You are considering purchasing a CNC machine which costs $250,000. This machine will have an estimated service life of 14 years with a salvage value of $15,000. Its annual operating and maintenance costs are estimated to be $38,000. To expect an 15% rate of return on your investment, what would be the required minimum annual revenues

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TomShelby TomShelby · Answer 1 · 2020-06-26T03:15:22+02:00

Answer:

$81,301.80

This is the yearly reveneus required to break even the project at 15% return

Explanation:

We need to solve for the equivalent annual cost to break-even financially at 15%

PV of the salvage value

[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]

Maturity $15,000.00

time 14.00

rate 0.15000

[tex]\frac{15000}{(1 + 0.15)^{14} } = PV[/tex]

PV 2,119.9299

list price: 250,000 - quota: 2,119.93 = 247,880.07

Now we solve for the equivallent annuity payment for this:

[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]

PV 247,880.07

time 14

rate 0.15

[tex]247880.07 \div \frac{1-(1+0.15)^{-14} }{0.15} = C\\[/tex]

C $ 43,301.795

Now, we add up the maintenance cost:

43,301.80 + 38,000 = 81,301.8

This is the yearly reveneus required to break even the project at 15% return