9 3: Applying Differential Analysis in Managerial Decision Making Business LibreTexts

Suppose the function
is a higher order polynomial, one that takes the shape of a curve with 2 or
more turning points. It would be easy to imagine a function where part
was below the horizontal tangent line, turned again, and came back up past the
line. The definition of concavity refers only to the part of the function
near the point where the tangent line touches the curve, it isn’t required to
hold everywhere on the curve. A very clear way to see how calculus helps us interpret economic information
and relationships is to compare total, average, and marginal functions. Although using quantitative factors for decision making is important, management must also consider qualitative factors. Using these quantitative factors to make decisions allows managers to support decisions with measurable data.

  1. The two calculations for incremental revenue and incremental cost are thus essential to determine the company’s profitability when production output is expanded.
  2. Opportunity costs—the benefits foregone when one alternative is selected over another—are differential costs, and must be included when performing differential analysis.
  3. (a) You are required to determine the differential cost of producing 1500 units by increasing capacity to 100%.
  4. The attempt to calculate and accurately predict such costs assist a company in making future investment decisions that can increase revenue and reduce costs.
  5. This new department would contribute $35,000 to the bookstore’s income.

The cost information provided by activity-based costing is generally regarded as more accurate than most traditional costing methods. Differential analysis provides a format for these types of decisions. The general rule is to select the alternative with the highest differential profit. (i) To process the entire quantity of ‘utility’ so as to convert it into 600 numbers of ‘Ace’. The concern at present produces per day 600 numbers of each of the two products for which 2,500 labour hours are utilised.

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). These fixed costs would continue to be incurred and would not be saved by closing the art supplies department.

Make or Buy Decisions

External costs are costs imposed on third parties or society as a whole, which are not accounted for by the business itself. These costs can include pollution, but they are not directly incurred by the business as a result of its decisions. Differential costs, sometimes called incremental, are the overall costs incurred while choosing between several options. Direct material and labour will be constant for the special order.

Understanding Incremental Cost

In the given problem, the company should set the level of production at 1,50,000 units because after this level differential costs exceed the incremental revenue. While variable costs fluctuate in direct proportion to production or activity levels, fixed costs are constant regardless of the degree of production. https://adprun.net/ Knowing the difference between the two makes determining which expenses apply to a certain decision easier. Differential cash flows refer to the net change in cash flows between two alternatives. Differential contribution margin is the net change in contribution margin between two choices.

Differential costs are a key idea in the fields of business and economics. Prepare differential cost analysis to ascertain acceptance or rejection of the order. The costs that do not change in the alternatives are not part of the analysis.

Format of Differential Costing

Therefore the baseball is \(3.4\) meters above Earth’s surface after \(2\) seconds. It is worth noting that the mass of the ball cancelled out completely in the process of solving the problem. Evaluate the second derivative at Q equals 24 to determine concavity.

However, management may want a more concise explanation of why profit is $10,000 higher when all three product lines are maintained. Discontinuing a product to avoid the losses and increase profits – decision to drop a product line. It is a useful tool for making strategic decisions in various business contexts. Its numerous uses are essential for maximizing revenue, allocating resources efficiently, and attaining strategic objectives. Deciding how much to charge for goods or services is an essential choice for any organization.

Differential cost is the difference in total costs between two acceptable alternative courses of action. Differential cost may be a fixed cost, variable cost, or a combination of both. Company executives use differential cost analysis to choose between options to make viable decisions to impact the company positively.

Long-run incremental cost (LRIC) is a forward-looking cost concept that predicts likely changes in relevant costs in the long run. It includes relevant and significant costs that exert a material impact on production cost and product pricing in the long run. They can include the price of crude oil, electricity, any essential raw material, etc. The calculation of incremental cost shows a change in costs as production expands. That way, we can not only evaluate
costs at a particular level, but we can see how our marginal costs are changing
as we increase or decrease our level of production.

A baseball is thrown upward from a height of \(3\) meters above Earth’s surface with an initial velocity of \(10\) m/s, and the only force acting on it is gravity. Of course, this is not realistic, and as our models become more realistic in
the multivariate section, we will add constraints differential cost formula
to our optimization problems. Note that we were able to prove average cost is minimized when Q is 12, without
having to actually determine the average cost. Recall from past section on linear
functions that the slope of a horizontal line or function is equal to

Hence, they will be considered irrelevant for decision-making, as they are not affected by increase in sales volume. However, if some additional fixed costs are incurred for increased sales volume that will be considered for computation. 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.

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