Dime a Dozen Diamonds makes synthetic diamonds by treating carbon. Each diamond
ID: 2763315 • Letter: D
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 $2.2 million and is depreciated straight-line over 10 years to a salvage value of zero.
a. What is the accounting break-even level of sales in terms of number of diamonds sold? (Do not round intermediate calculations.) Break-even sales diamonds per year
b. What is the NPV break-even level of diamonds sold per year assuming a tax rate of 40%, a 10-year project life, and a discount rate of 12%? (Do not round intermediate calculations. Round your answer to the nearest whole number.) Break-even sales diamonds per year
Explanation / Answer
Answer:
Total Fixed Costs = Factory and administrative expenses + Depreciation = 212,000 + 2,200,000/10
=$ 432,000
Contribution per unit = Selling price per unit - variable cost per unit = 120 - 40 = $ 80
(a) Accounting break-even level of sales in terms of number of diamonds sold = Total Fixed Costs / Contribution per unit
= 432,000 / 80 = 5,400 units
or 5,400 * 120 = $648,000
(b) Let number of units sold be x at break-even-
At NPV break-even level of diamonds sold per year, initial outflows will be equal to total present value of inflows.Hence
2,200,000 (Machinery Costs) = 271.21 x - 221,488.74 ( Total present value of inflows)
(2,200,000 + 221,488.74) / 271.21 = x
x = 8928 units
NPV break-even level of diamonds sold per year = 8928 units or 8928 *120 = $ 1,071,360
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 Contribution (120-40) * x 80x 80x 80x 80x 80x 80x 80x 80x 80x 80x Less: Factory and adminstrative costs 212,000 212,000 212,000 212,000 212,000 212,000 212,000 212,000 212,000 212,000 Less: Depreciation 220,000 220,000 220,000 220,000 220,000 220,000 220,000 220,000 220,000 220,000 Earning before tax (80 x - 432,000) (80 x - 432,000) (80 x - 432,000) (80 x - 432,000) (80 x - 432,000) (80 x - 432,000) (80 x - 432,000) (80 x - 432,000) (80 x - 432,000) (80 x - 432,000) Less: tax @40% on earning before tax (32 x - 172,800) (32 x - 172,800) (32 x - 172,800) (32 x - 172,800) (32 x - 172,800) (32 x - 172,800) (32 x - 172,800) (32 x - 172,800) (32 x - 172,800) (32 x - 172,800) Earning after tax (48 x - 259,200) (48 x - 259,200) (48 x - 259,200) (48 x - 259,200) (48 x - 259,200) (48 x - 259,200) (48 x - 259,200) (48 x - 259,200) (48 x - 259,200) (48 x - 259,200) Add: Depreciation 220,000 220,000 220,000 220,000 220,000 220,000 220,000 220,000 220,000 220,000 Cash Inflow (48 x - 39,200) (48 x - 39,200) (48 x - 39,200) (48 x - 39,200) (48 x - 39,200) (48 x - 39,200) (48 x - 39,200) (48 x - 39,200) (48 x - 39,200) (48 x - 39,200) P.V. factor @ 12.00% 0.8929 0.7972 0.7118 0.6355 0.5674 0.5066 0.4523 0.4039 0.3606 0.3220 Present Value of cash inflows (cash inflow* factor) (42.86 x - 35,000) (38.27 x - 31,250) (34.17 x - 27,902) (30.50 x - 24,912) (27.24 x - 22,243) (24.32 x - 19,860) (21.71 x - 17,732) (19.39 x - 15,832) (17.31 x - 14,136) (15.45 x - 12,621) Total present value of cash inflows 271.21 x - 221,488.74Related Questions
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