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(Prob. 5.32) The industrial engineering department for Invade Air Fresheners has found that a new packing machine should save $45,000 for each of the next 8 years. The machine will require a major overhaul at the end of 5 years costing $12,000. The machine’s expected salvage value after 8 years is 7.5% of its original cost. If money is worth 5%, determine the amount Invade should be willing to pay for the machine.

Respuesta :

TomShelby

Answer:

It will be willing to pay up to $297,853.46

Explanation:

First, we calculate  present value of the cash saving

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

C 45000

time 8

rate 0.05

[tex]45000 \times \frac{1-(1+0.05)^{-8} }{0.05} = PV\\[/tex]

PV $290,844.57

Then, the present Value of the salvage value

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

Maturity   7.50 %

time   8.00

rate   0.05

[tex]\frac{7.5}{(1 + 0.05)^{8} } = PV[/tex]  

PV   5.08 %

This is calculate as a percent, because we are not given with a cash value.

Last, the 12,000 major overhaul

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

Maturity   -12,000.00

time   8.00

rate   0.05

[tex]\frac{12000}{(1 + 0.05)^{8} } = PV[/tex]  

PV   -8,122.07

This PV is negative as it is a cash out-flow

Lastly, we add them all:

290,844.57 + 0.0508PV - 8,122.07 = PV

And solve for PV

290,844.57 - 8,122.07 = PV - 0.0508PV

282,722.5‬ = 0.9492PV

282,722.5/0.9492 = PV

PV = 297,853.455541 = 297,853.46

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