Question

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?

Answer #1

**Answer:**

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