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Question 1163375: 4. Supposes that ZT owner of Sports Feet Manufacturing is considering whether to produce a new line of footwear. ZT has considered the processing needs for the new product as well as the market potential. He has also estimated that the variable cost for each product manufactured is 20 birr and the fixed cost per year is birr 80,000.
(a) If ZT offers the footwear at a selling price of birr 25, how many pairs must he sell to break even? (3pts)
(b) If ZT sells 4000 pairs at the birr 25 price, what will be the contribution to profit?(3pts)
Answer by CPhill(2264)   (Show Source):
You can put this solution on YOUR website! To determine the break-even point and potential profit for Sports Feet Manufacturing, we use basic cost-volume-profit (CVP) analysis.
### Given Data:
* **Variable Cost ($VC$):** 20 birr per pair
* **Fixed Cost ($FC$):** 80,000 birr per year
* **Selling Price ($P$):** 25 birr per pair
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### (a) Break-even Analysis
The break-even point is the quantity ($Q$) where total revenue equals total costs (profit is zero). We use the following formula:
$$Q = \frac{FC}{P - VC}$$
1. **Calculate the Contribution Margin per unit:**
$$\text{Contribution Margin} = 25 - 20 = 5 \text{ birr per pair}$$
2. **Calculate the Break-even Quantity:**
$$Q = \frac{80,000}{5} = 16,000 \text{ pairs}$$
**Result:** ZT must sell **16,000 pairs** of footwear to break even.
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### (b) Contribution to Profit at 4,000 pairs
Profit is calculated by subtracting total costs from total revenue.
$$\text{Profit} = (\text{Selling Price} \times Q) - (\text{Variable Cost} \times Q + \text{Fixed Cost})$$
$$\text{Profit} = Q(P - VC) - FC$$
1. **Substitute the values for $Q = 4,000$:**
$$\text{Profit} = 4,000(25 - 20) - 80,000$$
$$\text{Profit} = 4,000(5) - 80,000$$
$$\text{Profit} = 20,000 - 80,000$$
$$\text{Profit} = -60,000 \text{ birr}$$
**Result:** If ZT sells only 4,000 pairs, the contribution to profit is **-60,000 birr** (a loss of 60,000 birr).
> **Note:** Since 4,000 pairs is significantly below the break-even point of 16,000 pairs, the business will operate at a loss until sales increase.
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