# 10.1 Differential Analysis

#### Differential analysis

Differential analysis involves analyzing the different costs and benefits that would arise from alternative solutions to a particular problem. Relevant revenues or costs in a given situation are future revenues or costs that differ depending on the alternative course of action selected. Differential revenue is the difference in revenues between two alternatives. Differential cost or expense is the difference between the amounts of relevant costs for two alternatives.[1] Future costs that do not differ between alternatives are irrelevant and may be ignored since they affect both alternatives similarly. Past costs, also known as sunk costs, are not relevant in decision making because they have already been incurred; therefore, these costs cannot be changed no matter which alternative is selected.

For certain decisions, revenues do not differ between alternatives. Under those circumstances, management should select the alternative with the least cost. In other situations, costs do not differ between alternatives. Accordingly, management should select the alternative that results in the largest revenue. Many times both future costs and revenues differ between alternatives. In these situations, the management should select the alternative that results in the greatest positive difference between future revenues and expenses (costs).

To illustrate relevant, differential, and sunk costs, assume that Joanna Bennett invested $400 in a tiller so she could till gardens to earn$1,500 during the summer. Not long afterward, Bennett was offered a job at a horse stable feeding horses and cleaning stalls for $1,200 for the summer. The costs that she would incur in tilling are$100 for transportation and $150 for supplies. The costs she would incur at the horse stable are$100 for transportation and $50 for supplies. If Bennett works at the stable, she would still have the tiller, which she could loan to her parents and friends at no charge. The tiller cost of$400 is not relevant to the decision because it is a sunk cost. The transportation cost of $100 is also not relevant because it is the same for both alternatives. These costs and revenues are relevant (note: differential means difference):  Performing tilling service Working at horse stable Differential Revenues$1,500 $1,200$300 Costs 150 50 100 Net benefit in favor of tilling service $200 Based on this differential analysis, Joanna Bennett should perform her tilling service rather than work at the stable. Of course, this analysis considers only cash flows; nonmonetary considerations, such as her love for horses, could sway the decision. In many situations, total variable costs differ between alternatives while total fixed costs do not. For example, suppose you are deciding between taking the bus to work or driving your car on a particular day. The differential costs of driving a car to work or taking the bus would involve only the variable costs of driving the car versus the variable costs of taking the bus. Suppose the decision is whether to drive your car to work every day for a year versus taking the bus for a year. If you bought a second car for commuting, certain costs such as insurance and an auto license that are fixed costs of owning a car would be differential costs for this particular decision. Before studying the applications of differential analysis, you must realize that opportunity costs are also relevant in choosing between alternatives. An opportunity cost is the potential benefit that is forgone by not following the next best alternative course of action. For example, assume that the two best uses of a plot of land are as a mobile home park (annual income of$100,000) and as a golf driving range (annual income of $60,000). The opportunity cost of using the land as a mobile home park is$60,000, while the opportunity cost of using the land as a driving range is \$100,000.

Companies do not record opportunity costs in the accounting records because they are the costs of not following a certain alternative. Thus, opportunity costs are not transactions that occurred but that did not occur. However, opportunity cost is a relevant cost in many decisions because it represents a real sacrifice when one alternative is chosen instead of another.

In the next section, we will look at examples of differential analysis.