Answer :
Lathe B has a lower break-even quantity, indicating that it would require fewer sales to cover its costs compared to Lathe A.
The break-even number of gears and revenue at break-even for Lathe A and Lathe B.
We can use the given formulas:
BEP(x) = F / (P - V)
BEP($) = F / (1 - V/P)
Profit = (P - V) * x - F
Data:
Price of gear (P) = $150
Cost to make a gear on Lathe A (V_A) = $75
Cost to make a gear on Lathe B (V_B) = $12
Cost of Lathe A (F_A) = $580,000
Cost of Lathe B (F_B) = $175,000
Sales forecast (x) = 1,200 gears
(a) Break-even number of gears for Lathe A and revenue at break-even:
BEP_A(x) = F_A / (P - V_A)
BEP_A(x) = $580,000 / ($150 - $75)
BEP_A(x) = $580,000 / $75
BEP_A(x) ≈ 7,733.33 gears (rounded up to the nearest whole gear)
Revenue at break-even for Lathe A:
Revenue_A = P * BEP_A(x)
Revenue_A = $150 * 7,733.33
Revenue_A ≈ $1,160,000 (rounded to the nearest dollar)
(b) Break-even number of gears for Lathe B and revenue at break-even:
BEP_B(x) = F_B / (P - V_B)
BEP_B(x) = $175,000 / ($150 - $12)
BEP_B(x) = $175,000 / $138
BEP_B(x) ≈ 1,268.12 gears (rounded up to the nearest whole gear)
Revenue at break-even for Lathe B:
Revenue_B = P * BEP_B(x)
Revenue_B = $150 * 1,268.12
Revenue_B ≈ $190,218 (rounded to the nearest dollar)
(c) Based on the break-even analysis, the decision on which lathe to purchase depends on the sales forecast and cost considerations. If the sales forecast is expected to exceed the break-even quantity, then the lathe with the lower break-even quantity should be chosen.
However, other factors such as the quality, capacity, maintenance, and future growth potential of the lathes should also be considered in the purchasing decision.
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