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 $160. The materials cost for a standard diamond is $60. The fixed costs incurred each year for factory upkeep and administrative expenses are $218,000. The machinery costs $2.1 million and is depreciated straight-line over 10 years to a salvage value of zero.

What is the accounting break-even level of sales in terms of number of diamonds sold?

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.)

Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $160. The materials cost for a standard diamond is $60. The fixed costs incurred each year for factory upkeep and administrative expenses are $218,000. The machinery costs $2.1 million and is depreciated straight-line over 10 years to a salvage value of zero.

Explanation / Answer

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 = $2,100,000 / 10 = $210,000 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 = ($218,000 + $210,000) / ($160 - $60) = $428,000 / $100 = 4280 At the break even point: Revenues = q.p = 4,280 x $160 = $684,800 Variable costs = q.v = 5,978 x $60 = $256,800 Fixed costs = $218,000 Total Costs = $256,800 + $218,000 = $474,800 Depreciation = $2,100,000 / 10 years = $210,000 per year. Tax rate (T) = 0.4 Cash Flow = (1-T)*(Revenues - Total Expenses) + T * Depreciation = = 0.6*($684,800 - $474,800) + 0.4*$210,000 = = $126,000 + $84,000 = = $210,000 Present value of cash flow (PV)= Cash Flow * Annuity factor The 12%, 10-year annuity factor is 5.650 , then: PV = $210,000 x 5.650 = $1,186,500

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