Example (3): We have three alternatives highway improvements to consider. In which should we choose to...

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Example (3): We have three alternatives highway improvements to consider. In which should we choose to invest? All will last

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Answer 1

Answer #1

We should choose the alternative with the highest NPV.

Alternative 1

Annual saving = 5000 + 3000 + 500 + 1500 = $10,000.

Present value of annual savings is calculated using PV function in Excel ;

rate = 3%

nper = 50

pmt = 10000

PV is calculated to be $257,298

NPV = PV of savings - construction cost = $257,298 - $185,000 = $72,298.

fPV(3%,50,10000) A1 A В E ($257,298) 1 0

Alternative 2

Annual saving = 5000 + 6500 + 500 + 2500 = $14,500.

Present value of annual savings is calculated using PV function in Excel ;

rate = 3%

nper = 50

pmt = 14500

PV is calculated to be $373,082.

NPV = PV of savings - construction cost = $373,082 - $220,000 = $153,082.

fiPV(3%,50,14500) A2 A C E ($373,082) 2

Alternative 3

Annual saving = 7000 + 6000 + 2800 + 3000 = $18,800.

Present value of annual savings is calculated using PV function in Excel ;

rate = 3%

nper = 50

pmt = 18800

PV is calculated to be $483,720.

NPV = PV of savings - construction cost = $483,720 - $310,000 = $173,720.4

fPV(3%,50,18800) АЗ A В D Е ($483,720)

Alternative 3 should be chosen as it has the highest NPV.

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Answer 2

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