# Reem Company is considering buying a machine. The firm’s required rate of return is 10%. Find payback period

Reem Company is considering buying a machine. The firm’s required rate of return is 10%. Find payback period

answer:

Year | Cash Flows | Cumulative cash flows |

0 | ($30,000) | ($30,000) |

1 | $6,000 | ($24,000) |

2 | $6,000 | ($18,000) |

3 | $6,000 | ($12,000) |

4 | $6,000 | ($6,000) |

5 | $6,000 | $0 |

The payback year is 5 years because in this year the cumulative cash flows is equal to the initial investment .

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b) The NPV = – $ 30,000 + $ 6000 / 1.10^{1} + $ 6000 / 1.10^{2} + $ 6000 / 1.10^{3} + $ 6000 / 1.10^{4} + $ 6000 / 1.10^{5}

NPV = -$ 7255.28

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c) The ratio, called a profitability index (PI), is calculated by dividing the present value of expected future cash flows by the amount of the initial cash outlay

Year | Cash Flows | Present value of cash flows |

0 | ($30,000) | |

1 | $6,000 | 5454.55 |

2 | $6,000 | 4958.68 |

3 | $6,000 | 4507.89 |

4 | $6,000 | 4098.08 |

5 | $6,000 | 3725.53 |

Total | 22744.72 |

PI = $ 22,744.72 / $ 30,000

PI = 0.76

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d) The company should not purchase the machine because the Net present value of the machine is negative and also the profitability index is less than one .