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 $100. The materials cost for a standard diamond is $50. The fixed costs incurred each year for factory upkeep and administrative expenses are $180,000. The machinery costs $1.3 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? Break-even sales is 6,200 b. What is the NPV break-even level of sales assuming a tax rate of 30%, 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

I hope this helps..!! The machinery cost of $1 million is depreciated straight-line over 10 years to a salvage value of zero. That means the Depreciation per year is: D = $1,000,000 / 10 = $100,000 The break-even level of sales is the sales point at which EBIT = 0 ; in other words: sales break-even point = level of sales necessary to cover operating costs. At the break-even level of sales: EBIT = Revenues - Variable costs - Fixed costs - Depreciation = 0 then: Revenues - Variable costs = Fixed costs + Depreciation If we call: q = quantity sold; p = price per unit; v = variable cost per unit, then Revenues = q.p and Variable costs = q.v We will have: Revenues - Variable costs = q.p - q.v = q.(p - v) Revenues - Variable costs = q.(p - v) = Fixed costs + Depreciation Then: q = (Fixed costs + Depreciation) / (p - v) q = ($200,000 + $100,000) / ($100 - $30) = $300,000 / $70 = 4285.71 The break-even level of sales in terms of number of diamonds sold is 4,286 diamonds. ----------------------- b. What is the NPV break-even sales assuming a tax rate of 35 percent, a 10-year project life and a discount rate of 12 percent? At the break even point: Revenues = q.p = 5,978 x $100 = $597,800 Variable costs = q.v = 5,978 x $30 = $179,340 Fixed costs = $200,000 Total Costs = $179,340 + $200,000 = $379,340 Depreciation = $1,000,000 / 10 years = $100,000 per year. Tax rate (T) = 0.35 Cash Flow = (1-T)*(Revenues - Total Expenses) + T * Depreciation = = 0.65*($597,800 - $379,340) + 0.35*$100,000 = = $141,999 + $35,000 = = $176,999 Present value of cash flow (PV)= Cash Flow * Annuity factor The 12%, 10-year annuity factor is 5.650 , then: PV = $176,999 x 5.650 = $1,000,044.35 NPV = PV - Initial Investment = = $1,000,044.35 - $1,000,000 = = $44.35

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