Pricing Products and Services
Appendix A
© 2012 McGraw-Hill Education (Asia)
Learning outcomes
Compute the profit-maximizing price of a product or
service using the economics model.
Compute the profit-maximizing price of a product or
service using the price elasticity of demands and
variable cost.
Compute the selling price of a product using the
absorption costing approach.
Compute the target cost for a new product or
service.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 2
Learning Objective 1
Compute the profitmaximizing price of
a product or service
using the economics
model.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 3
The Economist’s Approach to Pricing
Elasticity of Demand
The price elasticity of demand measures the
degree to which the unit sales of a product or
service are affected by a change in unit price.
Change
Change
in
versus in Unit
Price
Sales
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 4
Price Elasticity of Demand
Demand for a product is inelastic if a
change in price has little effect on the
number of units sold.
Example
The demand for designer
perfumes sold at cosmetic
counters in department
stores is relatively inelastic.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 5
Price Elasticity of Demand
Demand for a product is elastic if a
change in price has a substantial effect
on the number of units sold.
Example
The demand for gasoline is
relatively elastic because if
a gas station raises its price,
unit sales will drop as
customers seek lower
prices elsewhere.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 6
Price Elasticity of Demand
As a manager, you should set higher
(lower) markups over cost when
demand is inelastic (elastic)
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 7
Price Elasticity of Demand
Єd =
ln(1 + % change in quantity sold)
ln(1 + % change in price)
Price elasticity of demand
Natural log function
I can estimate the price
elasticity of demand for a
product or service using
the above formula.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 8
Price Elasticity of Demand
Suppose the managers of Nature’s Garden believe
that every 10 percent increase in the selling price of
its apple-almond shampoo will result in a 15
percent decrease in the number of bottles of
shampoo sold.
Let’s calculate the price elasticity of
demand.
For its strawberry glycerin soap, managers of
Nature’s Garden believe that the company will
experience a 20 percent decrease in unit sales if its
price is increased by 10 percent.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 9
Price Elasticity of Demand
For Nature’s Garden apple-almond shampoo.
Єd =
Єd =
Єd =
McGraw-Hill Education (Asia)
ln(1 + % change in quantity sold)
ln(1 + % change in price)
ln(1 +
(-0.15))
ln(1 + (0.10))
ln(0.85)
=
ln(1.10)
-1.71
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 10
Price Elasticity of Demand
For Nature’s Garden strawberry glycerin soap.
Єd =
Єd =
Єd =
McGraw-Hill Education (Asia)
ln(1 + % change in quantity sold)
ln(1 + % change in price)
ln(1 +
(-0.20))
ln(1 + (0.10))
ln(0.80)
=
ln(1.10)
-2.34
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 11
Price Elasticity of Demand
The price elasticity of demand for the
strawberry glycerin soap is larger, in absolute
value, than the apple-almond shampoo. This
indicates that the demand for strawberry
glycerin soap is more elastic than the demand
for apple-almond shampoo.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 12
Factors affecting price elasticity
Scope of the market
Information within the market
Availability of substitutes
Complementary products
Disposable income
Necessities
Habit
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 13
Market Structure and Price
Perfect Competition: Many buyers and sellers; no
one of which is large enough to influence the market.
Monopolistic Competition: Has both the
characteristics of both monopoly and perfect
competition.
Oligopoly: Few sellers.
Monopoly: Barriers to entry are so high that there is
only one firm in the market.
14
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 14
Market Structure and Price
15
McGraw-Hill Education (Asia)
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Slide 15
Profit maximisation model
A mathematical model can be used to determine an
optimal selling price.
The model is based on the economic theory that
profit is maximised at the output level where
marginal cost (MC) is equal to marginal revenue.
The model uses calculus knowledge which is
beyond the scope of the syllabus, therefore we will
use the following basic principles:
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 16
Basic principles
It is worthwhile producing a product if the extra
revenue from selling one more unit is greater than
the costing of producing it. (MR > MC).
It is not worthwhile producing a product if the extra
cost of producing it is greater than the extra revenue
from it. (MC > MR).
Therefore, a firm should produce units up to the
point where the marginal revenue equals the
marginal cost (MR = MC).
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 17
The basic price equation
P = a – bX
where:
P = price
X = quantity demanded
a and b are constants, where b is the slope of the
curve and calculated as (change in price/change in
quantity)
For example:
If you are told that demands falls by 25 units for every
increase in price of N$1, then b = -0.04 (1/25).
