Management Accounting
Pricing Decision Analysis
The setting of a price for a product is one of the most important decisions and
certainly one of the more complex. A change in price not only directly affects revenue
but has major consequences on other decisions. If price is lowered, for example,
then sales is most likely to increase. Therefore, additional production is needed with
all its attendant requirements concerning material, labor and overhead. Any student
who has completed a course in principles of economics understands that the theory
of price is at the center of economic thought.
In management accounting, the analysis of price is not as nearly complex or
mathematically sophisticated as in economic theory. The assumptions in management
accounting are much simpler and more practical oriented.
The focus of this chapter will be on the following:
1. Review of some basic economic fundamentals
2. Pricing using cost-volume-profit analysis
3. The special offer decision
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Basic Economic Fundamentals
The economists have theorized that firm is subject to the economic laws of supply
and demand. Each firm has a demand curve that it must consider in setting price. In addition, the economists have identified four major types of markets a firm may
operate in:
1. Pure competition
2. Monopoly
3. Oligopoly
5. Monopolistic competition
The main tenet of demand is that as price is lowered, consumers will purchase
more goods. To assist in analysis and understanding, economists often portray the
demand curve as a straight line sloping downward and to the right as shown here
in Figure 13.1. Because the demand curve has many mathematical properties,
economists frequently use mathematics to explains the meaning and importance of
demand.
FIGURE 13.1 • Example of a Demand Curve
Price $
110
100
90
80
70
60
50
40
30
20
10
0
200
400
600
800
1,000
Quantity
When three or more firms compete in the same market and basically sell the same
product, the market is called an oligopolistic market. How price is set in this type of
market has been and still continues to be the subject of much debate. In general, it is
believed that eventually the firms will come to an equilibrium price. Any firm then that
significantly raises its price will face a large loss of sales. If a firm attempts to gain
greater profits and market share by lowering price, then the other firms in the industry
will also immediately lower their price. The consequence of all firms lowering price
will eventually be an overall decrease in industry net income.
Management Accounting
While the exact nature or slope of the demand curve is seldom known in a given
industry, the academic question still remains: what is the best price assuming the
demand curve is known? As indicated in Figure 13.1, assume that we have the
following demand schedule
Price
Quantity
Revenue
$100
$ 90
$ 80
$ 70
$ 60
$ 50
$ 40
$ 30
$ 20
$ 10
100
200
300
400
500
600
700
800
900
1,000
$10,000
$18,000
$24,000
$28,000
$30,000
$30,000
$28,000
$24,000
$18,000
$10,000
The above schedules seems to indicate that the best price is either $60 or $50. In
each case, sales is maximized at $30,000. However, the objective of a business is not
to maximize sales dollars but to maximize net income. In this instance, an expense or
cost function is needed. In management accounting, as in economics, it is assumed
that there are two types of expenses: fixed and variable: Fixed and variable expenses
in management accounting may be graphically presented as shown in Figure 13.2
Figure 13.2 • Illustration of Total Expenses
Expenses
(000)
20
15
10
5
0
300
600
Fixed = $5,000
Variable = $10.00
900
1,200
1,400 Quantity
Based on the demand schedule and the expense function, it is possible to
present total revenue and expenses in the same graph as shown in Figure 13.3. By
combining the demand schedule and cost function, we can derive a profit equation
as will now be demonstrated.
