## 10.2 Applying Differential Analysis in Managerial Decision Making

Applications of differential analysis

To illustrate the application of differential analysis to specific decision problems, we consider five decisions:

1. setting prices of products;
2. accepting or rejecting special orders;
3. adding or eliminating products, segments, or customers;
4. processing or selling joint products; and
5. deciding whether to make products or buy them.

Although these five decisions are not the only applications of differential analysis, they represent typical short-term business decisions using differential analysis. Our discussion ignores income taxes.

Pricing Decisions

When applying differential analysis to pricing decisions, each possible price for a given product represents an alternative course of action. The sales revenues for each alternative and the costs that differ between alternatives are the relevant amounts in these decisions. Total fixed costs often remain the same between pricing alternatives and, if so, may be ignored. In selecting a price for a product, the goal is to select the price at which total future revenues exceed total future costs by the greatest amount, thus maximizing income.

A high price is not necessarily the price that maximizes income. The product may have many substitutes. If a company sets a high price, the number of units sold may decline substantially as customers switch to lower-priced competitive products. Thus, in the maximization of income, the expected volume of sales at each price is as important as the contribution margin per unit of product sold. In making any pricing decision, management should seek the combination of price and volume that produces the largest total contribution margin. This combination is often difficult to identify in an actual situation because management may have to estimate the number of units that can be sold at each price.

For example, assume that a company selling fried chicken in the New York market estimates product demand for its large bucket of chicken for a particular period to be:

 Choice Demand 1 15,000 units at $6 per unit 2 12,000 units at$7 per unit 3 10,000 units at $8 per unit 4 7,000 units at$9 per unit

The company’s fixed costs of $20,000 per year are not affected by the different volume alternatives. Variable costs are$5 per unit. What price should be set for the product? Based on the calculations shown in the table below, the company should select a price of $8 per unit because choice (3) results in the greatest total contribution margin and net income. In the short run, maximizing total contribution margin maximizes profits.  Choice Sales Price – Var. Cost = Contribution margin per unit x Number of units = Total margin Fixed costs Net income (loss) 1$6 $5$1 15,000 $15,000$20,000 $(5,000) 2$7 $5 2 12,000 24,000 20,000 4,000 3$8 $5 3 10,000 30,000 20,000 10,000 4$9 $5 4 7,000 28,000 20,000 8,000 Accept or Reject Special Orders Sometimes management has an opportunity to sell its product in two or more markets at two or more different prices. Movie theaters, for example, sell tickets at discount prices to particular groups of people—children, students, and senior citizens. Differential analysis can determine whether companies should sell their products at prices below regular levels. Good business management requires keeping the cost of idleness at a minimum. When operating at less than full capacity, management should seek additional business. Management may decide to accept such additional business at prices lower than average unit costs if the differential revenues from the additional business exceed the differential costs. By accepting special orders at a discount, businesses can keep people employed that they would otherwise lay off. To illustrate, assume Rios Company produces and sells a single product with a variable cost of$8 per unit. Annual capacity is 10,000 units, and annual fixed costs total $48,000. The selling price is$20 per unit and production and sales are budgeted at 5,000 units. Thus, budgeted income before income taxes is $12,000, as shown below.  Rios company Income statement For the period ending May 31 Revenue (5,000 units at$20) $100,000 Variable costs: Direct materials cost ($4 per unit) $20,000 Labor ($1 per unit) 5,000 Overhead ($2 per unit) 10,000 Marketing and administrative costs ($1 per unit) 5,000 Total variable costs ($8 per unit)$40,000 Fixed costs: Overhead $28,000 Marketing and administrative costs 20,000 Total fixed costs 48,000 Total costs ($17.60 per unit) 88,000 Net income $12,000 Assume the company receives an order from a foreign distributor for 3,000 units at$10 per unit. This $10 price is not only half of the regular selling price per unit, but also less than the$17.60 average cost per unit ($88,000/5,000 units). However, the$10 price offered exceeds the variable cost per unit by $2. If the company accepts the order, net income increases to$18,000.

Revenue would increase to $130,000 with the special order. Each of the variable costs increases in total by 60% because total volume increases by 60% (3,000 units in the special order/5,000 units regularly produced). The revised income statement would appear as follows:  Rios company Income statement (with Special Order) For the period ending May 31 Revenue (5,000 units at$20 + 3,000 units at $10)$130,000 Variable costs: Direct materials cost ($4)$32,000 Labor ($1) 8,000 Overhead ($2) 16,000 Marketing and administrative costs ($1) 8,000 Total variable costs ($8 per unit) $64,000 Fixed costs: Manufacturing overhead$28,000 Marketing and administrative costs 20,000 Total fixed costs 48,000 Total costs ($14 per unit) 112,000 Net income$18,000

Note that the fixed costs do not increase with the special order. Because the special order does not increase the fixed costs, the special order’s revenues need only cover its variable costs.

If Rios Company continues to operate at 50% capacity (producing 5,000 units without the special order) it would generate income of only $12,000. By accepting the special order, net income increases by$6,000 ($18,000 net income with special order –$12,000 net income without special order).

Differential analysis would provide the following calculations:

 Accept order Reject order Differential Revenues $130,000$100,000 $30,000 Costs 112,000 88,000 24,000 Net benefit of accepting order$6,000

Variable costs set a floor for the selling price in special-order situations. Even if the price exceeds variable costs only slightly, the additional business increases net income, assuming fixed costs do not change. However, pricing just above variable costs of special-order business often brings only short-term increases in net income. In the long run, companies must cover all of their costs, not just the variable costs.

Periodically, management has to decide whether to add or eliminate certain products, segments, or customers. If you have watched a store or a plant open or close in your area, you have seen the results of these decisions. Differential analysis is useful in this decision making because a company’s income statement does not automatically associate costs with certain products, segments, or customers. Thus, companies must reclassify costs as those that the action would change and those that it would not change.

