4 Dime a Dozen Diamonds makes synthetic diamonds by treating

4. Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $100. The material cost for a standard diamond is $40. 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. a) What is the accounting break-even level of annual sales in terms of number of diamonds sold? Assume the company is in the 35% tax bracket. What is the NPV break-even level of sales assuming a tax rate of 35%, a 10-year project life and a discount rate of 12%?

Solution

Accounting Break Even Sales:

Selling Price per Diamond = $100

Material Cost $40

Contribution per Dimaond = $60

Fixed Costs = $200,000

+ Depreciation $100,000

Total Fixed Expenses = $300,000

Break even Annual Sales = Fixed Costs/Contribution per Unit

= 300,000/60 = 5000 units

NPV Level:

Let the units be x

Contribution = 60x

- Fixed Costs 200,000

Less: Depreciation 100,000

Profit Before Tax = 60x-300,000

Tax = 35%

Profit After Tax = 39x-195,000

+ Depreciation 100,000

Net Cash Flows = 39x - 95,000

NPV = Present Value of Cash Inflows - Present Value of Cash Outflows

= (39x-95,000)*PVAF(12%, 10 years) - 1,000,000

=(39x-95000)5.650 - 1,000,000

=220.35x - 536,750 - 1,000,000

At break even level, NPV = 0

Hence. 0 = 220.35x - 1536,750

x = 6,974 units (approx)