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Figure 13.3 Graph of Revenue and Expenses
$
40
30
Sales
20
Net Income
Total cost
10
300
500
700
900
Quantity
The demand curve in Figure 13.1 and the expense function shown in figure 13.2
can be mathematically defined as follow:
P
=
Po - k(Q)
P - Price
Po - Price at the Y-intercept
k - The slope of the demand curve line
If we solve for Q, then we the get the following:
Po - P
Q = –––––––––
k
TC =
F + V(Q)
(1)
(2)
F - Total fixed expenses
V - Variable cost rate
Q - Quantity of goods
Revenue may be defined simply as follows: S = P(Q). Based on this revenue
equation and equations (1) and (2) net income may be computed as follows:
I = P(Q) - V(Q - F
(3)
Consequently, using equation (1), we can now define net income as:
Po - P Po - P
I = P ––––––– - V ––––––– - F
(4)
k
k
If the goal is to maximize net income, then the price that maximizes net income
can be found by finding using calculus and finding the first derivative of equation 3. The first derivative of equation 4 using turns out to be:
Management Accounting
1
––– (Po - 2P + V)
k
(5)
Profit is maximized at the point where the slope of equation 5 is zero. So if we set
the first derivative to zero we have the following:
1
––– (Po - 2P + V) = 0
k
Solving for P we get
Po + V
P = –––––––––
(6)
2
This equation allows us to determine the best price without preparing a complete
schedule of price, quantity, and net income as has been done in Figure 13.4.
In Figure 13.4, the best price is shown as $60. This price agrees with the price
determined by our price formula derived above:
110 + $10
$120
P = ––––––––––– = ––––– = $60
2
2
A company’s marketing strategy can have a profound effect on its demand curve.
Even though the demand curve is not known with any precision, it is still generally
recognized by economists and marketing analysts that the following marketing
decisions can shift the demand curve upwards and to the right.
1. Advertising
2. Increase in size of sales force
3. Increase in sales people’s compensation
4. Increase in the quality of the product
However, any change in the above must be approached cautiously and also be
based on adequate analysis of the known economic and marketing environment.
Even though changes in these marketing factors may increase sale, any increase in
sales can be easily offset by increases in the associated expenses.
Figure 13.4
Price
$100
$90
$80
$70
$60
$50
$40
$30
$20
$10
Quantity
100
200
300
400
500
600
700
800
900
1,000
Revenue
Total Expenses
Net income
$10,000
$18,000
$24,000
$28,000
$30,000
$30,000
$28,000
$24,000
$18,000
$10,000 $ 6,000
$ 7000
$ 8,000
$ 9,000
$10,000
$11,000
$12,000
$13,000
$14,000
$15,000
$ 4,000
$11,000
$16,000
$19,000
$20,000
$19,000
$16,000
$11,000
$ 4,000
($ 1,000)
Note: Total fixed cost $5,000, variable cost rate $10,000
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248 | CHAPTER THIRTEEN • PRICING DECISION ANALYSIS
Cost-volume-profit Analysis Approach to Setting Price
Since the demand curve is seldom known accurately in the real world of business,
equation (6) is not likely to be used. Pricing is more likely to be based on cost plus a
reasonable markup. Cost volume profit analysis may be used to compute a tentative
price.
I = P(Q) - V(Q) - F
We may solve for P or price as follows:
I + F = P(Q) - V(Q)
I + F = Q(P - V)
I F
–– + ––
Q Q
=
P -
I F
P = ––– + –––
Q Q
V
+
V
(7)
The above equation may be interpreted as follows
I / Q - Denotes desired income per unit of product
F/Q
-
Denotes the amount from each sale that is necessary to cover
the fixed expenses of the business. It is equivalent to an
overhead rate.
Represents that portion of each sale that must be used to pay
the variable expenses.
This equation, then, points out that price must be sufficient to cover three
elements:
1. Desired net income
2. Variable expenses
3. Fixed expenses
V
-
Assume the following:
Fixed expenses
Variable cost rate
Desired net income
Quantity
$ 500,000
$
60
$1,000,000
10,000
Based on equation 7, the required price to attain the net income goal of $1,000,000
may be computed as follows:
$1,000,000
P = ––––––––– +
10,000
$500,000
––––––––+ $60 = $100 + $50 + $60 = $210
10,000
The major fault of this approach is that it does not necessarily follow that customers
will pay $210 per unit and that at this price 10,000 units can be sold. In order to lower
price, management has four options:
1. Set a lower net income goal
2. Reduce fixed expenses
Management Accounting
3. Reduce the variable cost per unit of product
4. Sell more units than originally desired
The Special Offer Decision (Additional Volume of Business)
Frequently, a business will be asked to sell a larger than normal quantity at a
price considerably lower than the normal selling price. The offered price may be even
below the average cost per unit. Oddly enough, It is possible to increase net income
by selling below average cost. Given that this is true, the question becomes: under
what conditions may such a price offer be accepted? The general rule is that the offer
may be accepted, if the special price is greater than the average variable cost rate of
manufacturing.
