


Last year, a battery manufacturing company in Toronto incurred a loss of $713,000.00

• Question 1 (3)

by producing and selling 36,000 batteries. If their total revenue for the year was $15,300,000.00 and the break-even volume of the plant is 55,400 batteries, calculate:

• Question 2 (3)




• Question 3 (3)

a. The selling price of each battery

• Question 4 (3)




• Question 5 (4)

Round to the nearest cent

Question 6 (3)




Question 7 (3)

b. The variable costs for each battery

Question 8 (3)







Round to the nearest cent


Let's break down and solve the problem step by step.

### Given:
- **Total Revenue**: \$15,300,000.00
- **Total Number of Batteries Sold**: 36,000 batteries
- **Total Loss**: \$713,000.00
- **Break-even Volume**: 55,400 batteries

### Question 3a: The selling price of each battery
To calculate the selling price per battery, we use the formula:

\[
\text{Selling Price per Battery} = \frac{\text{Total Revenue}}{\text{Total Number of Batteries Sold}}
\]

\[
\text{Selling Price per Battery} = \frac{15,300,000.00}{36,000}
\]

\[
\text{Selling Price per Battery} = \$425.00
\]

**Answer: The selling price of each battery is \$425.00**

### Question 7b: The variable costs for each battery

First, let's understand the loss incurred. The company lost \$713,000. This loss can be attributed to the difference between the revenue generated by selling 36,000 batteries and the costs (fixed + variable costs).

#### Total Cost Incurred:
Total cost incurred by the company can be calculated as:

\[
\text{Total Cost} = \text{Total Revenue} + \text{Total Loss}
\]

\[
\text{Total Cost} = 15,300,000 + 713,000 = 16,013,000
\]

#### Fixed Costs:
The break-even point occurs when total costs equal total revenue, and there is no profit or loss. At the break-even volume, the revenue covers both fixed and variable costs.

Let $ F $ be the fixed costs and $ V $ be the variable cost per battery. At the break-even point:

\[
\text{Total Revenue at Break-even} = \text{Selling Price per Battery} \times \text{Break-even Volume}
\]

\[
F + V \times \text{Break-even Volume} = \text{Selling Price per Battery} \times \text{Break-even Volume}
\]

Substituting the values:

\[
F + 55,400V = 55,400 \times 425
\]

\[
F + 55,400V = 23,545,000
\]

Now, we know that the total costs for 36,000 batteries were $ \$16,013,000 $:

\[
F + 36,000V = 16,013,000
\]

By solving these two equations, we can find $ F $ and $ V $.

1. First, calculate $ F $ from the break-even equation:

\[
F = 23,545,000 - 55,400V
\]

2. Substitute this into the total cost equation:

\[
23,545,000 - 55,400V + 36,000V = 16,013,000
\]

\[
23,545,000 - 19,400V = 16,013,000
\]

\[
19,400V = 23,545,000 - 16,013,000
\]

\[
19,400V = 7,532,000
\]

\[
V = \frac{7,532,000}{19,400}
\]

\[
V \approx 388.35
\]

**Answer: The variable cost per battery is approximately \$388.35.**

Would you like to go over any of these steps in detail or have any questions? Here are some related questions:

1. What would happen to the break-even volume if the selling price per battery increased?
2. How can the company reduce its break-even volume?
3. If the company produced and sold 55,400 batteries, what would be their profit or loss?
4. How do fixed costs influence the break-even point?
5. If the variable costs increased by 10%, how would it affect the overall profit or loss?
6. What strategies can the company use to lower its variable costs?
7. How would a decrease in total revenue impact the break-even volume?
8. What is the significance of knowing the break-even volume in business planning?

**Tip**: When analyzing business costs, always consider both fixed and variable costs to get a clear picture of the company's financial health.

Understand the financial implications of battery production for a Toronto-based company. Calculate selling price, variable costs, and break-even volume using detailed examples and formulas. Essential insights for business managers and analysts.

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