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 18
The basic price equation
The marginal revenue equation can be found by
doubling the value of b: MR = a – 2bX
The marginal cost is the variable cost of production.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 19
Procedure for establishing the optimum
price of a product
1. Establish the linear relationship between price (P)
and the quantity demanded (Q). The equation takes
the form:
P = a – bQ
Where ‘a’ is the intercept and ‘b’ is the gradient of the
line. As the prices increases, the quantity demanded
will decrease. The equation of a straight line
P = a – bQ can be used to show the demand for a
product at a given price:
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 20
Demand curve of product using the price
equation
‘a’
P = a - bQ
0
Origin
Note: ‘b’ is always negative because of the inverse relationship between
price and quantity.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 21
Procedure for establishing the optimum
price of a product
2. Double the gradient to find the marginal revenue:
MR = a – 2bQ.
3. Establish the marginal cost: MC. This is simply the
variable cost per unit.
4. To maximise profit, equate MC and MR and solve
for Q.
5. Substitute the value of Q into the price equation to
find the optimum price.
6. It may be necessary to calculate the maximum
profit.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 22
Example
a)
b)
c)
d)
e)
f)
At a price of N$200, a company will be able to sell 1 000 units of
its product in a month. If the selling price is increased to N$220,
the demand will fall to 950 units. It is also known that the product
has a variable cost of N$140 per unit, and fixed costs will be N$36
000 per month.
Requirement:
Find an equation for the demand function (that is, the price as a
function of quantity demanded);
Write down the marginal revenue function;
Write down the marginal cost;
Find the quantity that maximises profit;
Calculate the optimum price;
What is the maximum profit?
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 23
Exercise 1
Maximum demand for a company’s product M is
100 000 units per annum. The demand will be
reduced by 40 units for every increase of N$1 in
the selling price. The company has determined
that the profit is maximised at a sales volume of
42 000 units per annum.
Requirement:
What is the profit maximising selling price for
product M?
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 24
Exercise 2
Another product, K, incurs a total cost of N$10 per unit sold, as follows:
N$ per unit
Variable production cost
4
Variable selling cost
2
Fixed production cost
3
Fixed selling and admin cost
1
Total cost
10
The marginal revenue (MR) and demand functions for product K are:
MR = 200 – 0.4X; p = 200 – 0.2X
Where p = price, x = quantity demanded per period.
Requirement:
What is the profit maximising selling price of product K, and what
quantity will be sold per period at this price.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 25
Limitations of the profit maximisation model
It is unlikely that organisations will be able to determine the
demand function for their products or services with any
degree of accuracy.
The majority of organisations aim to achieve a target profit,
rather than the theoretical maximum profit.
Determining an accurate and reliable figure for marginal or
variable cost poses difficulties for the management
accountant.
Unit marginal costs are likely to vary depending on the
quantity sold. For example bulk discounts may reduce the unit
materials cost for higher output volumes.
Other factors, in addition to price, will affect the demand, for
example, the level of advertising or changes in the income of
customers.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 26
Learning Objective 2
Compute the profitmaximizing price of a
product or service using
the price elasticity of
demands and variable
cost.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 27
The Profit-Maximizing Price (Marginal cost
plus)
Under certain conditions, the profit-maximizing price
can be determined using the following formula:
ProfitЄd
maximizing =
1 Єd
1
markup on
+
variable cost
Using the above markup, the selling price would be
set using the formula:
Variable
Єd
Profit-maximizing
× cost per
=
price
1 Єd
unit
+
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 28
The Profit-Maximizing Price
Let’s determine the profit-maximizing price for the
apple-almond shampoo sold by Nature’s Garden.
The shampoo has a variable cost per unit of $2.00.
Price elasticity of demand =
-1.71
Profit-1.71
maximizing
=
-1.71
markup
+1
on variable cost
McGraw-Hill Education (Asia)
-
= 1.41 or 141%
1
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 29
The Profit-Maximizing Price
Now let’s turn to the profit-maximizing price for the
strawberry glycerin soap sold by Nature’s Garden.
The soap has a variable cost per unit of $0.40.
Price elasticity of demand =
-2.34
Profit-2.34
maximizing
=
-2.34
markup
+1
on variable cost
McGraw-Hill Education (Asia)
-
= 0.75 or 75%
1
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 30
The Profit-Maximizing Price
The 75 percent markup for the strawberry
glycerin soap is lower than the 141 percent
markup for the apple-almond shampoo. This
is because the demand for strawberry
glycerin soap is more elastic than the
demand for apple-almond shampoo.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 31
The Profit-Maximizing Price
This graph depicts how the profit-maximizing markup is
generally affected by how sensitive unit sales are to price.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 32
The Profit-Maximizing Price
Nature’s Garden is currently selling 200,000 bars
of strawberry glycerin soap per year at the price
of $0.60 a bar. If the change in price has no
effect on the company’s fixed costs or on other
products, let’s determine the effect on
contribution margin of increasing the price by 10
percent.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 33
The Profit-Maximizing Price
Contribution margin will increase by $1,600.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 34
Learning Objective 3
Compute the selling
price of a product
using the absorption
costing approach.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 35
The Cost Base
Under the absorption approach to cost-plus
pricing, the cost base is the absorption costing
unit product cost rather than the variable cost.
