A small producer of machine tools wants to move to a larger building, and has id

Question

A small producer of machine tools wants to move to a larger building, and has identified two alternatives. Location A has annual fixed costs of $220,000 and variable costs of $8,000 per unit; location B has annual fixed costs of $420,000 and variable costs of $6,000 per unit. The finished items sell for $19,000 each.

b-1.

b-2.

a. At what volume of output would the two locations have the same total cost? Volume of output   units

b-1.

For what range of output would location A be superior? Range of output 0 to

b-2.

For what range would B be superior? Range of output or more

Explanation / Answer

a. At what volume of output would the two locations have the same total cost?

Ans -

Location A has annual fixed costs of $220,000 and variable costs of $8,000 per unit; location B has annual fixed costs of $420,000 and variable costs of $6,000 per unit.

Let output be x units when 2 locations have the same total cost.

Total cost for location A = $220,000 + $8,000 x ... (1)

Total cost for location B = $420,000 + $6,000 x .... (2)

For the same total cost, equating (1) and (2), we get

$220,000 + $8,000 x = $420,000 + $6,000 x

So, $8,000 x - $6,000 x = $420,000 - $220,000

So, $2,000 x = $200,000

So, x = 100 units

$220,000 + $8,000 x = $220,000 + $800,000 = $1,020,000

Therefore, at 100 units of volume of output the two locations would have the same total cost of $1,020,000.

b-1. For what range of output would location A be superior?

Ans - Range of output is 0 to 100 units.

b-2. For what range would B be superior?

Ans - Range of output 100 or more.

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