If the variable cost per unit to produce a skateboard is​ $15 and the contribution rate is​ 30%, what is the contribution​ margin?

To determine the contribution margin per unit, we need to understand the relationship between the contribution rate and the selling price of the skateboard.

The contribution rate (or contribution margin ratio) represents the percentage of the selling price that contributes to covering fixed costs and generating profit. We have:

- Variable cost per unit: $15$
- Contribution rate: $30\%$ or $0.30$

Let's denote:
- Selling price per unit as $P$
- Contribution margin per unit as $CM$

The contribution margin ratio formula is:

\[
\text{Contribution Margin Ratio} = \frac{\text{Contribution Margin (CM)}}{\text{Selling Price (P)}}
\]

Rearrange to find $CM$:

\[
CM = \text{Contribution Margin Ratio} \times P
\]

Since we know the variable cost and contribution margin ratio, we can find $P$ first by using:

\[
\text{Contribution Margin Ratio} = \frac{P - \text{Variable Cost}}{P}
\]

Substitute values and solve for $P$:

\[
0.30 = \frac{P - 15}{P}
\]

Multiply both sides by $P$ to eliminate the denominator:

\[
0.30P = P - 15
\]

Rearrange to solve for $P$:

\[
P - 0.30P = 15
\]

\[
0.70P = 15
\]

\[
P = \frac{15}{0.70}
\]

\[
P = 21.43
\]

Now, calculate the contribution margin:

\[
CM = P - \text{Variable Cost}
\]

\[
CM = 21.43 - 15
\]

\[
CM = 6.43
\]

### Answer:
The contribution margin per unit is **$6.43**.

Would you like further explanation or have any questions?

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### Related Questions:
1. How would the contribution margin change if the contribution rate increased to 40%?
2. What is the impact on profitability if the variable cost per unit is reduced to $12?
3. How do fixed costs impact the overall profit given a specific contribution margin?
4. What is the break-even point in units if fixed costs are $1,000?
5. How would a change in selling price affect the contribution rate and margin?

### Tip:
Knowing the contribution margin is essential for determining the break-even point and making decisions on pricing, production levels, and cost control.

If the variable cost per unit to produce a skateboard is $15 and the contribution rate is 30%, what is the contribution margin?

Discover how to calculate the contribution margin for skateboard production when the variable cost is $15 and the contribution rate is 30%. Learn the key formulas and steps involved in finding that the contribution margin per unit is $6.43.

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