Question

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 $50. The fixed costs incurred each year for factory upkeep and administrative expenses are $201,000. The machinery costs $1.1 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? (Do not round intermediate calculations.) Break-even sales= ?? Diamonds per year

b. What is the NPV break-even level of diamonds sold per year 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.) Break-even sales= ?? Diamonds per year

Answer 1

a. Accoutning break-even level sales.

Number of quantity for break-even = (Fixed Cost + Depreciation)/Contribution Margin

Contribution margin = Sales - Variable Cost = $100 - $50 = $50

Depreciation/Year = 1,100,000/10 = $110,000

Number of quantity for break-even = (201,000 + 110,000)/50 = 6,220 --> Breakeven sales quantity

Company should sell 6,220 diamonds per year for break-even

b. NPV break-even level of diamonds.

Total cashflow = (1 - Tax rate) * (Revenue - Variable Cost - Fixed Cost) + Tax rate * Depreciation

Let Q be the number of diamonds to be sold.

Total Cash flow = (1 - 40%) * (100Q - 50Q - 201,000) + (40% * 110,000)

Total cashflow = (0.60) * (50Q - 201,000) + 44,000 = 30Q - 120,600 + 44,000 = 30Q - 164600

10-year 10% annuity PV factor (from PVIF_a table) = 6.14457

(30Q - 164600) * 6.14457 = Initial Investment

(30Q - 164600) * 6.14457 = 1,100,000

Q = 11,454 --> NPV Breakeven sales quantity