Question

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 last and what would the value of the machine be? What is the NPV of the machine?

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Answer #1

Answer:

Most likely number &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 AnnuallY Factor @ 8% for 5 Years 3.99
Present Value of cashflows (4000* 3.99) 15970.84

Value of Machine in absolute terms without probability = 15970.80

Value of Machinery-taking expected life probability

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

Present Value of Machinery for expected Ile =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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