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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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