Question

Two different manufacturing processes are being considered for making a new product. The first process is less capital-intensive, with fixed costs of only $50,000 per year and variable costs of $700 per unit. The second process has fixed costs of $400,000 but has variable costs of only $200 per unit. a. What is the break-even quantity beyond which the second process becomes more attractive than the first

Answer 1

Answer:

700 units

Explanation:

fixed cost for first process ( F₁ ) = $50000

variable costs of first process ( V₁ ) = $700

fixed cost of second process ( F₂ ) = $400000

variable cost of second process ( V₁ ) = $200

break-even quantity ( y ) = ?

note : variable costs are costs that vary/change as the quantity of goods and services produced changes

A) the break-even quantity beyond which the second process can be calculated by equating the total costs of both processes

F₁ + V₁ ( y ) = F₂ + V₂( y )

50000 + 700 y = 400000 + 200 y

500 y = 400000 - 50000

therefore y = 700 ( break even quantity beyond which the second process is attractive )

Answer 2

Answer:

700 units

Explanation:

FC1 : Fixed Costs from process 1

VC1 : Variable cost per unit from process 1

FC2 : Fixed Costs from process 2

VC2 : Variable cost per unit from process 2

FC1 = $50,000

VC1 = $700 per unit

FC2 = $400,000

VC2 = $200 per unit

To calculate the break-even (quantity) point we must equate the TC1 (Total cost of process 1) to TC2 (Total cost of process 2)

TC1 = TC2

FC1 + VC1(y) = FC2 + VC2(y)      where y is the break-even units

50,000 + 700y = 400,000 + 200y

500y = 350,000

y = 350,000 / 500

y = 700 Units