How many pitchers of each type must be sold to break even in the coming year?
To break even in the coming year, Crane Inc. needs to sell 22,510 plastic pitchers and 19,490 glass pitchers.
Calculating Break-even Point for Crane Inc.
Introduction:
Crane Inc. sells two types of water pitchers, plastic, and glass. The plastic pitchers cost $30 for the company to produce and are sold for $40 each. On the other hand, glass pitchers cost $24 to produce and are sold for $45 each. The fixed costs for the company are $1,185,600 per year. The current sales plan includes selling 14,000 plastic pitchers and 28,000 glass pitchers in the upcoming year.
Calculations:
1. Plastic Pitchers:
The total cost for plastic pitchers = Cost per plastic pitcher * Number of plastic pitchers to be sold
Total cost for plastic pitchers = $30 * 14,000 = $420,000
2. Glass Pitchers:
The total cost for glass pitchers = Cost per glass pitcher * Number of glass pitchers to be sold
Total cost for glass pitchers = $24 * 28,000 = $672,000
3. Total Revenue:
Total revenue from selling plastic pitchers = Selling price per plastic pitcher * Number of plastic pitchers to be sold
Total revenue from plastic pitchers = $40 * 14,000 = $560,000
Total revenue from selling glass pitchers = Selling price per glass pitcher * Number of glass pitchers to be sold
Total revenue from glass pitchers = $45 * 28,000 = $1,260,000
Total revenue for both types of pitchers = $560,000 + $1,260,000 = $1,820,000
4. Break-even Calculation:
Total revenue needs to cover fixed costs = $1,820,000 - $1,185,600 = $634,400
5. Contribution Margin:
Contribution margin per plastic pitcher = Selling price per plastic pitcher - Cost per plastic pitcher = $40 - $30 = $10
Contribution margin per glass pitcher = Selling price per glass pitcher - Cost per glass pitcher = $45 - $24 = $21
6. Solving for Break-even Point:
Let x be the number of plastic pitchers and y be the number of glass pitchers to be sold.
Equation 1: $10x + $21y = $634,400
Equation 2: x + y = 42,000
Solving these equations simultaneously, we find x = 22,510 and y = 19,490.
Therefore, to break even in the coming year, Crane Inc. needs to sell 22,510 plastic pitchers and 19,490 glass pitchers.