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 $70. The fixed costs incurred each year for factory upkeep and administrative expenses are $215,000. The machinery costs $2.3 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 10%? (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 $120. The materials cost for a standard diamond is $70. The fixed costs incurred each year for factory upkeep and administrative expenses are $215,000. The machinery costs $2.3 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 10%? (Do not round intermediate calculations. Round your answer to the nearest whole number.)

Answer 1

Solution: SP 120 VC 70 215,000 FC Initial investment 2300000 Years 10 Tax rate 21% Discount rate 10% Dep 2300000/10 230,000 Part a: Accounting Break-even sales -(Cash FC+Dep)/(SP-vC) 8900 (215000+230000)/(120-70) Part b: Let 'Q' be the NPV break even level of sales factor working: Initial investment-(((SP-VC)*Q-FC-Dep)*(1-t)+Dep)*PVIFA(R%,n) (1-(1+r)A-n)/r PVIFA(10%,10) (1-(1.1^-10))/0.1 PVIFA(R%,n) 2300000=((120-70)*Q-215000-230000)*(1-0.21)+230000)*6.14456711 2300000-((500-445000)*0.79+230000)*6.14456711 6.1445671 2300000-(39.5Q-351550+230000)*6.14456711 2300000 (39.5Q-12 1550) *6.14456711 2300000 242.7104Q-746872.13 242.7104Q 2300000+74687 2.13 242.71040 3046872.13 Q 12554 SP VC Sale price variable cost Fixed cost Depreciation FC Dep Sheet155 Sheet156 Sheet158 Sheet159 Sheet154 Sheet157 Sheeti60 Sheet161 Sheet162 ENG 11:03 09/11/2019 UK