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 $40. The fixed costs incurred each year for factory upkeep and administrative expenses are $212,000. The machinery costs $2.2 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? (Do not round intermediate calculations.)

b. What is the NPV break-even level of diamonds sold per year assuming a tax rate of 21%, a 10-year project life, and a discount rate of 12%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

a) The Accounting break even point refers to the operating point where the total operating costs are recovered

Accounting Break level of Sales (No. of units) =Fixed Cost / (Selling price per unit - Variable cost per unit

= $212000/($120-$40)

=2650

No. of diamonds sold must be 2650 for accounting break even to be achieved

b) Let the no. of diamonds sold be X for break even NPV

Cashflows each year (1-10) are calculated as (all figures in $)

Revenues = 120*X

Less: Variable Cost = 40*X

Less: Fixed Cost = 212000

Less: Depreciation = 2,200,000/10 = 220,000

Profit before Tax = (80*X- 432000)

Less: Tax @21% = 0.21*(80*X- 432000)

Profit after Tax = 0.79*(80*X- 432000)

Add:Depreciation = 220000

Cashflows = 63.2*X -121280

So, NPV = -2200000 + (63.2*X -121280)/0.12*(1-1/1.12^10)

For Break even NPV = 0

So, (63.2*X -121280)/0.12*(1-1/1.12^10) = 2200000

=> 5.650223* (63.2*X -121280) = 2200000

=> (63.2*X -121280) =389365.16

=> 63.2*X =510645.16

=> X = 8079.82 or 8080

No. of diamonds sold must be 8080 for NPV break even to be achieved