The initial cost of machinery for producing a certain item is $50,000. The machinery will have a five-year life with no salvage value. The manufacturing process has a fixed cost of $5,000 per year and a variable cost of $16 per unit. At an interest rate of 8% per year, the number of units that must be sold at $20 per unit for breakdown is nearest to:

4,381 units per year

Explanation:

fixed costs per year (other than depreciation) = $5,000

contribution margin per unit = $20 - $16 = $4

in order for the project to break even, the NPV must be $0

this means that our discounted annual cash flow must be equal to $50,000

discounted annual cash flow = present value / PV annuity factor

PV annuity factor, 8%, 5 periods = 3.9927

annual cash flow = $50,000 / 3.9927 = $12,523

each annual cash flow = $4X - $5,000 = $12,523

$4X = $17,523

X = $17,523 / $4 = 4,380.75 ≈ 4,381 units

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