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 35%, 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.	Depreciation on Machinery($1,400,000/10 years)	$140,000
	Fixed cost-others	$220,000
	Total Fixed cost	$360,000
	Contribution margin per unit($100-$40)	$60
	Break-even point in units(Total Fixed cost/Contribution margin per unit)	6,000 diamonds
b.	Let's take Q as the number of diamonds sold
	Cash flow =(1-.35)(Revenue-expenses) + 0.35*Depreciation
	=0.65($100Q - $40Q - $220,000) + 0.35*$140,000
	=39Q - 94,000
	The 10%, 10-year annuity factor is 6.14457, At Break-even point NPV is 0
	(39Q - 94,000)*6.14457 = $1,400,000
	239.63823Q - $577,589.58 = $1,400,000
	239.63823Q = $1,977,589.58
	Q =8,252.40 or 8,252 diamonds