Question

Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $130. The materials cost for a standard diamond is $80. The fixed costs incurred each year for factory upkeep and administrative expenses are $206,000. The machinery costs $1.2 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 40%, a 10-year project life, and a discount rate of 12%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

Part (a)

Accounting break even level of sales = (Fixed Cost + Depreciation)/(Sales-Variable Cost)

Fixed Costs = $206,000

Depreciation = $1,200,000/10 = $120,000

Break even level of sales = ($206,000+$120,000)/($130-$80)

= 6520 diamonds

Part (b)

NPV break even level of diamonds-

Let NPV break even be X

Cash Flows per year = ($130X-$80X-$206,000)(1-0.4)+($120,000*0.40) (tax saving on depreciation)

= $30X-$123,600+$48,000

=$30X-$75,600

Present value annuity factor at 12% for 10 years = 5.650

Present value of cash flows = ($30X-$75,600)*5.650

= $169.5X-$427,140

Initial investment = $1,200,000

So, $169.5X-$427,140= $1,200,000

X = 9600 Diamonds