Question

Machine A costs $30,000 to purchase and is worth $9,000 in 5
years. Machine B costs $15,000 to purchase and is worth $2,000 in 2
years. Assume that these machines are needed for 20 years and can
be repurchased at the same price in the future. (use 13% interest
rate)

Compute the Annual Equivalent Cost of each machine and subtract
those values. Record the difference as a POSITIVE if Machine A is
best, or a NEGATIVE if Machine B is best.

Answer #1

Machine A: | |

AW of first cost = 30000*(0.13*1.13^5)/(1.13^5-1) = | $ 8,529.44 |

[The formula for finding PV of annuity is adapted and used] | |

AW of Salvage value = 9000*0.13/(1.13^5-1) = | $ 1,388.83 |

AEC = 8529.44-1388.83 = | $ 7,140.61 |

Machine B: | |

AW of first cost = 15000*(0.13*1.13^2)/(1.13^2-1) = | $ 8,992.25 |

AW of Salvage value = 2000*0.13/(1.13^2-1) = | $ 938.97 |

AEC = 8992.25-938.97 = | $ 8,053.28 |

Difference in AEC = 7140.61-8053.28 = | $ -912.67 |

Machine A is best as its AEC is lowest |

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