Question

A company is considering two methods for obtaining a certain part. Method A will involve purchasing a machine for $40,000 with a life of 5 years, a $2,400 salvage value, and a fixed annual operating cost of $8,000. Additionally, each part produced by the method will cost $8. Method B will involve purchasing the part from a subcontractor for $30 per part. At an interest rate of 10% per year, determine the number of parts per year required for the two methods to break even. (Enter your answer as a number without the dollar $ sign.)

Answer 1

Soln. Information from question:

Cost of Machine (investment) = 40000 dollars

Life of machine, n = 5 years

Salvage value after 5 years = 2400 dollars

Fixed annual operating cost = 8000 dollars

Variable cost of production = 8 dollars per part

Sales price of product = 30 dollars per part

Interest rate per year, r    = 10%

Present value of the salvage value = Salvage value after n years / (1+r)ⁿ

= 2400 / (1+0.1)⁵ = 1490 dollars

Rate of depreciation of asset or machine = (40000 - 1490)/5 = 7702 dollars per year

Break even is a point in a business when revenues equals to the cost

Number of parts to be produced to reach break even = Total Fixed costs / (sales price/part - variable cost/part)

= Total fixed costs / (30 - 8)

= Total fixed costs / 22

For the first year, total fixed cost = 40000 + 8000 = 48000 dollars

Hence, Number of parts to be produced during first year to reach break even = 48000 / (30 - 8) = 2182

Value of asset in second year = Previous year value - Depreciation per year = 40000 - 7702 =

For the second year, total fixed cost = (40000 - 7702) + 8000 = 40298 dollars

Calculated number of parts required to be produced to reach break even for each year can be tabulated as follows:

Year	Value of asset, dollars	Fixed cost/year, dollars	Total fixed cost, dollars	Sales price/ part, dollars	Variable cost/ part, dollars	Number of parts required to be produced to reach beak even
1	40000	8000	48000	30	8	2182
2	32298	8000	40298	30	8	1832
3	24596	8000	32596	30	8	1482
4	16894	8000	24894	30	8	1132
5	9192	8000	17892	30	8	782