Answer:
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:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 85,000
time 10
rate 0.1
[tex]85000 \times \frac{1-(1+0.1)^{-10} }{0.1} = PV\\[/tex]
PV $522,288.2040
overheaul cost at year 6: 95,000
[tex]\frac{Overhaul}{(1 + rate)^{time} } = PV[/tex]
Overhaul: 95,000.00
time 6.00
rate 0.1
[tex]\frac{95000}{(1 + 0.1)^{6} } = PV[/tex]
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:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV $880,913.22
time 10
rate 0.1
[tex]880913.22 \div \frac{1-(1+0.1)^{-10} }{0.1} = C\\[/tex]
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
