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?

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

Hi,

Please find the answers as follows:

Part A:

Accounting Break Even = (Fixed Costs + Depreciation)/Contribution Margin = (180000 + 130000)/50 = 6200 diamonds

Dollar Value = 6200*100 = $620000

Part B:

NPV Break Even = (1-.30)*(100Q - 50Q - 180000) + .30*130000

= .70*(50 Q - 180000) + 39000

= 35Q - 126000 + 39000

= 35Q - 87000

At NPV = 0

=(35Q - 87000)*5.650 = 1300000

= 197.75Q - 491550 = 1300000

Q = (1300000 + 491550)/197.75 = 9060 diamonds

Answer is 9060 diamonds.

Thanks.

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