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 $211,000. The machinery costs $2.0 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 10%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Explanation / Answer

a. Computation of accounting break-even level of sales in terms of number of diamonds sold:
Formula for breakeven sales in units= fixed cost / contribution per unit
= $211,000 + Depreciation (2,000,000 / 10 years) / sales - variable cost
= 411,000 / 60 = 6,850
Therefore, break-even level of sales in terms of number of diamonds sold = 6,850

b. Computation of NPV break-even level of diamonds sold per year:
NPV = cash inflows * Present value factor at 10%, 10 years - cash outflows = zero at Break even level
here, first we need to calculate cash flows:
Cash flows = (Contribution - fixed cost) * (1-tax rate) + (depreciation * tax rate)
Let us assume Q as quantity
= (60Q - 211,000)* 0.65 + 200,000*0.35
= 39Q - 137,150 + 70,000
= 39Q - 67,150

Therefore, NPV = cash inflows * Present value factor at 10%, 10 years - cash outflows
=> 39Q - 67,150 * (6.1446) = 2,000,0000
239.64Q = 2,000,0000 + 412,609.89
Q = 10,068
Therefore, NPV break-even level of diamonds sold per year = 10,068

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