Question

Stahelin Valves produces a single component, a valve. The valve sells for $34 per unit. Fixed costs are $1,596,000 annually. Production and sales of 406,100 units annually results in profit before taxes of $1,246,700. What is the unit variable cost?

Answer 1

To find the unit variable cost, you can use the contribution margin approach. The contribution margin is the amount left after covering the variable costs, which goes towards covering the fixed costs and generating profit.

Let's denote the unit variable cost as "VC."

The total contribution margin can be calculated as follows:

Total Contribution Margin = (Selling Price per Unit - Unit Variable Cost) * Number of Units Sold

Given:
- Selling Price per Unit = $34
- Number of Units Sold = 406,100
- Fixed Costs = $1,596,000
- Profit Before Taxes = $1,246,700

We can set up the equation:

Total Contribution Margin = (34 - VC) * 406,100

Now, we can solve for VC:

Total Contribution Margin = Profit Before Taxes + Fixed Costs

(34 - VC) * 406,100 = 1,246,700 + 1,596,000

(34 - VC) * 406,100 = 2,842,700

Now, divide both sides by 406,100 to solve for VC:

34 - VC = 2,842,700 / 406,100

34 - VC = 7

VC = 34 - 7

VC = $27

So, the unit variable cost is $27 per valve.