# 16 3.5 The Relevant Range and Nonlinear Costs

• Last updated
Dec 28, 2020
• Anonymous
• LibreTexts

## Learning Objectives

• Understand the assumptions used to estimate costs.

Question: Bikes Unlimited is making an important assumption in estimating fixed and variable costs. What is this important assumption and why might it be misleading?

Recall that Bikes Unlimited estimated costs based on projected sales of 6,000 units for the month of August. Although this is slightly higher than the highest sales of 5,900 units in April, Susan (cost accountant) determined that Bikes Unlimited had the production capacity to produce 6,000 units without significantly affecting total fixed costs or per unit variable costs. Thus she determined that a sales level of 6,000 units was still within the relevant range. However, Susan also made Eric (CFO) aware that Bikes Unlimited was quickly approaching full capacity. If sales were expected to increase in the future, the company would have to increase capacity, and cost estimates would have to be revised.

Question: Another important assumption being made by Bikes Unlimited is that all costs behave in a linear manner. Variable, fixed, and mixed costs are all described and shown as a straight line. However, many costs are not linear and often take on a nonlinear pattern. Why do some costs behave in a nonlinear way?

Definition

Two important assumptions must be considered when estimating costs using the methods described in this chapter.

1. When costs are estimated for a specific level of activity, the assumption is that the activity level is within the relevant range.
2. Costs are estimated assuming that they are linear.

Both assumptions are reasonable as long as the relevant range is clearly identified, and the linearity assumption does not significantly distort the resulting cost estimate.

## Review problem 3.8

1. Using the data in Note 3.21 “Review Problem 3.5”, identify the relevant range.
2. Why is it important to determine the relevant range?