Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond

Question

Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $120. The materials cost for a standard diamond is $60. The fixed costs incurred each year for factory upkeep and administrative expenses are $212,000. The machinery costs $2.2 million and is depreciated straight-line over 10 years to a salvage value of zero. a. What is the accounting break-even level of sales in terms of number of diamonds sold? b. What is the NPV break-even level of sales assuming a tax rate of 40%, a 10-year project life, and a discount rate of 12%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Explanation / Answer

Sale Price (a) $120.00 Material Cost (b) $60.00 Contribution Per Unit (c = a-b) $60.00 Fixed Cost (d) $212,000.00 Depreciation ( e) $220,000.00 Total Fixed Cost (f=d+e) $432,000.00 Accounting Breakeven Sales 7200 (Fixed Cost/Contribution per unit) NPV Sales = [(60*x - 432000) * 0.60 + 220000] * Annuity Factor at 12% for 10 years or, 0 = (36x - 259200 + 220000)*6.194374 or, 0 = 22.9975x - 242819 or, x = 1088.89 or 1089 units

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