A firm plans to begin production of a new small appliance. The manager must deci
ID: 442404 • Letter: A
Question
A firm plans to begin production of a new small appliance. The manager must decide whether to purchase the motors for the appliance from a vendor at $9 each or to produce them in-house. Either of two processes could be used for in-house production; Process A would have an annual fixed cost of $170,000 and a variable cost of $5 per unit, and Process B would have an annual fixed cost of $190,000 and a variable cost of $4 per unit. Determine the range of annual volume for which each of the alternatives would be best. (Round your first answer to the nearest whole number. Include the indifference value itself in this answer. Enter your last answer as a whole number).
A firm plans to begin production of a new small appliance. The manager must decide whether to purchase the motors for the appliance from a vendor at $9 each or to produce them in-house. Either of two processes could be used for in-house production; Process A would have an annual fixed cost of $170,000 and a variable cost of $5 per unit, and Process B would have an annual fixed cost of $190,000 and a variable cost of $4 per unit. Determine the range of annual volume for which each of the alternatives would be best. (Round your first answer to the nearest whole number. Include the indifference value itself in this answer. Enter your last answer as a whole number).
Explanation / Answer
The point of indifference between Purchase from Process A and Process B
Machine A = Machine B
FC + VC * Q = FC + VC * Q
FC = Fixed Cost , VC = Variable Cost , Q = Number of Appliance ( Quantity in Units)
Total Cost = FC + VC * Q
$170,000 + $5Q = $190,000 + $4Q
Q = 20,000
The point of indifference between Purchase from Vendor and Process A
$9Q = $170,000 + $5Q
Q = 170,000 / 4
Q = 42500
The point of indifference between Purchase from Vendor and Process B
$9Q = $190,000 + $4Q
$5Q = $190,000
Q = 38,000
Comparing the Total Cost in the above table we conclude that
(i) For Annual Volume of 38,000 or above the manager should select production in house at $4 per unit. ( Process B)
(ii) For Annual Volume of 38,000 or less, the manager should purchase from vendor.
(iii) Process A (production in house at $5 per unit) is never the best alternative.
For annual volumes of 38,000 or less, Purchase from vendor. For annual volumes at or above that amount, it is best to produce in house at a cost of $5 per unit.
Unit Process A ( Total Cost) Process B (Total Cost) Outsource from vendor ( Total Cost) 5000 195000 210000 45000 10000 220000 230000 90000 15000 245000 250000 135000 20000 270000 270000 180000 25000 295000 290000 225000 30000 320000 310000 270000 35000 345000 330000 315000 38000 360000 342000 342000 38001 360005 342004 342009 42500 382500 360000 382500 40000 370000 350000 360000 50000 420000 390000 450000 60000 470000 430000 540000 70000 520000 470000 630000 80000 570000 510000 720000Related Questions
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