Cost relationships may change at output levels outside of the relevant range

The relevant range refers to a specific activity level that is bounded by a minimum and maximum amount. Within the designated boundaries, certain revenue or expense levels can be expected to occur. Outside of that relevant range, revenues and expenses will likely differ from the expected amount. The concept of the relevant range is particularly useful in two forms of analysis, which are noted below.

Budgeting Relevant Range

When a company constructs a budget for a future period, it makes assumptions about the relevant range of activities within which the business is likely to operate. As long as the actual activity volume falls somewhere within the relevant range, and other assumptions are valid, budgeted revenues and expenses are more likely to be correct. In this case, the relevant range is most likely to be fairly close to the current activity level of a business, with minor modifications.

Cost Accounting Relevant Range

The assumed cost of a product, service, or activity is likely to be valid within a relevant range, and less valid outside of that range. in particular, a "fixed" cost is likely to remain fixed only within a relevant range of activity. Also, volume discounts from suppliers are only valid for certain purchasing volume quantities.

Examples of Relevant Range

For example, ABC Company constructs a budget within a relevant revenue range of no more than $20 million. If actual sales were to exceed that amount, then ABC would need to construct a new manufacturing facility.

As another example, ABC Company assumes that the cost of a green widget is $10.00 within a relevant range of no less than 5,000 units per year and no more than 15,000 units per year. If the actual unit volume is less than 5,000 units, the purchased cost of materials increases sufficiently to make the assumed cost of $10.00 per unit too low. Conversely, if the actual unit volume is higher than 15,000 units, the purchased cost of materials decreases sufficiently to make the assumed cost of $10.00 per unit too high.

As a third example, if ABC Company were to produce more than 20,000 of its yellow LED lights, it would need a third shift to produce them, which would require an additional $70,000 annual salary for a shift supervisor. Thus, the initial cost of the LED light is only valid for a relevant range that stops at 20,000 units. Above that amount, a new relevant range can be assumed for a different cost that assumes the inclusion of the cost of the shift supervisor in the cost of the product.

As a fourth example, ABC Company constructs a manufacturing facility, which has a fixed cost of $10 million to operate and maintain every year. However, if production levels exceed 3 million units per year, then this fixed cost will increase, because of additional wear and tear on the facility. Thus, the relevant range of this fixed cost is up to a maximum of 3 million units per year.

The relevant range is the range of activity where the assumption that cost behavior is a straight line (linear) is reasonably valid. Managerial accountants like to assume that the relationship between a cost and an activity run in a straight line. As an example, if you make 10 widgets, and the direct materials in the widget cost $1, then the assumption would be that for each widget above 10, you would need to purchase another $1 worth of direct materials.

What might make this not be the case? Perhaps, there is a discount on additional direct material at a given point. So from a relevant range standpoint, we need to determine at what point that number will change. Perhaps we get a discount after we purchase 100 components, at which time the cost of direct material will drop to .80 per widget. With variable costs then, the relevant range will be the range where the cost of adding one more, will be the same as the last. In this example, from 0-100 widgets, each additional widget will add $1 in cost to our direct materials. Once we go above 100, we are outside of the relevant range.

In fixed expenses, if our facility is designed to build 5,000 widgets per month, what will happen when we reach sales of 5,001 widgets? We will need to add to our space, thus increasing our fixed expenses.

Example

Frank’s Bikes manufacturers children’s bikes. They store the finished inventory in a rented warehouse which is designed to accommodate 25,000 bikes at one time. The warehouse rent per annum is $100,000 regardless of the number of bikes parked there, so it is a fixed cost.

During the financial year 2014, sales dropped but they kept producing bikes so they ended up with too many bikes to store in the rented space. Their ending inventory was 35,000 bikes! They had to rent another space for $50,000 to store the extra finished goods inventory.

The new warehouse will be big enough until they reach 55,000 bikes, so the total rent will remain at $150,000 until that time. Hopefully, they get manufacturing and sales aligned before that happens, but for now, that is the new relevant range.

The following graph explains the concept of relevant range. X-axis plots the number of units while Y-axis shows cost.

If they have 25,001 motor bikes in stock, they need the second warehouse! So the relevant range for the cost of $100,000 for rent would be from 0-25,000  bikes. From 25,001 to 55,000 bikes their rent would jump to $150,000. What would happen if they had 55,001 bikes that needed to be stored?

Why would cost behavior change outside of the relevant range?

What is a cost that changes with the level of output?

What is a cost that does not change when output changes?

What is the cost that remains unchanged within a relevant range of output?