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 $140. The materials cost for a standard diamond is $40. The fixed costs incurred each year for factory upkeep and administrative expenses are $203,000. The machinery costs $1.4 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? (Do not round intermediate calculations.)

b. What is the NPV break-even level of diamonds sold per year assuming a tax rate of 35%, a 10-year project life, and a discount rate of 14%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Explanation / Answer

Requirement a: Accounting breakeven level of sales: a Selling price per diamond 140 b Less: Material Cost 40 c Contribution 100 d Fixed Costs 203000 e Breakeven Sales (d/c) 2030 Requiremnet b: Let x be the NPV Breakeven level of sales Calculation of recurring cash flows: Sales 140x Less: Material Cost 40x Contribution 100x Less: Fixed Costs 203000 Profit before taxes 100x-203000 Less: Taxes (35%) 35x-71050 Profit after taxes 65x-131950 Depreciation 1400000/10 140000 Cash Flow after taxes 65x+8050 Calculation of NPV: Year Cash Flow PVF(14%) PV of Cash Flow 0 -1400000 1 -1400000 1 to 10 65x+8050 5.216115646 339.04751699x+41989.7309503 339.04751699x-1358010.26905 At NPV breakeven level of sales, NPV = 0 This implies, 339.04751699x-1358010.26905 0 x 1358010.26905/339.04751699 4005.3685 NPV Breakeven level of sales 4006

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