Question

Merrimac Manufacturing has always purchased a certain component part from a supplier on the East Coast for $40 per part. The supplier is reliable and has maintained the same price structure for years. Recent improvements in operations and reduced product demand have cleared up some capacity in Merrimac’s own plant for producing component parts. The particular part in question can be produced internally by Merrimac at $25 per part, with an annual fixed investment of $30,000.

a) Over what range (quantity) of product would each of the two options be the preferred one?

b) As an alternative, a new supplier located nearby is offering to produce parts on the following cost schedule. For the first 100 parts, the cost is $52 per part. For each part in excess of 100, the cost per unit drops to $35 per part. Considering just the two suppliers, over what range (quantity) of product would each supplier be the preferred one?

Answer 1

Let
Supplier from East Coast be S1
New supplier located nearby be S2

Answer a

Lets x be the number of units needed to reach the break-even point between Merrimac's cost of producing the component internally and purchase cost from S1
=> At breakeven point
cost of producing the component internally will be equal to purchase cost from S1, any quantity above x will make total per-unit cost of producing the component internally effectively cheaper.
So,
(unit cost from S1)*x = (Fixed annual cost) + (per-unit cost for internal production)*x

=> 40*x = 30000 + 25*x
=> x = 30000 / 15 = 2000 units


for Annual Quantity of components < 2000 => East Coast should be preferred

for Annual Quantity of components > 2000 => Internal production should be preferred


Answer b
Lets y be the number of units needed to reach the break-even point between S1 and S2.

=> At breakeven point
purchase cost from the S2 will be equal to purchase cost from the S1, any quantity above x will make total Purchase cost from the S2 effectively cheaper.

(unit cost from S1)*y =     (cost of first 100 units from S2) + (unit cost from S2 in excess of first 100 units)*(y-100)

40*y = 52*100 + (35*(y-100)) = 5200 + 35y - 3500
=>5*y = 1700
=> y = 340 units.

for Annual Quantity of components < 340 => East Coast should be preferred

for Annual Quantity of components > 340 => Internal production should be preferred


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