Costs can be classified into two categories, fixed and variable costs. These costs behave differently based on the level of sales volumes. Suppose we are running a restaurant and have identified certain costs along with the number of annual units sold of 1000.
Item: Raw Materials (cost for hamburgers)
Total Annual Cost: 650
Item: Building Rent
Total Annual Cost: 9000
Identify which cost item above is fixed and variable and why? What is the cost per unit of each? Suppose we increased our sales volume to 6000 units and then to 8000 units the following year (and are still within the relevant range), what would be the total annual cost and unit cost of fixed and variable costs?
To identify which cost item is fixed and variable, we need to understand their behavior with changes in sales volume.
Fixed costs remain constant regardless of the number of units sold. These costs typically include expenses like building rent. In this case, the building rent cost of $9000 is fixed because it does not change with the number of hamburgers sold.
Variable costs, on the other hand, fluctuate directly with the number of units sold. These costs are typically related to the production of goods or services. In this case, the raw materials cost for hamburgers, which is $650, is a variable cost because it changes with the number of units sold.
Next, let's calculate the cost per unit for each item:
Cost per unit of raw materials = Total annual cost of raw materials / Number of units sold
Cost per unit of raw materials = $650 / 1000 = $0.65 per unit
Since the building rent is a fixed cost, the cost per unit remains the same regardless of the number of units sold. Therefore, the cost per unit of building rent is:
Cost per unit of building rent = Total annual cost of building rent / Number of units sold
Cost per unit of building rent = $9000 / 1000 = $9 per unit
Now, let's calculate the total annual cost and unit cost for fixed and variable costs assuming different sales volumes:
For 6000 units sold:
Fixed cost: Building rent remains constant at $9000
Variable cost: Raw materials cost per unit = $0.65
Total annual cost of raw materials for 6000 units = Raw materials cost per unit * Number of units sold = $0.65 * 6000 = $3900
Total annual cost = Fixed cost + Variable cost
Total annual cost = $9000 + $3900 = $12900
Unit cost = Total annual cost / Number of units sold
Unit cost = $12900 / 6000 = $2.15 per unit
For 8000 units sold:
Fixed cost: Building rent remains constant at $9000
Variable cost: Raw materials cost per unit = $0.65
Total annual cost of raw materials for 8000 units = Raw materials cost per unit * Number of units sold = $0.65 * 8000 = $5200
Total annual cost = Fixed cost + Variable cost
Total annual cost = $9000 + $5200 = $14200
Unit cost = Total annual cost / Number of units sold
Unit cost = $14200 / 8000 = $1.775 per unit
In summary:
For 6000 units sold, the total annual cost is $12900, with a unit cost of $2.15 for fixed and variable costs.
For 8000 units sold, the total annual cost is $14200, with a unit cost of $1.775 for fixed and variable costs.
In the given scenario, let's analyze the costs based on their behavior and calculate their cost per unit for the initial sales volume of 1000 units:
1. Raw Materials (cost for hamburgers):
- Behavior: This cost is directly related to the number of units sold and therefore varies with changes in sales volume.
- Cost per unit: Total annual cost / Total annual units sold
Cost per unit = 650 / 1000
Cost per unit = $0.65
2. Building Rent:
- Behavior: This cost remains constant regardless of the number of units sold and is not impacted by sales volume.
- Cost per unit: Since this is a fixed cost, it does not change with sales volume and remains the same irrespective of the number of units sold.
Cost per unit = $9000 / 1000
Cost per unit = $9
Now let's calculate the total annual cost and unit cost for both fixed and variable costs when the sales volume increases to 6000 units and then to 8000 units in subsequent years.
For the increased sales volume of 6000 units:
1. Raw Materials:
- Total annual cost: Cost per unit * Total annual units sold
Total annual cost = $0.65 * 6000
Total annual cost = $3900
- Cost per unit: Total annual cost / Total annual units sold
Cost per unit = $3900 / 6000
Cost per unit = $0.65
2. Building Rent:
- Total annual cost: This remains unchanged as it is a fixed cost and not affected by the increase in sales volume.
Total annual cost = $9000
- Cost per unit: Since this is a fixed cost, it does not change with sales volume and remains the same.
Cost per unit = $9000 / 6000
Cost per unit = $1.50
For the increased sales volume of 8000 units:
1. Raw Materials:
- Total annual cost: Cost per unit * Total annual units sold
Total annual cost = $0.65 * 8000
Total annual cost = $5200
- Cost per unit: Total annual cost / Total annual units sold
Cost per unit = $5200 / 8000
Cost per unit = $0.65
2. Building Rent:
- Total annual cost: This remains unchanged as it is a fixed cost and not affected by the increase in sales volume.
Total annual cost = $9000
- Cost per unit: Since this is a fixed cost, it does not change with sales volume and remains the same.
Cost per unit = $9000 / 8000
Cost per unit = $1.125
To summarize:
- Raw Materials (cost for hamburgers) is a variable cost, which means it varies based on the number of units sold. Its cost per unit remains constant at $0.65, regardless of the sales volume.
- Building Rent is a fixed cost, which means it remains constant regardless of the number of units sold. Its cost per unit changes with different sales volumes ($9 for 1000 units, $1.50 for 6000 units, and $1.125 for 8000 units).