If a company has significant manufacturing costs that are fixed in nature and the
company has excess capacity, then the manufacturing of additional units does not
cause any increase in the fixed costs. The only costs that increase are the variable
manufacturing costs. So theoretically, as long as the offered price is above the
average variable manufacturing costs, an increase in net income can take place.
To illustrate, consider the following example:
The ABC company is currently manufacturing and selling 100 units. The selling
price is $40 per unit. The company has the production capacity to make 150 units. A
special offer has been received from a company to purchase 30 units at $22 per unit.
The company making the offer is not a regular customer and will not be in competition.
Other information was provided by the company’s accountant is as follows:
Variable costs:
Manufacturing cost per unit
$12
Selling
$5
Fixed
$1,000
If the offer is accepted, the $5 per unit of selling cost will still be incurred.
Analysis using the Full Income Approach
In this approach, the revenue and expenses from total sales ( regular sales +
special offer sales) are included in the analysis.
Reject Offer Accept Offer
S = 100
S = 130
––––––
––––––
Sales
$4,000
$4,660
Expenses:
Cost of goods sold ($12)
$1,200
$1,560
Selling ($5)
500
650
Fixed1,000
$1,000
––––––––––––
$2,700
$3,210
––––––––––––
Net income
$1,300
$1,450
––––––––––––
If the offer is accepted, net income should increase by $150.
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250 | CHAPTER THIRTEEN • PRICING DECISION ANALYSIS
Analysis using the Incremental Analysis Approach
In this approach, the regular sales are treated as irrelevant because whether or
not the special offer is accepted, the regular sales will remain the same.
Increase in Revenue (30 x $22) $660
Increase in Expenses
Cost of goods sold
$360.00
Selling expenses
150.00
______ 510
–––––
Increase in net income $ 150
–––––
The acceptance of the special offer is strictly a short term decision and should
not become a regular pricing practice. The conditions which should exist in order to
accept a special offer include:
1. The sale must be legal
2. The sale should not be to a regular customer
3. The sale should not be to a competitor
4. The purchaser should not be led to believe that future sales will be
at the same price
5. Excess capacity exists
Another reason that a large special offer might be accepted is to keep factory
workers on the production line. Laying off workers and then retooling for production
can be expensive.
While the acceptance of an offer now and then can add to company profits, the
practice of selling below total average cost can not work, if that practice becomes the
rule rather than the exception. Consider the following examples which in each case
the price is just above the variable costs
Sales
Sale
Sale
Sale
Total
No. 1
No. 2
No. 3
No. 4
________
_______
________
_______
_______
Sales
$1,000
$ 800
$1,200
$ 500
$3,500
Variable expenses
800
640
$ 960
400
2,800
––––––
––––––
––––––
––––––
––––––
Contribution
$ 200
$ 160
$ 240
$ 100
$ 700
Fixed expenses
$1,000
––––––
Net loss
($ 300)
––––––
In this example, all sales make a contribution and without any one of the four
sales the loss would be even greater. However, the fact that all the sales make a
contribution does not mean the company will be profitable, as is clearly illustrated
above. Even though all sales make a contribution, the company is still operating at
a loss.
Accepting offers at less than normal price should not become a regular practice.
Eventually, all customers will expect preferential treatment. In the short run and for
Management Accounting
several reasons, it might be prudent to accept such an offer to add to overall net
income or to keep factory workers employed. In the long, run such a practice will not
make a company profitable that is already operating at a loss.
Summary
Because pricing is such an important decision, any change in price should be
approached cautiously and should be based on an analysis of all available economic
and marketing information. Even though a demand curve may exist is a general
way, the lack of specific information on its exact nature means that in many if not
most cases price tends to be based on cost. When price is based on cost, hopefully
the company’s marketing strategy will generate the sales required to cover cost and
generate the desired net income.
