Harvey Automobiles uses a standard part in the manufacture of several of its trucks. The cost of producing 50,000 parts is $170,000, which includes fixed costs of $80,000 and variable costs of $90,000. By outsourcing the part, the company can avoid 30% of the fixed costs. If Harvey Automobiles buys the part, what is the most Harvey Automobiles can spend per unit so that operating income equals the operating income from making the part?
A)$3.40
B)$2.92
C)$3.88
D)$1.60

Question

Quizplus · Accepted Answer

To find the maximum cost per unit, we need to compare the operating income from making the part to the operating income from buying the part.

Operating income from making the part:
Revenue = 50,000 units x Price per unit
Variable costs = $90,000
Fixed costs = $80,000
Operating income = Revenue - Variable costs - Fixed costs
Operating income = 50,000x - 90,000x - 80,000
Operating income = -40,000x + 80,000, where x is the price per unit.

Operating income from buying the part:
Cost per unit = $170,000/50,000 = $3.40
30% of fixed costs saved = $80,000 x 0.30 = $24,000
New fixed cost = $80,000 - $24,000 = $56,000
Cost per unit = $3.40 x 70% + $56,000/50,000 = $2.92

If Harvey Automobiles buys the part for $2.92 per unit, the operating income is:
Revenue = 50,000 units x $2.92 per unit = $146,000
Variable costs = $0 (since they are buying the part)
Fixed costs = $56,000
Operating income = Revenue - Variable costs - Fixed costs
Operating income = $146,000 - $0 - $56,000 = $90,000

Setting the operating income from buying the part equal to the operating income from making the part:
-$40,000x + $80,000 = $90,000
-$40,000x = $10,000
x = -$10,000/$40,000
The highest price per unit that Harvey Automobiles can pay and still have the same operating income is $0.25 less than the cost to produce it themselves, which is $3.40 - $0.25 = $3.15 per unit. Since this is not one of the answer choices, we round up to the next option, which is $2.92 per unit. Therefore, the best choice is B.

Harvey Automobiles Uses a Standard Part in the Manufacture of Several