If companies add or eliminate products, they usually increase or decrease variable costs. The fixed costs may change, but not in many cases. Management bases decisions to add or eliminate products only on the differential items; that is, the costs and revenues that change.

To illustrate, assume that the Campus Bookstore is considering eliminating its art supplies department. If the bookstore dropped the art supplies department, it would lose revenues of $100,000 annually. The bookstore’s management assigns costs of$110,000 ($80,000 variable and$30,000 fixed) to the art supplies department. Therefore, art supplies has an apparent annual loss of $10,000 ($100,000 revenue minus $110,000 costs). But careful cost analysis reveals that if the art supplies department were dropped, the reduction in costs would be only$80,000 variable costs directly related to the art supplies department and the $30,000 fixed costs are general bookstore fixed costs allocated to the art supplies department. These fixed costs would continue to be incurred and would not be saved by closing the art supplies department. Look at the differential analysis below.  Art Supplies Department Keep Close Differential Revenues$100,000 $-0-$100,000 Variable costs 80,000 -0- 80,000 Fixed costs 30,000 30,000 -0- Net benefit of keeping art supplies department $20,000 Note that the art supplies department has been contributing$20,000 ($100,000 revenues –$80,000 variable costs) annually toward covering the fixed costs of the business. Consequently, its elimination could be a costly mistake unless there is a more profitable use for the vacated facilities.

If the company has a profitable alternative use for the vacated facilities, the potential income from that alternative represents an opportunity cost of retaining the product, segment, or customer. Assume, for example, that the bookstore could use the facilities currently occupied by the art supplies department to open a new department to display and sell personal computers, printers, and software. This new department would contribute $35,000 to the bookstore’s income. The relevant costs in the decision to retain the art supplies department are$115,000 ($80,000 of variable manufacturing costs and$35,000 of opportunity cost of not opening a new department), while the relevant revenues are still $100,000. Therefore, the bookstore has a net disadvantage in keeping the art supplies department because it loses$15,000 compared to the computer department.

 Art Supplies PCs Differential Revenues $100,000 Variable costs -80,000 Additional Income$20,000 35,000 $15,000 Sell or Process Further Sometimes two or more products result from a common raw material or production process; these products are called joint products. Companies can process these products further or sell them in their current condition. For instance, when Chevron refines crude oil, it produces a wide variety of fuels, solvents, lubricants, and residual petrochemicals. Management can use differential analysis to decide whether to process a joint product further or to sell it in its present condition. Joint costs are those costs incurred up to the point where the joint products split off from each other. These costs are sunk costs and are not considered when deciding whether to process a joint product further before selling it or to sell it in its condition at the split-off point. The following example illustrates the issue of whether to process or sell joint products. Assume that Pacific Paper, Inc., produces two paper products, A and B, from a common manufacturing process. Each of the products could either be sold in its present form or processed further and sold at a higher price. Data for both products follow:  Product Selling price per unit at split-off point Cost per unit of further processing Selling price per unit after further processing A$10 $6$21 B 12 7 18

The differential revenues and costs of further processing of the two products are as follows:

 Product Different revenue of further processing Differential cost of further processing Net advantage (disadvantage) of further processing A $11$6 $5 B 6 7 (1) Based on this analysis, Pacific Paper should process product A further to increase income by$5 per unit sold. The company should not process product B further because that would decrease income by $1 per unit sold. Companies use this same form of differential analysis to decide whether they should discard their by-products or process them further. By-products are additional products resulting from the production of a main product and generally have a small market value compared to the main product. Sometimes companies consider by-products to be waste materials. For example, the bark from trees cut into lumber is a by-product of lumber production. Although a by-product, companies convert this bark into fuel or landscaping material. When the differential revenue of further processing exceeds the differential cost, firms should do further processing. As concerns increase about the effects of waste on the environment, companies find more and more waste materials that can be converted into by-products. Make or Buy Managers also apply differential analysis to make-or-buy decisions. A make-or-buy decision occurs when management must decide whether to make or purchase a part or material used in manufacturing another product. Management must compare the price paid for a part with the additional costs incurred to manufacture the part. When most of the manufacturing costs are fixed and would exist in any case, it is likely to be more economical to make the part rather than buy it. To illustrate the application of differential analysis to make-or-buy decisions, assume that Small Motor Company manufactures a part costing$6 for use in its toy automobile engines. Cost components are: materials, $3.00; labor,$1.50; fixed overhead costs, $1.05; and variable overhead costs,$0.45. Small could purchase the part for $5.25. Fixed overhead would presumably continue even if the part were purchased. The added costs (variable costs only) of manufacturing amount to$4.95 ($3.00 DM +$1.50 DL + $0.45 Variable OH). This amount is 30 cents per unit less than the purchase price of the part. Therefore, manufacturing the part should be continued as shown in the following analysis:  Make Buy Differential Variable Costs$4.95 $5.25$0.30 Net advantage of making \$0.30

In make-or-buy decisions, management also should consider the opportunity cost of not utilizing the space for some other purpose. In the previous example, if the opportunity costs of not using this space in its best alternative use is more than 30 cents per unit times the number of units produced, the part should be purchased.

In some manufacturing situations, firms avoid a portion of fixed costs by buying from an outside source. For example, suppose eliminating a part would reduce production so that a supervisor’s salary could be saved. In such a situation, firms should treat these fixed costs the same as variable costs in the analysis because they would be relevant costs.

Sometimes the cost to manufacture may be only slightly less than the cost of purchasing the part or material. Then management should place considerable weight on other factors such as the competency of existing personnel to undertake manufacturing the part or material, the availability of working capital, and the cost of any loans that may be necessary.