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?

Solutions

Expert Solution

Most likely number of years of machine life = (1 + 1^st 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 1 year ago

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