Dear Professor Cram:

Can you explain how to solve for fixed costs, variable costs, and total costs?

Renee, Bahamas

Thanks for your question, Renee.

Since I don't know how much you already know, let's start with some definitions.

- Fixed costs are those costs which do not change as production or sales change within a relevant range.
- Variable costs are directly proportional to sales or production volumes.
- Mixed costs have components of both but can be divided into their fixed and variable components.

The challenge is identifying costs and determining whether they are fixed, variable, or mixed (and then splitting out the mixed into fixed and variable.)

By reviewing costs at two different production or sales levels, it is possible to determine the variable rates (just like finding the slope of a line in algebra.)

- Variable Costs = (cost per unit) X (number of units)

- Total Costs = (fixed costs) + (variable costs)

Here is a simplistic example to demonstrate the concept:

## Bogus Manufacturing Company – selected data

- Five sales reps are paid 5% commissions plus $500 monthly salary each
- Utilities cost $1,000 per month plus $0.10 per unit manufactured
- Materials cost is $0.75 per unit
- Equipment cost $500,000 and has an expected life of 3,000,000 units with no salvage value
- Rent is $10,000 per month
- Other salaries are $20,000 per month

From these, we can identify the fixed and variable costs:

- Five sales reps are paid 5% commissions plus $500 monthly salary each
- Fixed Costs = $500/month X 5 sales reps = $2,500 per month

- Variable Costs = 5% of sales

- Utilities cost $1,000 per month plus $0.10 per unit manufactured
- Fixed Costs = $1,000 per month

- Variable Costs = $0.10 per unit produced

- Materials cost is $0.75 per unit
- Variable Costs = $0.75 per unit produced (under GAAP this will go into inventory until sold and then show up in the Cost of Goods Sold – I am going to ignore that in this example and recognize the cost as we use the materials)

- Equipment cost $50,000 and has an expected life of 3,000,000 units with no salvage value
- Depreciation here will be on units of production method at rate of $500,000/3,000,000 units = $0.1667 per unit in Variable Costs

- Rent is $10,000 per month Fixed Costs
- Other salaries are $20,000 per month Fixed Costs

Let's group the costs:

- Fixed Costs
- $ 2,500 per month for 5 sales reps
- $ 1,000 per month Utilities
- $ 10,000 per month Rent
__+ $20,000__per month Salaries- $33,500 per month Fixed Costs

- Variable Costs
- $ 0.05 per unit sales commissions (5%)
- $ 0.75 per unit produced Materials
- $ 0.10 per unit Utilities
__+ $0.1667__per unit Depreciation- $1.0167 per unit Variable Costs

Now that we have identified the cost components, let us solve for Total Cost. Let's expand the example data:

- Manufacture and sell 100,000 units at a Selling Price of $3.50 per unit during one month
- Fixed Costs are $33,500
- Variable Costs are 5% of sales + $1.0167/unit

From this data, we can find variable costs (VC) and total costs (TC)

- [Sales are $350,000 (100,000 units @ $3.50 each)]
- VC = 5% X $350,000 + 100,000 X $1.01667
- VC = $17,500 + $101,667 = $119,167
- TC = FC + VC
- TC = $33,500 + $119,167 = $152,667

From this, we know a lot of things. We can calculate their profit. We can even figure what sales are required to just break even called Break Even Point.

I hope this helps. Let us know if you need anything else.

Good Studying,

Professor Cram