Dime a Dozen Diamonds makes synthetic: diamonds by treating cartoon Each diamond
ID: 2765184 • Letter: D
Question
Dime a Dozen Diamonds makes synthetic: diamonds by treating cartoon Each diamond can be sold for $140 The materials cost for a standard diamond is $40 The fixed costs incurred each year for factory upkeep and administrative expenses are $203,000 The machinery costs $14 million and is depreciated straight-line over 10 years to a salvage value of zero. What is the accounting break-even level of sales intermediate calculations) in terms of number of diamonds (Do not round Break-even sales diamonds per yea' What is the NPV break even level of diamonds sold per year assuming a tax rate of 35% a 10-year preset Me. and a discount rate of 14%? (Do not round Intermediate calculations. Round your answer to the nearest whole number.) Break even sales diamonds per yearExplanation / Answer
Solution:
Depreciation expense is $1,400,000/10 = $140,000 per year, and
Fixed costs are $203,000.
Therefore:
Accounting break-even revenue = (Depreciation expense + Fixed costs)/Pre-tax profit
Accounting break-even revenue = ($140,000 + $203,000)/1
Accounting break-even revenue = 343,000
The firm must sell 3,430 diamonds annually.
2. Let Q be the number of units sold
Cash flow = [(1 0.35) × (revenue expenses)] + (1.40 × depreciation)
Cash flow = [(1 0.35) × (140Q – 40Q – 203,000)] + 0.35 x (1.40 × depreciation)
Cash flow = [0.65 × (140Q – 40Q – 203,000)] + 0.35 x $140,000
Cash flow = 65Q – 131,950 + $49,000
Cash flow = 65Q – 82,950
PV of cash flow = (65Q – 82,950) (PVIFA @ 14%, 10)
PV of cash flow = (65Q – 82,950) [(1.14^10 – 1)/ (0.14*1.14^10)]
PV of cash flow = (65Q – 82,950) (5.2161)
Therefore, NPV equal to zero
-$1,400,000 + (65Q – 82,950) (5.2161) = 0
(65Q – 82,950) (5.2161) = 1,400,000
65Q = 351,349
Q = 5,405
Hence, break-even sales is 5,405 diamonds per year
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