Question

A project has an initial cost of $52,125, expected net cash inflows of $12,000 per year for 8 years, and a cost of capital of 12%. What is the project's NPV? (Hint: Begin by constructing a time line.)

, What is the project IRR?

What is the project's payback period?

What is the project's discounted period?

Answer #1

Discount rate | 12.000% | ||||||||

Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Cash flow stream |
-52125 | 12000 | 12000 | 12000 | 12000 | 12000 | 12000 | 12000 | 12000 |

Discounting factor | 1.000 | 1.120 | 1.254 | 1.405 | 1.574 | 1.762 | 1.974 | 2.211 | 2.476 |

Discounted cash flows project | -52125.000 | 10714.286 | 9566.327 | 8541.363 | 7626.217 | 6809.122 | 6079.573 | 5428.191 | 4846.599 |

NPV = Sum of discounted cash flows | |||||||||

NPV Project = | 7486.68 | ||||||||

Where | |||||||||

Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||||||

Discounted Cashflow= | Cash flow stream/discounting factor |

Project | |||||||||

IRR is the rate at which NPV =0 | |||||||||

IRR | 16.00% | ||||||||

Year | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Cash flow stream |
-52125.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 | 12000.000 |

Discounting factor | 1.000 | 1.160 | 1.346 | 1.561 | 1.811 | 2.100 | 2.436 | 2.826 | 3.278 |

Discounted cash flows project | -52125.000 | 10344.929 | 8918.130 | 7688.118 | 6627.753 | 5713.636 | 4925.597 | 4246.246 | 3660.592 |

NPV = Sum of discounted cash flows | |||||||||

NPV Project = | 0.000 | ||||||||

Where | |||||||||

Discounting factor = | (1 + discount rate)^(Corresponding period in years) | ||||||||

Discounted Cashflow= | Cash flow stream/discounting factor | ||||||||

IRR= | 16.00% |

Project | Discount rate= | 12.00% | |||

Year | Cash flow stream | Cumulative cash flow | Discounting factor | Discounted cash flows project | Cumulative discounted CF |

0 | -52125 | -52125 | 1 | -52125 | -52125.00 |

1 | 12000 | -40125 | 1.12 | 10714.28571 | -41410.71 |

2 | 12000 | -28125 | 1.2544 | 9566.326531 | -31844.39 |

3 | 12000 | -16125 | 1.404928 | 8541.362974 | -23303.02 |

4 | 12000 | -4125 | 1.57351936 | 7626.216941 | -15676.81 |

5 | 12000 | 7875 | 1.762341683 | 6809.122269 | -8867.69 |

6 | 12000 | 19875 | 1.973822685 | 6079.573454 | -2788.11 |

7 | 12000 | 31875 | 2.210681407 | 5428.190584 | 2640.08 |

8 | 12000 | 43875 | 2.475963176 | 4846.598736 | 7486.68 |

Payback period is the time by which undiscounted cashflow cover the intial investment outlay | |||||

this is happening between year 4 and 5 | |||||

therefore by interpolation payback period = 4 + (0-(-4125))/(7875-(-4125)) | |||||

4.34 Years | |||||

Discounted payback period is the time by which discounted cashflow cover the intial investment outlay | |||||

this is happening between year 6 and 7 | |||||

therefore by interpolation payback period = 6 + (0-(-2788.11))/(2640.08-(-2788.11)) | |||||

6.51 Years | |||||

Where | |||||

Discounting factor =(1 + discount rate)^(corresponding year) | |||||

Discounted Cashflow=Cash flow stream/discounting factor |

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