Math Problem Statement

Your company plans to produce a new product, a wireless computer mouse. Two machines can be used to make the mouse, Machines A and B. The price per mouse will be $25.00 regardless of which machine is used. The fixed and variable costs associated with the two machines are shown below. At the expected sales level of 90,000 units, how much higher or lower will the firm's expected EBIT be if it uses Machine B with high fixed costs rather than Machine A with low fixed costs, i.e., what is EBITB - EBITA ?

Machine A	Machine B

Price per mouse (P) $25.00 $25.00 Fixed costs (F) $100,000 $400,000 Variable cost/unit (V) $17.00 $10.00 Exp. unit sales (Q) 90,000 90,000

Solution

To calculate the difference in the expected EBIT (Earnings Before Interest and Taxes) between using Machine B and Machine A, we follow these steps:

Step 1: Calculate Total Revenue (TR) for both machines

Total Revenue (TR)=Price per mouse (P)×Expected unit sales (Q)\text{Total Revenue (TR)} = \text{Price per mouse (P)} \times \text{Expected unit sales (Q)} TR=25×90,000=2,250,000TR = 25 \times 90,000 = 2,250,000

Step 2: Calculate Total Costs (TC) for both machines

Total Costs (TC)=Fixed Costs (F)+(Variable Cost per Unit (V)×Expected unit sales (Q))\text{Total Costs (TC)} = \text{Fixed Costs (F)} + (\text{Variable Cost per Unit (V)} \times \text{Expected unit sales (Q)})

Machine A:

TCA=100,000+(17×90,000)=100,000+1,530,000=1,630,000TC_A = 100,000 + (17 \times 90,000) = 100,000 + 1,530,000 = 1,630,000

Machine B:

TCB=400,000+(10×90,000)=400,000+900,000=1,300,000TC_B = 400,000 + (10 \times 90,000) = 400,000 + 900,000 = 1,300,000

Step 3: Calculate EBIT for both machines

EBIT=Total Revenue (TR)Total Costs (TC)\text{EBIT} = \text{Total Revenue (TR)} - \text{Total Costs (TC)}

Machine A:

EBITA=2,250,0001,630,000=620,000EBIT_A = 2,250,000 - 1,630,000 = 620,000

Machine B:

EBITB=2,250,0001,300,000=950,000EBIT_B = 2,250,000 - 1,300,000 = 950,000

Step 4: Calculate the difference in EBIT (EBIT_B - EBIT_A)

Difference=EBITBEBITA=950,000620,000=330,000\text{Difference} = EBIT_B - EBIT_A = 950,000 - 620,000 = 330,000

Final Answer:

The firm's expected EBIT will be $330,000 higher if it uses Machine B instead of Machine A.

Let me know if you'd like a detailed breakdown or have more questions! Here are some additional related questions:

  1. What is the break-even point for each machine in terms of units sold?
  2. How would changes in variable costs impact the EBIT for each machine?
  3. If sales volume dropped to 70,000 units, how would the EBIT comparison change?
  4. How do fixed and variable costs impact operating leverage between the two machines?
  5. What is the margin of safety for each machine at the expected sales level?

Tip: Always analyze both fixed and variable costs when comparing production options, as they significantly influence profitability depending on sales volume.

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Math Problem Analysis

Mathematical Concepts

Cost Accounting
Profitability Analysis
EBIT Calculation

Formulas

Total Revenue (TR) = Price per unit (P) * Expected unit sales (Q)
Total Costs (TC) = Fixed Costs (F) + (Variable Cost per unit (V) * Expected unit sales (Q))
EBIT = Total Revenue (TR) - Total Costs (TC)

Theorems

Break-even analysis
Cost-volume-profit analysis

Suitable Grade Level

Grades 11-12