1.	Rubber and Steel Company is planning to manufacture a new product. The variable manufacturing costs will be $ 59 per unit and the fixed costs are estimated to be $ 6633. The selling price of the product is to be $144 per unit. Variable selling expense is expected to be$18 per unit.

(a) Calculate the contribution margin per unit.


(b) Determine the contribution rate.


(c) Calculate the break-even point in units.


(d) Determine the break-even point in sales dollars.


Let's solve each part step by step for the Rubber and Steel Company's cost and revenue analysis.

### (a) **Contribution margin per unit:**
The **contribution margin** per unit is calculated as the difference between the selling price and the total variable costs per unit.

\[
\text{Contribution Margin} = \text{Selling Price per unit} - (\text{Variable Manufacturing Cost per unit} + \text{Variable Selling Expense per unit})
\]

Using the given dataLet's solve each part step by step for the Rubber and Steel Company's cost and revenue analysis.

### (a) **Contribution margin per unit:**
The **contribution margin** per unit is calculated as the difference between the selling price and the total variable costs per unit.

\[
\text{Contribution Margin} = \text{Selling Price per unit} - (\text{Variable Manufacturing Cost per unit} + \text{Variable Selling Expense per unit})
\]

Using the given 
- Selling price per unit = $144
- Variable manufacturing cost per unit = $59
- Variable selling expense per unit = $18

\[
\text{Contribution Margin} = 144 - (59 + 18) = 144 - 77 = 67
\]

So, the **contribution margin per unit** is **$67**.

---

### (b) **Contribution rate:**
The **contribution rate** (also called the contribution margin ratio) is the contribution margin expressed as a percentage of the selling price.

\[
\text{Contribution Rate} = \frac{\text{Contribution Margin}}{\text{Selling Price}} \times 100
\]

\[
\text{Contribution Rate} = \frac{67}{144} \times 100 \approx 46.53\%
\]

So, the **contribution rate** is **46.53%**.

---

### (c) **Break-even point in units:**
The **break-even point in units** is the number of units that must be sold for the total revenue to cover both fixed and variable costs. It can be calculated using the formula:

\[
\text{Break-even Point (Units)} = \frac{\text{Fixed Costs}}{\text{Contribution Margin per Unit}}
\]

Using the given fixed costs:
- Fixed costs = $6633
- Contribution margin per unit = $67 (calculated in part a)

\[
\text{Break-even Point (Units)} = \frac{6633}{67} \approx 99.01
\]

Rounding up, the **break-even point** is **100 units**.

---

### (d) **Break-even point in sales dollars:**
The **break-even point in sales dollars** can be calculated by multiplying the break-even point in units by the selling price per unit. Alternatively, it can be calculated using the contribution rate:

\[
\text{Break-even Point (Sales Dollars)} = \frac{\text{Fixed Costs}}{\text{Contribution Rate}}
\]

Using the contribution rate from part b:
\[
\text{Break-even Point (Sales Dollars)} = \frac{6633}{0.4653} \approx 14250.55
\]

So, the **break-even point in sales dollars** is **$14,250.55**.

---

### Summary of Results:
- **(a) Contribution Margin per Unit** = $67
- **(b) Contribution Rate** = 46.53%
- **(c) Break-even Point (Units)** = 100 units
- **(d) Break-even Point (Sales Dollars)** = $14,250.55

Do you want further details or have any questions? 

---

Here are some related questions to explore this further:

1. How would an increase in fixed costs affect the break-even point?
2. What is the impact on contribution margin if variable manufacturing costs increase?
3. How would reducing the selling price affect the break-even sales dollars?
4. If fixed costs increase to $8000, what is the new break-even point in units?
5. What would the contribution margin be if the variable selling expense decreased to $15 per unit?

**Tip:** Always monitor both variable and fixed costs, as changes to either can significantly impact profitability and the break-even point.

Rubber and Steel Company is planning to manufacture a new product. The variable manufacturing costs will be $59 per unit and the fixed costs are estimated to be $6633. The selling price of the product is to be $144 per unit. Variable selling expense is expected to be $18 per unit. (a) Calculate the contribution margin per unit. (b) Determine the contribution rate. (c) Calculate the break-even point in units. (d) Determine the break-even point in sales dollars.

Learn how to calculate the contribution margin, contribution rate, and break-even point in both units and sales dollars for Rubber and Steel Company's new product. This example includes detailed steps and essential cost-volume-profit analysis concepts, making it ideal for business and finance students.

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