Question

Dime a dozen diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $100. The material cost for the standard diamond is $30$. The fixed costs for the factory and admin expenses is $200,000 a year. The machinery costs $1 million and is depreciated straight line over 10 years to a salvage value of zero.

A. What is the accounting breakeven level of sales?

B. What is the NPV breakeven level of Sales?

Answer 1

A)	Depreciation			=	1000000/10
				=	100,000
	Fixed cost			=	200,000
	Contribution margin			=	$100-$30
				=	$70
	Contribution margin (in % of sales)			=	70/100
				0.7 or 70%
		Accounting BEP (in sales value)		=	(Fixed cost+depreciation)/contribution %
				=	($200,000+100,000)/0.7
				=	$428,571
B)	Now,for NPV break even sales,discountng rate is not given,
	We assume discounting rate =8% (you may assume different rate,answer would be different in that case)
			Cashflow	=	{(Sales*contribution margin)-fixed cost}*PVAF(8%,10 years)
	At NPV breakeven level,initial investment=PV of cashflow
			1,000,000	=	{(sales*0.7)-200000)*6.7101
			1,000,000	=	4.6971*sales-1342020
			2,342,020	=	4.6971*sales
			$498,610	=	Sales
		Sales at NPV break even point		=	$498,610
	Note
	Rate is must for any NPV calculation.
	If the question does not provide any rate(like in this case),either question is incomplete or
	it require you to assume a rate & go ahead.