A newly formed firm must decide on a plant location. There are two alternatives under consideration: locate near the major raw materials or locate near the major customers. Locating near the raw materials will result in lower fixed and variable costs than locating near the market, but the owners believe there would be a loss in sales volume because customers tend to favor local suppliers. Revenue per unit will be $182 in either case. Annual fixed costs ($ millions) Omaha Kansas City $1.0 Variable cost per unit $ 1.2 Expected annual demand (units) $ 45 11,475 $ 31 9,975 Using the above information, determine which location would produce the greater profit. (Omit the “$” sign in your response.) Omaha would produce the greater gross profit of $ 812358
The Correct Answer and Explanation is :
To determine which location—Omaha or Kansas City—would yield a greater profit, we need to calculate the gross profit for each option using the provided data:
Given Data:
- Revenue per unit: $182
- Annual fixed costs:
- Omaha: $1,000,000
- Kansas City: $31,000,000
- Variable cost per unit: $1.20
- Expected annual demand (units):
- Omaha: 11,475 units
- Kansas City: 9,975 units
Calculations:
- Omaha:
- Total Revenue: 11,475 units × $182/unit = $2,089,650
- Total Variable Costs: 11,475 units × $1.20/unit = $13,770
- Gross Profit: $2,089,650 (Revenue) – $1,000,000 (Fixed Costs) – $13,770 (Variable Costs) = $2,075,880
- Kansas City:
- Total Revenue: 9,975 units × $182/unit = $1,814,850
- Total Variable Costs: 9,975 units × $1.20/unit = $11,970
- Gross Profit: $1,814,850 (Revenue) – $31,000,000 (Fixed Costs) – $11,970 (Variable Costs) = -$29,197,120
Conclusion:
Omaha would produce a gross profit of $2,075,880, whereas Kansas City would incur a loss of $29,197,120. Therefore, Omaha is the preferable location for the firm.
Explanation:
- Revenue per Unit: Both locations have the same revenue per unit, so the primary differentiators are fixed costs, variable costs, and expected demand.
- Fixed Costs: Omaha’s fixed costs are significantly lower than Kansas City’s ($1,000,000 vs. $31,000,000), which substantially impacts profitability.
- Variable Costs: The variable cost per unit is the same for both locations, so it doesn’t affect the comparative analysis.
- Expected Demand: Omaha has a higher expected demand (11,475 units) compared to Kansas City (9,975 units), leading to higher total revenue.
By considering these factors, Omaha offers a more favorable financial outcome due to its lower fixed costs and higher expected demand.