Management Accounting 243 Pricing Decision Analysis

Management Accounting 243 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

244 CHAPTER THIRTEEN PRICING DECISION ANALYSIS 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 245 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 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 0 300 600 900 1,200 1,400 Quantity Fixed = $5,000 Variable = $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 combining the demand schedule and cost function, we can derive a profit equation as will now be demonstrated.

246 CHAPTER THIRTEEN PRICING DECISION ANALYSIS Figure 13.3 Graph of Revenue and Expenses $ 40 30 Sales 20 Net Income 10 Total cost 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 = P o - k(q) P - P o - Price Price at the Y-intercept k - The slope of the demand curve line If we solve for Q, then we the get the following: P o - P Q = (1) k TC = F + V(Q) (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: I P o - P P o - P = P - V k k - F (4) 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 247 1 (P o - 2P + V) (5) k 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 (P o - 2P + V) = 0 k Solving for P we get P o + 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 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

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 + = P - V Q Q P = I F + Q Q + 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. 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 three elements: 1. Desired net income 2. Variable expenses 3. Fixed expenses Assume the following: Fixed expenses $ 500,000 Variable cost rate $ 60 Desired net income $1,000,000 Quantity 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 $500,000 P = + + $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. Set a lower net income goal 2. Reduce fixed expenses

Management Accounting 249 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 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.

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 251 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:

252 CHAPTER THIRTEEN PRICING DECISION ANALYSIS Production (units) last period 10,000 Fixed costs: Manufacturing $50,000 Selling $30,000 Variable costs (last period) Manufacturing $80,000 Selling $20,000 Selling price (regular) $ 20,00 Buyer s offered price $ 12.00 Increase 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 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 253 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.

254 CHAPTER THIRTEEN PRICING DECISION ANALYSIS