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 $210,000. The machinery costs $1.8 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 30%, 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

Each dollar of sales generates $1.00 of pretax profit.

Depreciation is $180,000 and fixed costs are $210,000.

Accounting break-even revenues are therefore: (180,000 + 210,000)/ 1.00 = $390,000

The firm must sell 3,900 diamonds annually

Part B

Let Q = the number of diamonds sold

Cash Flow = (1 – 0.3) * (Revenue – expenses) + 0.3 * depreciation

Cash Flow = (0.7) * (140Q - 40Q - 210,000) + 0.3 * 180,000

Cash FLow = 70Q - 147,000 + 54,000

Cash FLow = 70Q - 93,000

Annuity factor for 14% discount rate adn 10 year life is = 5.216116

(70Q - 93,000) * 5.216116 = 1,800,000

365.1281 Q - 485,098.76 = 1,800,000

365.1281 Q = 2,285,098.76

Q = 6,258

6,258 diamonds per year

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