Problem 10-10 Break-Even (LO2) Dime a Dozen Diamonds makes synthetic diamonds by

Question

Problem 10-10 Break-Even (LO2)

Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. 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 $216,000. The machinery costs $2.5 million and is depreciated straight-line over 10 years to a salvage value of zero.

What is the accounting break-even level of sales in terms of number of diamonds sold?

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%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. 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 $216,000. The machinery costs $2.5 million and is depreciated straight-line over 10 years to a salvage value of zero.

Explanation / Answer

a)

Profit per diamond is 140 - 40 = 100

to breakeven they must sell 216000 / 100 = 2160 diamonds.

If including the material the breakeven is ( 2,500,000 / 10 + 216000 ) / 100 = 4660 diamonds

b)

using a discount rate of 12%, the post tax profit should be x say

2500000 = x / 1.12 + ... + x/1.12^10 = 5.65x

x = 442,460.41

let the pretax profits be p

tax is ( p - 2500000 / 10 ) * 0.35

Hence the profit is

p - ( p - 2500000 / 10 ) * 0.35 = 442,460.41

0.65p + 250000 * 0.35 = 442,460.41

p = 546092.94

Hence to get this P the sales is say s

s * 100 - 216000 = 546092.94

s = 7620.93

or S = 7621

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