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 $50. The fixed costs incurred each year for factory upkeep and administrative expenses are $207,000. The machinery costs $1.1 million and is depreciated straight-line over 10 years to a salvage value of zero.

a. What is the accounting break-even level of 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.)

Answer 1

Answer :

(a.) Calculation of  accounting break-even level of sales in terms of number of diamonds sold :

Accounting Breakeven = (Fixed Cost + Depreciation) / (Selling Price per unit - Variable cost per unit)

Depreciation = 1,100,000 / 10

= 110,000

Accounting Breakeven = (207000 + 110000) / (100 - 50)

= 317000 / 50

= 6340 units

(b.) Calculation of NPV break-even level  of diamonds sold per year

At brakeven Present value of cash inflow is equal to present value of cash outflow

Present Value of Cash outflow = Operating Cash Flow * PVAF @ 14% for 10 years

1,100,000 = Operating Cash Flow * 5.21611564608

Operating Cash Flow = 1,100,000 / 5.21611564608

= 210,884.894936

Operating Cash Flows = { [Quantity * ( Selling price per unit - Variable cost per unit) - Fixed Cost] * (1 - tax rate } + Tax shield on Depreciation

210884.894936 = {[ Quantity * (100 - 50) - 207,000] * (1 - 0.21) ] + (110000 * 0.21)

210884.894936 = {[50 Quanity - 207000] * 0.79 } + 23100

210884.894936 - 23100 = 39.5 Quantity - 163530

==> 39.5 Quantity = 187,784.894936 + 163530

Quantity = 351,314.894936 / 39.5

= 8894.05 units or 8894 units