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Q: Accounting break even point/ NPV ( Answered ,   0 Comments )
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 Subject: Accounting break even point/ NPV Category: Business and Money > Finance Asked by: mbastu-ga List Price: \$10.00 Posted: 09 Apr 2005 18:26 PDT Expires: 09 May 2005 18:26 PDT Question ID: 507326
 ```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 \$30. The fixed costs incurred each year for factory upkeep and administrative expenses are \$200,000. The machinery costs \$1 million a year 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? b. What is the NPV break-even sales assuming a tax rate of 35 percent, a 10-year project life and a discount rate of 12 percent? Solution Problem 8-9 Instructions In part a, enter the formula to calculate the break-even point. In part b, enter the formulas to calculate all the unknown items (you will know that your formulas are correct if the NPV is approximately equal to 0. a. What is the accounting break-even level of sales in terms of number of diamonds sold? Accounting break-even point diamonds b. What is the NPV break-even sales assuming a tax rate of 35 percent, a 10-year project life and a discount rate of 12 percent? Number of diamonds 5,978 Annuity factor 5.650 Revenue Variable Expenses Depreciation Fixed expenses \$0 Cash Flow Present value of cash flow \$0.00 Net present value (\$1,000,000.00)```
 ```Hi mbastu!! a. What is the accounting break-even level of sales in terms of number of diamonds sold? The machinery cost of \$1 million is depreciated straight-line over 10 years to a salvage value of zero. That means the Depreciation per year is: D = \$1,000,000 / 10 = \$100,000 The break-even level of sales is the sales point at which EBIT = 0 ; in other words: sales break-even point = level of sales necessary to cover operating costs. At the break-even level of sales: EBIT = Revenues - Variable costs - Fixed costs - Depreciation = 0 then: Revenues - Variable costs = Fixed costs + Depreciation If we call: q = quantity sold; p = price per unit; v = variable cost per unit, then Revenues = q.p and Variable costs = q.v We will have: Revenues - Variable costs = q.p - q.v = q.(p - v) Revenues - Variable costs = q.(p - v) = Fixed costs + Depreciation Then: q = (Fixed costs + Depreciation) / (p - v) q = (\$200,000 + \$100,000) / (\$100 - \$30) = \$300,000 / \$70 = 4285.71 The break-even level of sales in terms of number of diamonds sold is 4,286 diamonds. ----------------------- b. What is the NPV break-even sales assuming a tax rate of 35 percent, a 10-year project life and a discount rate of 12 percent? At the break even point: Revenues = q.p = 5,978 x \$100 = \$597,800 Variable costs = q.v = 5,978 x \$30 = \$179,340 Fixed costs = \$200,000 Total Costs = \$179,340 + \$200,000 = \$379,340 Depreciation = \$1,000,000 / 10 years = \$100,000 per year. Tax rate (T) = 0.35 Cash Flow = (1-T)*(Revenues - Total Expenses) + T * Depreciation = = 0.65*(\$597,800 - \$379,340) + 0.35*\$100,000 = = \$141,999 + \$35,000 = = \$176,999 Present value of cash flow (PV)= Cash Flow * Annuity factor The 12%, 10-year annuity factor is 5.650 , then: PV = \$176,999 x 5.650 = \$1,000,044.35 NPV = PV - Initial Investment = = \$1,000,044.35 - \$1,000,000 = = \$44.35 NOTE: The above value is a good aproximation to zero, and the error is a result of some hidden roundings, you can see that taking the reverse way: At the breakeven point the NPV is zero, then: NPV = 5.650 x (0.65 .(q.p - q.v - FC) + 0.35 . D ) - \$1,000,000 = 0 then: \$1,000,000/5.650 - 0.35*\$100,000 = 0.65*q*(p-v) - 0.65*\$200,000 then: \$141,991.15 = 0.65*q*(\$100 - \$30) - \$130,000 then: \$271,991.15 = 0.65*q*\$70 ==> q = \$271,991.15 / (0.65*\$70) = 5977.83 diamonds; this result must be rounded to 5978 diamonds (this is the origin of the non zero result of the NPV). I hope this helps. If you find something unclear or missed please do not hesitate to request for a clarification, I will be glad to give you further assistance on this before you rate this answer. Best regards. livioflores-ga``` Clarification of Answer by livioflores-ga on 09 Apr 2005 21:33 PDT ```Hi!! Just one note about NPV break-even: Do not confuse it with the NPV of the break-even level of sales point. NPV break-even analysis calculates the level of sales that generates an NPV of zero, known also as the financial break-even. Sales higher than the zero NPV sales will produce positive NPV. This is equivalent to finding the sales level for which the cost of the project equals the present value of the cash flows. This is why we use: NPV break-even = PV - I = 0 or PV = I Hope this helps you to understand the second part of the problem. Regards. livioflores-ga```
 mbastu-ga rated this answer: and gave an additional tip of: \$5.00 ```I had all the correct formulas but when the NPV did not equal 0, I thought it was wrong. Thanks for your hard work and effort.```