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# Finance questions: Break even computation, degree of operating leverage

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9. Break-Even. 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 \$30. The fixed costs incurred each year for factory upkeep and administrative expenses are \$200,000. The machinery costs \$1 million and is depreciated straight-line over 10 years to a salvage value of zero.

21. Operating Leverage. A project has fixed costs of \$1,000 per year, depreciation charges of \$500 a year, revenue of \$6,000 a year, and variable costs equal to two-thirds of revenues.
a. If sales increase by 5 percent, what will be the increase in pretax profits?
b. What is the degree of operating leverage of this project?
c. Confirm that the percentage change in profits equals DOL times the percentage change in sales.

The government's only concession was to put a floor on the underwriters losses by giving them the option to resell their stock to the government at \$2.80 a share. The BP offering is described and analyzed in C. Muscarella and M. Vetsuypens, "The British Petroleum Stock Offering: An Application of Option Pricing", Journal of Applied Corporate Finance1 (1989), pp. 74-80.

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The solution presents the formulas together with explanations to come to the answers.

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9.
P=100
AVC=30
Since it's not clear if this machinery are already in existence or need to be purchased, we just take them into fixed costs.
Depreciation expense each year: 1000,000/10 = 100,000
FC=200,000+100,000= 300,000

Then marginal contribution is MC=P-AVC=100-30=70
Break-Even output = FC/MC= 300,000/70 = ...

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