11. Break-Even Analysis. Dime a Dozen Diamonds makes synthetic diamonds by treat
ID: 2709586 • Letter: 1
Question
11. Break-Even Analysis. 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 $200,000. The machinery cost $1 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?
b. What is the NPV break even level of sales assuming a tax rate of 35%, a 10 year project life, and a discount rate of 12%?
Explanation / Answer
Point A. Sales Price per unit $ 100
Less: Material Cost per unit $ 40
Contribution per unit ( $100- $40) $ 60
Fixed Cost
Administrative Exp $ 200000
Depreciation ($1000000/10) $ 100000
Total Fixed Cost $ 300000
Break Even Point ( iN Quantity ) = Total Fixed Cost/Contribution Per unit
$ 300000/60= 5000 units
(B) NPV Break Even Sales
Total Fixed Cost After Tax
Administrative Exp $ 200000
Depreciation ($1000000/10) $ 100000
Total Fixed Cost $ 300000
Less Tax @ 35% $ 105000
Fixed cost after tax $ 195000
10 years Cumulative Present Value of Fixed cost $ 1101945 ($195000* 5.651)
Contribution per unit after tax
Sales Price per unit $ 100
Less: Material Cost per unit $ 40
Contribution per unit ( $100- $40) $ 60
less Tax @ 35% $ 21
Contribution after Tax $ 39
Cumulative Present Value for 10 years ($39*5.651) $220.389
Note :
Cumulative Present value of $1 at 12% disc rate for 10 years is $ 5.651 (as per present value table)
NPV Break Even Point (in quantity)=
Cumulative Present value of fixed cost/ Cumu. present value of Contri. per unit
= $1101945/220.389
= 5000 unit per year
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