### Learning Outcomes

- Calculate the net present value of a capital project

To calculate the net present value of a capital project, start with the nominal cash flows. We’ll be using the JuxtaPos scenario where management is considering adding a line of puzzles that necessitates a new machine that will cost $230,000 with an estimated useful life of six years and a residual value of $40,000. Management is using the weighted average cost of capital of 15% as a hurdle rate

Net annual cash flows are as follows:

Description | Amount |
---|---|

Year 1 | $ 60,000 |

Year 2 | 60,000 |

Year 3 | 55,000 |

Year 4 | 55,000 |

Year 5 | 50,000 |

Year 6 (includes the $40,000 proceeds from sale) | 65,000 |

Next, using Excel, a financial calculator, or a PV table (as shown below), calculate the net present value of each cash flow. Use the factors from the 15% column.

Present Value of $1 | ||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Periods | 1% | 2% | 3% | 4% | 5% | 6% | 7% | 8% | 9% | 10% | 12% | 14% | 15% | 16% | 18% | 20% |

Period 1 | 0.990 | 0.980 | 0.971 | 0.962 | 0.952 | 0.943 | 0.935 | 0.926 | 0.917 | 0.909 | 0.893 | 0.877 | 0.870 | 0.862 | 0.847 | 0.833 |

Period 2 | 0.980 | 0.961 | 0.943 | 0.925 | 0.907 | 0.890 | 0.873 | 0.857 | 0.842 | 0.826 | 0.797 | 0.769 | 0.756 | 0.743 | 0.718 | 0.694 |

Period 3 | 0.971 | 0.942 | 0.915 | 0.889 | 0.864 | 0.840 | 0.816 | 0.794 | 0.772 | 0.751 | 0.712 | 0.675 | 0.658 | 0.641 | 0.609 | 0.579 |

Period 4 | 0.961 | 0.924 | 0.888 | 0.855 | 0.823 | 0.792 | 0.763 | 0.735 | 0.708 | 0.683 | 0.636 | 0.592 | 0.572 | 0.552 | 0.516 | 0.482 |

Period 5 | 0.951 | 0.906 | 0.863 | 0.822 | 0.784 | 0.747 | 0.713 | 0.681 | 0.650 | 0.621 | 0.567 | 0.519 | 0.497 | 0.476 | 0.437 | 0.402 |

Period 6 | 0.942 | 0.888 | 0.837 | 0.790 | 0.746 | 0.705 | 0.666 | 0.630 | 0.596 | 0.564 | 0.507 | 0.456 | 0.432 | 0.410 | 0.370 | 0.335 |

Period 7 | 0.933 | 0.871 | 0.813 | 0.760 | 0.711 | 0.665 | 0.623 | 0.583 | 0.547 | 0.513 | 0.452 | 0.400 | 0.376 | 0.354 | 0.314 | 0.279 |

Period 8 | 0.923 | 0.853 | 0.789 | 0.731 | 0.677 | 0.627 | 0.582 | 0.540 | 0.502 | 0.467 | 0.404 | 0.351 | 0.327 | 0.305 | 0.266 | 0.233 |

Period 9 | 0.914 | 0.837 | 0.766 | 0.703 | 0.645 | 0.592 | 0.544 | 0.500 | 0.460 | 0.424 | 0.361 | 0.308 | 0.284 | 0.263 | 0.225 | 0.194 |

Period 10 | 0.905 | 0.820 | 0.744 | 0.676 | 0.614 | 0.558 | 0.508 | 0.463 | 0.422 | 0.386 | 0.322 | 0.270 | 0.247 | 0.227 | 0.191 | 0.162 |

Period 11 | 0.896 | 0.804 | 0.722 | 0.650 | 0.585 | 0.527 | 0.475 | 0.429 | 0.388 | 0.350 | 0.287 | 0.237 | 0.215 | 0.195 | 0.162 | 0.135 |

Period 12 | 0.887 | 0.788 | 0.701 | 0.625 | 0.557 | 0.497 | 0.444 | 0.397 | 0.356 | 0.319 | 0.257 | 0.208 | 0.187 | 0.168 | 0.137 | 0.112 |

Period 13 | 0.879 | 0.773 | 0.681 | 0.601 | 0.530 | 0.469 | 0.415 | 0.368 | 0.326 | 0.290 | 0.229 | 0.182 | 0.163 | 0.145 | 0.116 | 0.093 |

Period 14 | 0.870 | 0.758 | 0.661 | 0.577 | 0.505 | 0.442 | 0.388 | 0.340 | 0.299 | 0.263 | 0.205 | 0.160 | 0.141 | 0.125 | 0.099 | 0.078 |

Year | Amount | Factor | Total |
---|---|---|---|

Year 1 | $ 60,000 | times the factor of 0.8700 | = $52,200 |

Year 2 | 60,000 | 0.7560 | $ 45,360 |

Year 3 | 55,000 | 0.6580 | $ 36,190 |

Year 4 | 55,000 | 0.5720 | $ 31,460 |

Year 5 | 50,000 | 0.4970 | $ 24,850 |

Year 6 | 65,000 | 0.4320 | $ 28,080 |

Total present value of cash inflows | Single Line$ 218,140 |

Then subtract the initial investment:

Description | Amount |
---|---|

Initial investment | $ (230,000) |

Net present value of project | Single Line$ (11,860)Double line |

This negative net present value tells us that the present value of all future cash flows, discounted at 15%, is less than the original price of the project, so it is as if we are spending $230,000 today and immediately receiving back only $218,140. In other words, the company is losing money on this project.

Here is an NPV problem worked out on video:

You can view the transcript for “Net Present Value (NPV)” here (opens in new window).

Before we calculate the Internal Rate of Return (IRR) on this project, check your understanding of the NPV method.