Question

A firm is currently buying a part at a cost of $12 each. It is considering buying a machine that will produce the part at a variable cost of $8. Each unit of input produces the part plus a by-product, which is sold for $1. The machine will cost $40,000 and will have a useful life of 5 years. The firm requires an 8% return. What annual volume is necessary to justify making the investment? Ignore income taxes. Round to the nearest unit.

Answer 1

Cost of buying a unit = $12

Variable cost of producing a unit = $8

Selling price per unit of by-product = $1

Net variable cost of producing a unit = Variable cost of producing a unit - Selling price per unit of by-product

= 8-1

= $7

Cost of machine = $40,000

Useful life of machine = 5 years

Annual depreciation of machine = Cost of machine / Useful life of machine

= 40,000/5

= $8,000

Annual expected return on investment = 8%

= 40,000 x 8%

= $3,200

Total annual fixed costs= Annual depreciation of machine + Annual expected return on investment

= 8,000+3,200

= $11,200

Let annual volume needed to justify the investment be K units

At volume of K units, cost of making and cost of buying will be same.

Cost of buying = 12K

Cost of making = 7K + 11,200

Hence,

12K = 7K + 11,200

5K = 11,200

K = 2,240

Hence, annual volume needed is $2,240 units.

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