Your company buys shafts for their air compressors from an external vendor. these are highly polished stainless steel and they are charged $2,850 each. you have looked at buying a large production lathe to make them. the lathe will cost $305,000 and it will take a full time operator at $60,000 per year in labor and a maintenance cost of $25,000 per year. making these parts in house will require $200 in materials per shaft. there will be a large maintenance overhaul cost in year 6 of $95,000. if your company marr is 10% and your project life is 10 years, how many shafts do you need to make this project break even?

it will need to sale 54.1 shaft per year to make it break even.

Explanation:

To break even financially considering the time value of money we need to afford the equivalent annual cost  which is, the PMT of the present worth:

present worth: sum of all cost:

invesmtent: lathe cost: 305,000

yearly cash outflow:

operator wages:    60,000 per year

maintenance cost: 25,000 per year

present value:

C85,000

time10

rate0.1

PV$522,288.2040

overheaul cost at year 6: 95,000

Overhaul: 95,000.00

time   6.00

rate  0.1

PV   53,625.02

Total invesmtent:

305,000  + 522,288.20 + 53,625.02 = 880,913.22‬

Now, we need to know a PTM which is equivalent to this cost to afford them and divide by the contribution per shafts:

PV  $880,913.22

time10

rate0.1

C  $ 143,364.570

The equivalent annual cost of the project is 143,364.57 to break even we must cover this cost:

contribution per shaft: 2,850 - 200 = 2,650

annual cost of the investment:  143,364.57

shaft break even: 143,364.57 / 2,650 = 54.100

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