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# NPV

## Net Present Value

A project's net present value (NPV) is the amount by which it is expected to increase firm value if proposed project's NPV is positive.

As an illustration on how to compute a project's NPV, we provide the following example. Sunshine Electric Car Company builds electric cars, and is considering investing in a new model, the R45. The new project requires an initial investment of $1 billion for robotic assembling tools and other specialized equipment. The average life of the equipment is five years with no salvage value. For simplicity we will ignore depreciation. The cost of capital for this project is 9.35%.

The projected cash flow for this project is: | ||||

Year 0 | -1,000,000 | |||

Year 1 | 150,000 | |||

Year 2 | 200,000 | |||

Year 3 | 275,000 | |||

Year 4 | 350,000 | |||

Year 5 | 400,000 | |||

NPV | $14,065.33 |

The net present value for the Sunshine R45 is positive and will increase firm value by $14 million.

## Projecting a Project Cash Flow

Calculating a project's NPV once we have the cash-flow forecasts is the simple part of capital budgeting. More difficult is estimating a project's expected cash flows. Project cash-flow forecasts are designed up from estimates of incremental revenues and costs linked with the project. For example, let say the Research & Development manger of Sunshine Electric Cars has come up with an idea for a new type of battery. The battery will boost mileage at a lower cost. R&D names the battery, Sunblast. The following financial information relates to the cost of building the new battery:

- The initial battery design cost and buying equipment is $150,000. This investment is expected to have a life of five years and deprecated using straight-line depreciation. None of the cost is expected to be recoverable at the end of the fifth year.

- The revenue in the first year is expected to be $60,000, growing 10 percent a year for the next four years.

- There will be one employee, and the total cost for this employee in year one is expected to be $30,000 growing at 5 percent a year for the next four years.

- The cost of materials (lead, copper, plastic, etc.) needed to manufacturer the battery is expected to be 40 percent of revenue in each of the five years.

- An inventory amounting to 5 percent of the revenue has to be maintained; investments in the inventory are made at the beginning of each year.

- The tax rate for Sunshine Electric Cars as a business is 40 percent.

- The cost of capital for this project is 12.14%.

- Working capital is salvaged at the end of the project.

- The revenue in the first year is expected to be $60,000, growing 10 percent a year for the next four years.

- There will be one employee, and the total cost for this employee in year one is expected to be $30,000 growing at 5 percent a year for the next four years.

- The cost of materials (lead, copper, plastic, etc.) needed to manufacturer the battery is expected to be 40 percent of revenue in each of the five years.

- An inventory amounting to 5 percent of the revenue has to be maintained; investments in the inventory are made at the beginning of each year.

- The tax rate for Sunshine Electric Cars as a business is 40 percent.

- The cost of capital for this project is 12.14%.

- Working capital is salvaged at the end of the project.

Based on this information, the estimated cash flows on the battery business is as follows:

Year 0 | 1 | 2 | 3 | 4 | 5 | |

Investment | (150,000) | |||||

Revenues | 60,000 | 66,000 | 72,600 | 79,860 | 87,846 | |

Labor | 30,000 | 31,500 | 33,075 | 34,729 | 36,465 | |

Materials | 24,000 | 26,400 | 29,040 | 31,944 | 35,138 | |

Depreciation | 30,000 | 30,000 | 30,000 | 30,000 | 30,000 | |

Operating Income | (24,000) | (21,900) | (19,515) | (16,813) | (13,758) | |

Taxes | (9,600) | (8,760) | (7,806) | (6,725) | (5,503) | |

After-tax Op. Income | (14,400) | (13,140) | (11,709) | (10,088) | (8,255) | |

+ Depreciation | 30,000 | 30,000 | 30,000 | 30,000 | 30,000 | |

- Change in Working Cap. | 3,000 | 300 | 330 | 363 | 399 | (4,392) |

Cash flow to firm | (153,000) | 15,300 | 16,530 | 17,928 | 19,513 | 26,138 |

PV at 12.14% | (153,000) | 13,644 | 13,145 | 12,713 | 12,339 | 14,739 |

3,000 | 3,300 | 3,630 | 3,993 | 4,392 | ||

Salvage PV at 12.14% | 2,477 | |||||

NPV | (83,944) |

The working capital is fully salvaged at the end of year five, resulting in a cash inflow of $4,392.

To compute the NPV, we will use Sunshine Electric Car's cost of capital of 12.14 percent. In doing so, we recognize that this is the cost of capital for a car company and that this is an investment in a battery plant. It is, however, a battery plant whose fortunes rest with how well the car company is doing and whose risk is therefore associated with the car company. The present value of the cash inflows is reduced by the initial investment of $150,000, resulting in an NPV of -$83,944. This suggests that this is not a good investment based on the cash flows it would generate.

This analysis is based on looking at the battery plant as a stand-alone entity and that the benefits of the battery plant is that it might attract more customers to the car company and get them to buy more electric cars. For purposes of this analysis, assume that the battery plant will increase electric car revenues by $500,000 in year one, growing at 10 percent a year for the following four years. In addition, assume that the pretax operating margin on these sales is 10 percent. The incremental cash flows from the synergy are:

1 | 2 | 3 | 4 | 5 | |

Increased revenues | 500,000 | 550,000 | 605,000 | 665,500 | 732,050 |

Operating Margin (%) | 10% | 10% | 10% | 10% | 10% |

Operating Income | 50,000 | 55,000 | 60,500 | 66,550 | 73,205 |

Operating income after tax (42%) | 29,000 | 31,900 | 35,090 | 38,599 | 42,459 |

PV of cash flows at 12.14% | 25,861 | 25,367 | 24,883 | 24,408 | 23,942 |

NPV | 40,517 |

The present value of the incremental cash flow generated for the electric car company as a consequence of the battery plant is $124,460. Incorporating this into a present value analysis yields the following:

NPV of battery plant = -$83,944 + $124,460 = $40,517

By incorporating the cash flows from the synergy into the analysis, we can see that the battery plant is a good investment for Sunshine Electric Car Company.

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