Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond
ID: 2713452 • Letter: D
Question
Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond can be sold for $120. The materials cost for a standard diamond is $70. The fixed costs incurred each year for factory upkeep and administrative expenses are $215,000. The machinery costs $2.3 million and is depreciated straight-line over 10 years to a salvage value of zero. What is the NPV break-even level of sales assuming a tax rate of 40%, a 10-year project life, and a discount rate of 10%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)
Explanation / Answer
Dime a Dozen Diamonds Details Amt $ Year Discount factor @10% Sales price/unit 120 1 0.909 Material cost/Unit 70 2 0.826 Contribution /unit 50 3 0.751 Contribution margin % 41.67% 4 0.683 5 0.621 Machine cost 2,300,000 6 0.564 Useful life in yrs 10 7 0.513 Depreciation /year 230,000 8 0.467 Other Fixed factory & Admin cost/year 215,000 9 0.424 Total Fixed cost/year 445,000 10 0.386 Tax rate 40% Annuity factor for PV at discount rate 10% 6.145 Post tax cash fow=Post tax income+depreciation Say , NPV break even sales =x Contribution = 0.4167x Post Tax Income =0.60(0.4167x-445000) Post tax cash flow = 0.60(0.4167x-445000) +230000 PV of this cash flow for 10 years will be = 2,300,000 at NPV break even Annuity factor for discounting @10% for 10 years =6.145 So , 6.145[0.60(0.4167x-445000)+230000]= 2,300,000 0.60(0.4167x-445000) +230000 = 374,288 0.25x -267000+230000=374,288 x=1,645,152 So NPV break even sales = $1,645,152
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