Question

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?

Answer 1

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

Step-by-step 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:

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 85,000

time 10

rate 0.1

`85000 * (1-(1+0.1)^(-10) )/(0.1) = PV\\`

PV $522,288.2040

overheaul cost at year 6: 95,000

`(Overhaul)/((1 + rate)^(time) ) = PV`

Overhaul: 95,000.00

time 6.00

rate 0.1

`(95000)/((1 + 0.1)^(6) ) = PV`

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 / (1-(1+r)^(-time) )/(rate) = C\\`

PV $880,913.22

time 10

rate 0.1

`880913.22 / (1-(1+0.1)^(-10) )/(0.1) = C\\`

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