Question

In: Operations Management

ABC’s production line of the Widget gadget has a fixed cost of $200,000 and the variable...

ABC’s production line of the Widget gadget has a fixed cost of $200,000 and the variable cost is $5 per unit.

a) If the company sells the first 9,000 units at a price of $20 and then sells all additional units at $17 per unit, what is the break-even point?

b) Suppose that the company is considering outsourcing this to DEF company. If so, it will save the fixed and variable costs per unit. If the cost of outsourcing is $12 per unit, over what range would each of the production options (in-house and outsourcing) be preferred? Assume that the price per unit will remain the same whether it produces the product internally or outsources it.

c) Johndoe Company is interested in buying the Widget gadget from ABC. Johndoe Company is open to letting ABC manufacture them in-house or outsource them under certain conditions. Johndoe will only buy the outsourced if ABC reduces the selling price to $18 per unit. Also, if ABC does outsource this, Johndoe will only buy 8,000 units. On the other hand, if ABC produces the product internally, Johndoe will be willing to pay $20 per unit for all the products and Johndoe will buy 12,000 widgits. Economically, which option (produce internally or outsource) is better for ABC?

Expert Solution

Given: Fixed Cost FC = $200,000

Variable cost = VC = $5

Selling price for 1st 9000 units = $20 per unit

Total Revenue for First 9000 units = $20 * 9000 = 180,000

Since this revenue < Fixed cost + Variable cost for 9000 units, we have to produce more units

Hence, for additional x units for breakeven,

Total cost = Total Revenue

FC + VC * (9000 + x) = $20 * 9000 + x * $17

200,000 + 5* (9000 + x) = 180,000 + 17x

245000 + 5x = 180000 + 17x

x = 5,416.67

Hence, total no. of units required = 9000 + 5416.67 = 14,416.67 = 14417 units

Breakeven units = 14,417 units

b) At crossover point, total cost for y unit for producing in-house = Total cost for outsourcing

FC + VC * y = Cost of outsourcing * y

200,000 + 5 * y = 12 * y

y = 28,571.43 = 28,571

Higher range is considered for higher fixed cost

Hence, for a range less than 28571 units, the outsourcing option is considered. For range more than 28571 units, in-house production is considered.

c) Total revenue for outsourcing option = $18 * 8000 units = $144,000

Total cost for outsourcing = $12*8000 = $96,000

Total Profit for outsourcing = 144000 - 96000 = $48,000

Total revenue for in-house production = $20 * 12000 = $240,000

Total cost for in-house production = FC + VC * 12000 = 200,000 + 5*12000 = 260,000

Total profit = 240,000 - 260,000 = $ (-20,000)

Since outsourcing has a profit and in-house production has a loss, the Outsourcing option is preferred.

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keosha answered 7 months ago

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