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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 fundamentals2. Pricingusingcost-volume-profitanalysis3. The special offer decision

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Basic Economic FundamentalsTheeconomistshavetheorizedthatfirmissubjecttotheeconomiclawsofsupply

anddemand.Eachfirmhasademandcurvethat itmustconsiderinsettingprice.Inaddition,theeconomistshaveidentifiedfourmajortypesofmarketsafirmmayoperate in:

1. Pure competition2. Monopoly3. Oligopoly5. 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 $

1101009080706050403020100

200 400 600 800 1,000 Quantity

Whenthreeormorefirmscompeteinthesamemarketandbasicallysellthesameproduct, 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 believedthateventuallythefirmswillcometoanequilibriumprice.Anyfirmthenthatsignificantlyraisesitspricewillfacealargelossofsales.Ifafirmattemptstogaingreaterprofitsandmarketsharebyloweringprice,thentheotherfirmsintheindustrywillalsoimmediatelylowertheirprice.Theconsequenceofallfirmsloweringpricewill eventually be an overall decrease in industry net income.

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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 $ 100 100 $10,000 $ 90 200 $18,000 $ 80 300 $24,000 $ 70 400 $28,000 $ 60 500 $30,000 $ 50 600 $30,000 $ 40 700 $28,000 $ 30 800 $24,000 $ 20 900 $18,000 $ 10 1,000 $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 thattherearetwotypesofexpenses:fixedandvariable:Fixedandvariableexpensesin 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

0300 600 900 1,200 1,400 Quantity

Fixed = $5,000Variable = $10.00

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 combiningthedemandscheduleandcostfunction,wecanderiveaprofitequationas will now be demonstrated.

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Figure 13.3 Graph of Revenue and Expenses

Sales

Net Income

Total cost

Quantity

$ 40

30

20

10

300 500 700 900

ThedemandcurveinFigure13.1andtheexpensefunctionshowninfigure13.2canbemathematicallydefinedasfollow:

P = Po - k(Q) P - PricePo - Price at the Y-interceptk - The slope of the demand curve line

If we solve for Q, then we the get the following: Po - P

Q = ––––––––– (1) k

TC = F + V(Q) (2)F - TotalfixedexpensesV - Variable cost rateQ - Quantity of goods

Revenuemaybedefinedsimplyas 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,usingequation(1),wecannowdefinenetincomeas:

Po - P Po - PI = P ––––––– - V ––––––– - F (4) k k

If the goal is to maximize net income, then the price that maximizes net income canbefoundbyfindingusingcalculusandfindingthefirstderivativeofequation3.Thefirstderivativeofequation4usingturnsouttobe:

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1 ––– (Po - 2P + V) (5) k

Profitismaximizedatthepointwheretheslopeofequation5iszero.Soifwesetthefirstderivativetozerowehavethefollowing:

1 ––– (Po - 2P + V) = 0 k

SolvingforP 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 $120P = ––––––––––– = ––––– = $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. Advertising2. Increase in size of sales force3. Increase in sales people’s compensation4. 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 Quantity Revenue Total Expenses Net income $ 100 100 $10,000 $ 6,000 $ 4,000 $ 90 200 $18,000 $ 7000 $ 11,000 $ 80 300 $24,000 $ 8,000 $ 16,000 $ 70 400 $28,000 $ 9,000 $ 19,000 $ 60 500 $30,000 $ 10,000 $ 20,000 $ 50 600 $30,000 $ 11,000 $ 19,000 $ 40 700 $28,000 $ 12,000 $ 16,000 $ 30 800 $24,000 $ 13,000 $ 11,000 $ 20 900 $18,000 $ 14,000 $ 4,000 $ 10 1,000 $10,000 $ 15,000 ($ 1,000)

Note: Total fixed cost $5,000, variable cost rate $10,000

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Cost-volume-profit Analysis Approach to Setting PriceSincethedemandcurveisseldomknownaccuratelyintherealworldofbusiness,

equation (6) is not likely to be used. Pricing is more likely to be based on cost plus a reasonable markup. Costvolumeprofitanalysismaybeusedtocomputeatentativeprice.

I = P(Q) - V(Q) - FWe may solve for P or price as follows:

I + F = P(Q) - V(Q)I + F = Q(P - V)I F

–– + –– = P - VQ Q

I FP = ––– + ––– + V (7)

Q Q

The above equation may be interpreted as followsI / Q - Denotes desired income per unit of productF/Q - Denotes the amount from each sale that is necessary to cover

the fixed expenses of the business. It is equivalent to anoverhead rate.

V - 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 threeelements:

1. Desired net income2. Variable expenses3. Fixed expenses

Assume the following:Fixed expenses $ 500,000Variable cost rate $ 60Desired net income $1,000,000Quantity 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 $500,000P = ––––––––– + –––––––– + $60 = $100 + $50 + $60 = $210 10,000 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. Setalowernetincomegoal2. Reducefixedexpenses

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3. Reduce the variable cost per unit of product4. Sellmoreunitsthanoriginallydesired

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.

Ifacompanyhassignificantmanufacturingcoststhatarefixedinnatureandthecompany has excess capacity, then the manufacturing of additional units does not causeanyincreaseinthefixedcosts.Theonlycoststhatincreasearethevariablemanufacturing costs. So theoretically, as long as the offered price is above theaverage 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 $4,660Expenses: Cost of goods sold ($12) $ 1,200 $ 1,560 Selling($5) 500 650 Fixed 1,000 $ 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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Analysis using the Incremental Analysis ApproachIn 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) $660Increase in Expenses Cost of goods sold $360.00 Sellingexpenses 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 legal2. The sale should not be to a regular customer3. The sale should not be to a competitor4. The purchaser should not be led to believe that future sales will be

at the same price5. 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.

Whiletheacceptanceofanoffernowandthencanaddtocompanyprofits,thepractice 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 $3,500Variable expenses 800 640 $ 960 400 2,800 –––––– –––––– –––––– –––––– ––––––Contribution $ 200 $ 160 $ 240 $ 100 $ 700Fixed 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 contributiondoesnotmeanthecompanywillbeprofitable,as isclearly illustratedabove. 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

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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 makeacompanyprofitablethatisalreadyoperatingataloss.

SummaryBecause 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,thelackofspecificinformationonitsexactnaturemeansthatinmanyifnotmost 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-profitanalysiscanbeused toseta tentativeprice.However, themajor flaw in this approach is that the required volume to attain the desired netincome 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 Explainwhyitisdifficultforacompanytojustsetanypriceandhavethevolumenecessarytomakethecompanyprofitable.

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 Explainhowthecost-volume-profitequationmaybeusedtocomputewith a tentative price.

Q.13.7 Basedonthecostvolumeprofitequation,whatarethethreeelementsthat 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 10,000Fixed costs: Manufacturing $50,000 Selling $30,000Variable costs (last period)Manufacturing $80,000Selling $20,000

Sellingprice(regular) $ 20,00Buyer’s offered price $ 12.00Increase in expenses other than variable expenses, assuming offer is accepted. $ 2,000

Full capacity (units)* 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 formwhether the buyer’s offer, if accepted,willcontribute 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 Sellingexpenses $ 25 Gen. and admin. $ 10Fixed 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.

Thecompanyiscurrentlymanufacturing8,000unitsofproductperquarter.Saleshavealsoaveraged8,000unitsperquarter.Currentlevelsoffixedcostswillnotbeaffected 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).

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Required:

If the offer is accepted, then by how much will net income increase or decrease? (Showyouranalysisindetail.)

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 $ 8.00Fixed 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 thedesired level of income.

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