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ABC Company is the manufacturer of a low-noise air-purification system. Its curr...
Sep 8, 2024
ABC Company is the manufacturer of a low-noise air-purification system. Its current capacity is 5,000 units/month, but ABC received orders totaling 4,500 units each month. Currently, ABC sells its system at a price of 100perunit,itsfixedcostis100 per unit, its fixed cost is 125,000/month, and its variable cost is 50/unit.Notethatcurrently,halfofABC’svariablecostismaterials,andtheotherhalfislaborcost(wagesforworkers).ABCwantstoconsidercuttingitspriceby1050/unit. Note that currently, half of ABC’s variable cost is materials, and the other half is labor cost (wages for workers). ABC wants to consider cutting its price by 10% to stimulate demand. If ABC expands its capacity, it will have to lease additional manufacturing machines, each of which will cost 5,000/month to lease and can add 500 units to ABC’s capacity. All existing workers are already working full-time. So, if ABC expands production, ABC has to either pay existing employees for overtime (1.5 times the regular wages) or hire new workers, who are expected to be paid 90% of the hourly wage of existing workers but produce only 75% of the hourly output of existing workers. (a) What is ABC’s current monthly profit (before the price cut)? (2 points) (b) What is the product’s per-unit variable cost for new workers? Should ABC use new workers rather than pay overtime wages to existing employees if it wants to expand production? (2 points) (c) What are the incremental breakeven unit sales for the 10% price cut? If ABC’s monthly order is estimated to increase by no more than 24% after the 10% price cut, should ABC implement the price cut? (6 points)
Solution by Steps
(a)
step 1
To calculate ABC's current monthly profit, we first determine total revenue, total costs, and then profit. The total revenue is given by the formula: Total Revenue=Price per unit×Units sold=100×4500\text{Total Revenue} = \text{Price per unit} \times \text{Units sold} = 100 \times 4500
step 2
Next, we calculate total costs, which include fixed costs and variable costs. The total variable cost is calculated as: Total Variable Cost=Variable Cost per unit×Units sold=50×4500\text{Total Variable Cost} = \text{Variable Cost per unit} \times \text{Units sold} = 50 \times 4500
step 3
Now, we can find total costs: Total Costs=Fixed Costs+Total Variable Cost=125000+(50×4500)\text{Total Costs} = \text{Fixed Costs} + \text{Total Variable Cost} = 125000 + (50 \times 4500)
step 4
Finally, we calculate profit: Profit=Total Revenue−Total Costs\text{Profit} = \text{Total Revenue} - \text{Total Costs}
Answer
ABC's current monthly profit is $75,000.
(b)
step 1
To find the per-unit variable cost for new workers, we first determine the wage for new workers. If existing workers earn 50,newworkersearn:50, new workers earn: New Worker Wage=0.9×50\text{New Worker Wage} = 0.9 \times 50$
step 2
Next, we calculate the output of new workers. If existing workers produce 1 unit, new workers produce: New Worker Output=0.75×1\text{New Worker Output} = 0.75 \times 1
step 3
The per-unit variable cost for new workers is then calculated as: Per-unit Variable Cost=New Worker WageNew Worker Output\text{Per-unit Variable Cost} = \frac{\text{New Worker Wage}}{\text{New Worker Output}}
step 4
We compare this cost with the overtime cost of existing workers, which is: Overtime Cost=1.5×50\text{Overtime Cost} = 1.5 \times 50
Answer
The per-unit variable cost for new workers is 60,whileovertimecosts60, while overtime costs 75. ABC should use new workers.
(c)
step 1
To find the incremental breakeven unit sales after a 10% price cut, we first calculate the new price: New Price=100×(1−0.1)\text{New Price} = 100 \times (1 - 0.1)
step 2
Next, we calculate the contribution margin per unit: Contribution Margin=New Price−Variable Cost=(90−50)\text{Contribution Margin} = \text{New Price} - \text{Variable Cost} = (90 - 50)
step 3
The fixed costs will increase due to leasing additional machines. If x x machines are leased, the new fixed cost is: New Fixed Costs=125000+5000x\text{New Fixed Costs} = 125000 + 5000x
step 4
The breakeven point in units is given by: Breakeven Units=New Fixed CostsContribution Margin\text{Breakeven Units} = \frac{\text{New Fixed Costs}}{\text{Contribution Margin}}
step 5
We then calculate the estimated increase in monthly orders: Estimated Orders=4500×(1+0.24)\text{Estimated Orders} = 4500 \times (1 + 0.24)
step 6
Finally, we compare the breakeven units with the estimated orders to determine if the price cut should be implemented
Answer
The incremental breakeven unit sales is 1,389 units. With estimated orders of 5,580 units, ABC should implement the price cut.
Key Concept
Understanding profit calculation, variable costs, and breakeven analysis is crucial for business decision-making.
Explanation
The answers provide insights into ABC's profitability, cost management, and pricing strategy, essential for maximizing revenue and efficiency.
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