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Gravely Gears (GG) makes gears using an automated machine costs $12,000 and has a 25% probability...

Gravely Gears (GG) makes gears using an automated machine costs $12,000 and has a 25% probability of breaking irreparably at the end of each year (assuming it was working in the previous year). The machine has a maximum five-year life and will be disposed of with zero value at the end of five years. The machine produces $4,000 of cash flow at the end of each year and the discount rate is 8% per year. What is the expected number of years the machine will lastand what would the value of the machine be? What is the NPV of the machine?

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Expert Solution

Most likely number of years of machine life = (1 + 1st year breaking down probability) * (1 + 2nd year breaking down probability)*(1 + 3rd year breaking down probability)*(1 + 4th year breaking down probability)*(1 + 5th year breaking down probability)

= (1 + 0.25) * (1 + 0.25) * (1 +0.25) * (1+ 0.25) * (1 + 0.25)

= 3.05 Year

Value of the Machine = Present Value of all future Cash Inflows

Cashflow Per year 4000
Term of Cashflows(Years) 5
Discount Rate 8%
Present Value Annuity Factor @ 8% for 5 years 3.99
Present Value of cashflows (4000*3.99) 15970.84

Value of Machine in absolute terms without probability= 15970.84

Value of Machinery taking expected life probability

Cashflow Per year 4000
Term of Cashflows(Years) 3.05
Discount Rate 8%
Present Value Annuity Factor @ 8% for 3.05 years 2.62
Present Value of cashflows (4000*3.99) 10466.18

Present Value of Machinery for expected life = 10466.18

NPV of the Machine = Present value of cash inflows - Initial investment

NPV If full life of the machine is considered = 15970.84 -12000 = 3970.84

NPV If expected life of the machine is considered = 10466.18 -12000 = -1533.82

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jeff jeffy answered 2 years ago
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