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 $220,000. The machinery costs $1.4 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 10%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

(a): 6,000 units

(b): 7,853 units

Calculations:

(a): Accounting break even = (fixed costs + annual depreciation)/(selling price per unit – variable cost per unit)

Annual depreciation = $1.4 million/10 years = $140,000 per year

Thus accounting break even = (220,000 + 140,000)/(100-40)

= 6,000 units

(b): Let NPV break-even be “x”

Thus (100-40)x - 220,000 – 140,000 = profit before tax

Or profit before tax = 60x – 360,000

Profit after tax = (1-0.21)*(60x – 360,000)

= 47.4x – 284,400

After tax cash flow = profit after tax + depreciation

= 47.4x – 284,400 + 140,000

= 47.4x – 144,400

Thus present value of cash flow = (47.4x – 144,400)* PVIFA (10%, 10)

= (47.4x – 144,400) * 6.14456711

(The PVIFA can also be rounded to 6.145)

Now at NPV break-even present value of cash flows = initial investment

Or (47.4x – 144,400) * 6.14456711 = 1,400,000

Or x = 7,853.24

This can be rounded to 7,853 units