The cost base includes direct materials, direct
labor, and variable and fixed manufacturing
overhead.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 36
Setting a Target Selling Price
Here is information provided by the management
of Ritter Company.
Assuming Ritter will produce and sell 10,000
units of the new product, and that Ritter typically
uses a 50% markup percentage, let’s determine
the unit product cost.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 37
Setting a Target Selling Price
The first step in the absorption costing approach to
cost-plus pricing is to compute the unit product cost.
Ritter has a policy of marking up unit product costs
by 50%. Let’s calculate the target selling price.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 38
Setting a Target Selling Price
The second step is to calculate the target selling
price ($30) by assigning the appropriate markup
($10) to the unit product cost ($20).
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 39
Determining the Markup Percentage
A markup percentage can be based on an industry
“rule of thumb,” company tradition, or it can be
explicitly calculated.
The equation for calculating the markup percentage on
absorption cost is shown below.
Markup %
on absorption =
cost
(Required ROI × Investment) + S & A expenses
Unit sales × Unit product cost
The markup must be high enough to cover S & A
expenses and to provide an adequate return on
investment.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 40
Determining the Markup Percentage
Let’s assume that Ritter must invest $100,000 in
the product and market 10,000 units of product
each year. The company requires a 20% ROI on all
investments. Let’s determine Ritter’s markup
percentage on absorption cost.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 41
Determining the Markup Percentage
Markup %
(20% × $100,000) + ($2 × 10,000 + $60,000)
on absorption =
10,000 × $20
cost
Variable S & A per unit
Total fixed S & A
Markup %
on absorption =
cost
McGraw-Hill Education (Asia)
($20,000 +
$80,000)
$200,000
= 50
%
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 42
Problems with the Absorption Costing Approach
The absorption costing approach essentially
assumes that customers need the forecasted unit
sales and will pay whatever price the company
decides to charge. This is flawed logic simply
because customers have a choice.
McGraw-Hill Education (Asia)
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Slide 43
Problems with the Absorption Costing Approach
Let’s assume that Ritter sells only 7,000 units at
$30 per unit, instead of the forecasted 10,000
units. Here is the income statement.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 44
Problems with the Absorption Costing Approach
Let’s assume that Ritter sells only 7,000 units at
$30 per unit, instead of the forecasted 10,000
units. Here is the income statement.
Absorption costing approach to pricing is a safe
approach only if customers choose to buy at
least as many units as managers forecasted
they would buy.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 45
Learning Objective 4
Compute the
target cost for a
new product or
service.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 46
Target Costing
Target costing is the process of determining the
maximum allowable cost for a new product and then
developing a prototype that can be made for that
maximum target cost figure. The equation for
determining a target price is shown below:
Target cost = Anticipated selling price – Desired profit
Once the target cost is determined, the
product development team is given the
responsibility of designing the product
so that it can be made for no more
than the target cost.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 47
Reasons for Using Target Costing
Two characteristics of prices and product costs
include:
1. The market (i.e., supply and demand)
determines price.
2. Most of the cost of a product is determined
in the design stage.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 48
Reasons for Using Target Costing
Target costing was developed in recognition
of the two characteristics summarized on
the previous screen.
Target costing begins the product development
process by recognizing and responding to
existing market prices. Other approaches
allow engineers to design products without
considering market prices.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 49
Reasons for Using Target Costing
Target costing focuses a company’s cost reduction
efforts in the product design stage of production.
Other approaches attempt to squeeze costs out of
the manufacturing process after they come to
the realization that the cost of a manufactured
product does not bear a profitable relationship
to the existing market price.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 50
Target Costing
Handy Appliance feels there is a niche for
a hand mixer with special features. The
marketing department believes that a price
of $30 would be about right and that about
40,000 mixers could be sold. An investment
of $2 million is required to gear up for
production. The company requires a 15%
ROI on invested funds.
Let’s see how we determine the target cost.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 51
Target Costing
Each functional area within Handy Appliance
would be responsible for keeping its actual
costs within the target established for that area.
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 52
End of Appendix A
McGraw-Hill Education (Asia)
Garrison, Noreen, Brewer, Cheng & Yuen
Slide 53