A Retired Auto Mechanic Hopes To Open A Rustproofing Shop
A Retired Auto Mechanic Hopes To Open A Rustproofing Shop Customers W
A retired auto mechanic hopes to open a rustproofing shop. Customers would be local new-car dealers. Two locations are being considered, one in the center of the city and one on the outskirts. The central city location would involve fixed monthly costs of $6,890 and labor, materials, and transportation costs of $30 per car. The outside location would have fixed monthly costs of $4,300 and labor, materials, and transportation costs of $40 per car. Dealer price at either location will be $90 per car.
a. Which location will yield the greatest profit if monthly demand is (1) 200 cars? (2) 300 cars?
b. At what volume of output will the two sites yield the same monthly profit? Volume of output [removed] cars.
Paper For Above instruction
The decision to select the optimal location for a rustproofing shop involves analyzing fixed and variable costs associated with each site, as well as projected sales volumes. The primary goal is to maximize profit, which is determined by total revenue minus total costs at each location under varying demand conditions. This analysis explores the profitability implications at different demand levels and identifies the break-even point where both sites yield equivalent profits.
Introduction
Location choice significantly impacts the profitability of small service businesses such as rustproofing shops. Fixed costs represent expenses that do not fluctuate with sales volume, like rent and salaries, while variable costs vary directly with the number of cars serviced. Understanding these cost structures enables the business owner to predict profits at different demand levels and determine the most advantageous location. This paper evaluates two potential sites for a rustproofing shop considering fixed costs, variable costs, dealer pricing, and projected customer demand.
Cost and Revenue Structures
Each location's financial parameters are summarized as follows: The central city location has fixed monthly costs of $6,890 and variable costs of $30 per car. The outside location has fixed costs of $4,300 and variable costs of $40 per car. The dealer price per car is consistent at $90 for both locations. Therefore, total revenue per month at any volume of cars (Q) is calculated as:
Revenue = $90 × Q
Profit at each location is derived from total revenue minus the sum of fixed costs and variable costs, expressed mathematically as:
Profit = (Price × Quantity) - Fixed Costs - Variable Cost per Car × Quantity
Profit Calculations at Different Demand Levels
1. When monthly demand is 200 cars
Central city location:
- Total revenue: $90 × 200 = $18,000
- Total variable costs: $30 × 200 = $6,000
- Total fixed costs: $6,890
- Monthly profit: $18,000 - $6,890 - $6,000 = $5,110
Outside location:
- Total revenue: $90 × 200 = $18,000
- Total variable costs: $40 × 200 = $8,000
- Total fixed costs: $4,300
- Monthly profit: $18,000 - $4,300 - $8,000 = $5,700
Thus, at 200 cars, the outside location yields higher profit by $590.
2. When monthly demand is 300 cars
Central city location:
- Total revenue: $90 × 300 = $27,000
- Total variable costs: $30 × 300 = $9,000
- Total fixed costs: $6,890
- Monthly profit: $27,000 - $6,890 - $9,000 = $11,110
Outside location:
- Total revenue: $90 × 300 = $27,000
- Total variable costs: $40 × 300 = $12,000
- Total fixed costs: $4,300
- Monthly profit: $27,000 - $4,300 - $12,000 = $10,700
At 300 cars, the central city location is more profitable by $410.
Therefore, the outside location is preferable at lower demand (200 cars), while the central location becomes more profitable at higher demand (300 cars). This competitive advantage shifts due to fixed and variable cost differences.
Profit-Equivalence Point Calculation
To determine the demand volume (Q) at which both locations yield the same profit, we set the profit equations equal:
(Price × Q) - Fixed_Costs 1 - Variable_Costs Q = (Price × Q) - Fixed_Costs 2 - Variable_Costs Q
Replacing with specific values:
90Q - 6,890 - 30Q = 90Q - 4,300 - 40Q
Simplifying the equation:
90Q - 6,890 - 30Q = 90Q - 4,300 - 40Q
Combining like terms:
(90Q - 30Q) - 6,890 = (90Q - 40Q) - 4,300
60Q - 6,890 = 50Q - 4,300
Subtract 50Q from both sides:
10Q - 6,890 = -4,300
Add 6,890 to both sides:
10Q = 2,590
Divide both sides by 10:
Q = 259 cars
This is the volume at which both locations yield identical monthly profits, being approximately 259 cars.
Conclusion
The analysis indicates that for monthly demands of fewer than approximately 259 cars, the outside location is more profitable due to its lower fixed costs offsetting higher variable costs. Conversely, for demands exceeding this volume, the city center location becomes more advantageous because its higher fixed costs are compensated by lower variable costs and higher revenue per car. Accurate demand forecasting is critical to strategic decision-making, and additional factors such as site visibility, accessibility, and future expansion potential should also influence the final choice.
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