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 $40. The fixed costs incurred each year for factory upkeep and administrative expenses are $219,000. The machinery costs $1.5 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 21%, a 10-year project life, and a discount rate of 14%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

a.	Break-even sales		diamonds per year
b.	Break-even sales		diamonds per year

Answer 1

a.) Accounting break even volume = (Fixed costs + Depreciation) / (Selling price per unit - Variable cost per unit)

= (219000 + 150000) / (100-40)

= 6150 Units

b.) Cash outflows = $1,500,000

Tax rate = 21%

Discount Factor = 14%

Fixed asset life = 10 Years

For NPV , we have to calculate present value of cash inflows

At NPV, PV of Cash inflows = PV Cash Outflows

For calculating quantity,

Let Q= the number of diamonds sold.

Cash flow = [(1 − Tax rate) × (revenue − expenses)] + (Tax rate × depreciation)

= (0.79 × (100Q− 40Q − 219,000)] + (0.21 × 150,000)

= 47.4Q − 173010 + 31500

= 47.4Q - 141510

14%, 10-year annuity factor = 5.2161

Therefore, for NPV to equal zero:

(47.4Q - 141510 ) × 5.2161 = $1,500,000

247.24Q = $2,238,130

Q= 9,053 diamonds per year i.e. NPV breakeven sales quantity