Question

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 S1 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 35 percent, a 10-year project life, and a discount rate of 12 percent?

Answer 1

Accounting break even = (Fixed costs+depreciation)/ (SP-Variable cost)

= (200000+1000000/10)/(100-30)

=4285.71

=4286 units

NPV break even is the sales at which NPV is zero

OCf = (Sales-Variable-fixed cost)*(1-Tax) + tax*depreciation

=(100x-30x-200000)*(1-0.35) + 0.35*1000000/10

= 45.5x- 130000+ 35000

= 45.5x-95000

Initial cost = PV of OCF

1000000= (45.5x-95000)*5.65

X=5977.83 or

5978 units