V = $30
What is the selling price per unit, P, that is necessary to achieve a gross profit of G = $5,000,000 on the sale of Q=200,000 units?
Answer:
Set the selling price equal to $55 per unit
Derived from the basic gross profit equation
G = R – COGS
G = PQ – VQ
Where the gross profit goal is given as G = $5,000,000 and calculate the selling price, P, to achieve it is calculated as
P = V + G/Q
P = 30 + 5,000,000/200,000
P = 30 + 5,000,000/200,000
P = $30 + $25 = $55 per unit
The calculation for choosing a price that generates a target gross profit, G, assumes that the student knows the definition of revenue, cost of goods sold, variable cost per unit sold, and gross profit.
5) Cost-Based Pricing; Using the Gross Return on Sales as the Target Profit
Units in the Home Market have a variable cost per unit:
Variable Cost per Unit V = $30
What is the selling price per unit, P, that is necessary to achieve a gross profit, G, that is 80% of Sales Revenue (i,e., GROS = 80%).
Answer:
Set the selling price equal to $150 per unit
Derived from the gross profit equation
G = R – COGS
G = PQ – VQ
Where the gross profit, G, is replaced with its functional form
G = GROS(R)
G = GROS x P x Q
GROS(P) = P – V
P – GROS(P) = V
P (1- GROS) = V
The selling price is calculated as
P = V/(1-GROS)
P = 30/ (1-0.80)
P = 30 /0.2 = $150 per unit
where
P = the selling price
V = the variable cost per unit
GROS = G/R = the gross (profit) return on sales
The calculation for choosing a price that generates a target rate of gross profit returned to revenue, GROS, assumes that the student knows the definition of gross return on sales, revenue, variable cost of each unit sold, and gross profit.
6) Cost-Based Pricing; Using the Markup on Price Ratio as the Target Profit
Units in the Home Market have a variable cost per unit.
Variable Cost per Unit V = $80
What is the selling price per unit, P, that is necessary to achieve a fair and normal markup on price that is 60% of Sales Revenue (i.e., Mp = 60%).
Answer:
Set the selling price equal to $200 per unit
Derived from the functional form of the markup on price ratio where (P-V) is the profit per unit sold
(P-V) = Mp(P)
P – Mp(P) = V
P(1 – Mp) = V
P = V/(1-Mp)
The selling price is calculated as
P = $80/ (1- 0.60)
P = $80 /0.4 = $200 per unit
where
P = the selling price
V = the variable cost per unit
Mp = (P-V)/P = markup on price
The most important weakness of cost based pricing is that the quantity you will sell is determined independently of the price that you set.
7) An Example of Competitive-Based Pricing
The average selling price of all the products competing against you in the home market is $80 and 3.4 is the version number (i.e., quality level) of the average competing product. Your product has reached version number 4. Given your relative competitive position on quality and the desired offer of at least the same value as you competitors, then what is the highest price you should set as your selling price?
Answer
The highest selling price you should set is $94.12 per unit.
Calculated as
Value, V, is defined as the ratio of the product’s quality, U, to its selling price, P.
V = U/P
The average competitors’ value, Va, is the ratio of the average product quality, Ua, to the average price, Pa
Va = Ua/Pa
Starting with the premise that your value, V, should never exceed the average value being offered by your competitors’ products, Va.
V = Va
U/P = Ua/Pa
P/Pa = U/Ua
Relative price, Pr is defined as the ratio of you price, P, to the average price, Pa,
and relative quality, Ur, is defined as the ratio of your quality, U to the average quality, Ua.
Pr = P/Pa
Ur = U/Ua
Therefore, when your value, V, is equal to the average value, Va, then your relative price, P, must equal your relative quality.
Pr = Ur
P/Pa = Ur
P = Pa x Ur
P = Pa x U/Ua
Your price = (average price) x Relative quality
P = Pa (U/Ua)
P = $80 x (4/3.4)
P = $80 x 117.65% = $94.12 per unit
The answer reflects the competitive pricing premise that if you have 110% of the average quality, then you should be able to charge 110% of the average price. The most important weakness of competitive based pricing is to assume that the engineer’s definition of quality corresponds to the customer’s perception of quality.
8) An example of Customer-Based Pricing using Customer Preferences
The average selling price of all three products competing in the Home market is $80 per unit. From a customer perspective, there are two product attributes that determine the quality of a product: 1) Durability 2) Speed.
The relative importance of the two attributes to the customer is Durability = 70% and Speed = 30%. Market research has to provide the degree to which each of the two competing brands (A and B) and your brand (C) are rated, and the amount of speed and durability in each brand, as shown in the following table:
Attribute / Importance Weight / Brand A / Brand B / Your Brand CDurability / 70% / 6 / 7 / 5
Speed / 30% / 5 / 4 / 8
Answer: Set the price at $82.81 to achieve value equal to the average competitive value.
Calculated from customers’ perceptions of quality using an expected-value model
Attribute / Importance Weight / Brand A / Brand B / Your Brand CDurability / 70% / 6x.7= 4.2 / 7x.7 = 4.9 / 5 x .7 = 3.5
Speed / 30% / 3 x .3 = .9 / 4 x .3 = 1.2 / 8 x .3 =2.4
Overall quality / 5.1 / 6.1 / 5.9
The average product quality is
Ua = (5.1 + 6.1 +5.9)/3 = 17.1/3 = 5.7
Your Brand C has a relative product quality, Ur, of
Ur = U/Ua = 5.9/5.7 =103.51% of the average product