Cost-volume-profit analysis can be used to set a tentative price. However, the
major flaw in this approach is that the required volume to attain the desired net
income at that price may not happen. Assuming some type of demand curve exists,
the volume indicated by the C-V-P price may not occur.
Q. 13.1
Explain why it is difficult for a company to just set any price and have
the volume necessary to make the company profitable.
Q. 13.2
Explain how a demand curve could be used to set price.
Q. 13.3
In a absence of any knowledge of its demand curve, how may a
company go about setting price?
Q. 13.4
Explain how it is possible for a company to accept a price offer that
is below the company’s average manufacturing cost and still for the
company to increase net income.
Q. 13.5
A special offer has been made to the Acme Company. However, the
company does not have excess capacity and to accept the offer it
would have to decrease its sales to regular customers. If this offer is
accepted, what would be the effect on net income?
‘
Q. 13.6
Explain how the cost-volume-profit equation may be used to compute
with a tentative price.
Q. 13.7
Based on the cost volume profit equation, what are the three elements
that management must consider in setting price?
Exercise 13.1 • Additional Volume of Business
Your company has received an offer to buy 1,000 units of your product, however,
the offer is to purchase at $12.00 per unit rather than at the normal selling price of
$20.00. You have been provided the following information:
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Production (units) last period
Fixed costs:
Manufacturing
Selling
Variable costs (last period)
Manufacturing
Selling
Selling price (regular)
Buyer’s offered price
Increase in expenses other than
variable expenses, assuming offer is
accepted.
Full capacity (units)*
10,000
$50,000
$30,000
$80,000
$20,000
$  20,00
$  12.00
$  2,000
12,000
* Production cannot exceed this amount
If the offer is accepted, no additional variable selling expenses will be incurred
such as commissions or shipping charges.
Required:
Show using incremental analysis form whether the buyer’s offer, if accepted, will
contribute to net income of the company.
Exercise 13.2 • Special Price Offer
The K. L. Widget company has received an offer from the Ajax Retail company.
The Ajax Company has offered to purchase 1,000 units of its product at $60 per
unit.
The cost of manufacturing and selling the Widget are as follows:
Variable costs
Manufacturing
$      18
Selling expenses
$      25
Gen. and admin.
$      10
Fixed
Manufacturing
$160,000
Selling
$200,000
General and admin.
$ 40,000
The current selling price is $180. If the offer is accepted the variable selling
expenses would be reduced to $5.00 per unit. No variable general and administrative
expenses would be incurred.
The company is currently manufacturing 8,000 units of product per quarter. Sales
have also averaged 8,000 units per quarter. Current levels of fixed costs will not be
affected by the acceptance of the offer.
The company has capacity to make 10,000 units. The average cost of
manufacturing 8,000 units is $103 ($53.00 + 400,000 /8,000).
Management Accounting
Required:
If the offer is accepted, then by how much will net income increase or decrease?
(Show your analysis in detail.)
Exercise 13.3 • Schedule of Net Income Based on Demand Curve and Cost
Function
The K. L. Widget Company has determined its demand curve and cost function
as follows:
P = $1,000 - .1(Q)
TC = $80(Q) + $500,000
Required:
Using a work sheet with the headings as suggested below, determine net income at a
price of $1,000 and decrement the price by $100 until price is equal to $100.
Price (P)
Quantity(Q)
Revenue
P(Q)
Variable
Cost
Fixed
Cost
Total
Cost
Net
Income
Exercise 13.4 • Cost-Volume-Profit Pricing
The R. K. Manufacturing Company has developed a new product. Estimated
costs of manufacturing and selling were provided as follows:
Variable costs:
Manufacturing
$   12.00
Selling
$    8.00
Fixed costs:
Manufacturing
$  50,000
Selling
$100,000
The company plans to make 10,000 units hopes to sell the same amount per
year. The company’s goal is to earn $80,000 per year by selling this product.
Required:
Use the cost-volume-profit equation to compute a price necessary to attain the
desired level of income.
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