# Differential Analysis

Differential analysis (also called incremental analysis) is a management accounting technique in which we examine only the changes in revenues, costs and profits that result from a business decision instead of creating complete income statements for each alternative.

Differential revenue (also called incremental revenue) is change in revenues that results from accepting one alternative over the other. Differential costs/expenses are the increase or decrease in costs/expenses that occur as a result of a decision.

Differential Revenue
= Revenue under Option A – Revenue under Option B

Differential Costs
= Costs under Option A – Costs under Option B

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. Similarly, differential profit (or loss) is the combined effect of differential revenues and differential costs. It is the net effect of a course of action on a company’s bottom line.

Differential Profit (Loss) = Differential Revenue – Differential Costs

Differential analysis is useful in CVP analysis. It is because we do not need to prepare complete income statements for both scenarios to arrive at a conclusion. We just need to consider only such revenues and costs which change.

## Example

The exact layout of the incremental analysis depends on the decision being analyzed. The following example illustrate how the process works.

Adam Sports, Inc. is a manufacturer of sports goods. In the last financial year, it sold 100,000 units at \$100 per unit. Its variable cost ratio is 60% and its fixed costs are \$2 million. Using differential analysis, find out the increase in profit if (a) units sold increase by 15%, (b) units sold increase by 10% and variable cost per unit decreases by 5% and (c) sales (in dollars) increase by 10% and fixed costs increase by 5%.

### Solution

#### Scenario A

 Differential revenue \$1,500,000 \$100 × 100,000 × 15% Differential variable costs (\$900,000) \$1,500,000 × 60% Differential profit \$600,000 \$1,500,000 - \$900,000

Since there is no change in fixed costs in Scenario A, we can also use the company’s contribution margin ratio to find out the increase in profit just from the increase in sales.

Contribution Margin Ratio
= 1 – Variable Cost Ratio
= 1 – 60%
= 40%

Differential Profit
= Increase in Sales × Contribution Margin Ratio
= \$1,500,000 × 40%
= \$600,000

#### Scenario B

 Differential revenue \$1,000,000 \$100 × 100,000 × 10% Differential variable cost per unit \$57 \$100 × 60% × (1 – 5%) Differential total variable costs (\$570,000) \$57 × 10,000 Differential contribution margin \$430,000 \$1,000,000 - \$570,000 Differential fixed costs - No change in fixed costs Differential profit \$430,000

#### Scenario C

 Differential units 10,000 100,000 × 10% Differential revenue \$1,000,000 \$100 × 10,000 Differential contribution margin \$400,000 \$1,000,000 × 40% Differential fixed costs (\$100,000) \$2,000,000 × 5% Differential profit \$300,000 \$400,000 - \$300,000