# NPV and Taxes

Net present value (NPV) is a technique used in capital budgeting to find out whether a project will add value or not. It involves finding future cash flows of an option and discounting them to find their present worth and comparing it to the initial outlay required.

Any calculation of net present value is incomplete if we ignore the income tax implications of the project. This is because governments in most of the countries collect tax from companies, which is based on the profits they generate. Taxes eat away a company’s profits and cash flows.

Taxes affect a net present calculation in two ways: first, they affect periodic operating cash flows; second, they affect the final salvage value of the project because any gain or loss on sale carries tax implications. Adjustment for taxes involves calculating after-tax net cash flows and after-tax salvage value (also called terminal value).

## Formula: after-tax net cash flows

The complexity in net present value calculation due to taxes arises from the simple fact that capital budgeting decisions are based on cash flows while income tax is calculated on net income. Net cash flows are different from net income because some expenses are non-cash such as depreciation, etc.

Following formulas are used in net present value calculation when there are tax implications.

After-tax net cash flows = (cash inflows – cash out flows) – income taxes

Income taxes = net income × tax rate

Where net income = cash inflows – cash out flows – non-cash expenses

Hence, income taxes = (cash inflows – cash out flows – non-cash expenses)×tax rate

After some algebraic manipulation, these formulas can be merged and simplified as follows:

After-tax net cash flows = cash inflows – cash outflows – (cash inflows – cash outflows – non-cash expenses) × tax rate

After-tax net cash flows = (cash inflows – cash outflows – non-cash expenses) × (1 – tax rate) + non-cash expenses

The increase in net cash flows due to decrease in taxes due to depreciation in called tax shield.

## Formula: after-tax salvage value

After tax salvage value = cash proceeds – tax on gain or loss

Tax on gain on loss = (cash proceeds – book value) × tax rate

After-tax salvage value = cash proceeds – (cash proceeds – book value) × tax rate

## Example

A4, Inc. is considering setting up a new paper mill at a cost of $100 million. It is expected to stay economical for 5 years after which the company expects to upgrade to a more efficient technology and sell it for $30 million.

Following is an extract from a report prepared by the marketing department and engineering department. All amounts are in million USD.

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

Revenue inflows | 90 | 85 | 80 | 70 | 60 |

Costs outflows | 50 | 46 | 40 | 36 | 40 |

Net cash flows before tax | 40 | 39 | 40 | 34 | 20 |

A tax rate of 30% is applicable to both income and gains and is not expected to change in 5 years. Tax code requires the company to depreciate the plant over 5 years with $10 million salvage value.

A discount rate of 8% is appropriate.

Calculate NPV. Consider tax implications.

__Solution__

All amounts are in million USD.

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

Revenue inflows | 90.0 | 85.0 | 80.0 | 70.0 | 60.0 | |

Costs outflows | – | 50.0 | 46.0 | 40.0 | 36.0 | 40.0 |

Before-tax net cash flows | 40.0 | 39.0 | 40.0 | 34.0 | 20.0 | |

Depreciation | – | 18.0 | 18.0 | 18.0 | 18.0 | 18.0 |

Income before taxes | 22.0 | 21.0 | 22.0 | 16.0 | 2.0 | |

Taxes @ 30% | – | 6.6 | 6.3 | 6.6 | 4.8 | 0.6 |

After-tax net income | 15.4 | 14.7 | 15.4 | 11.2 | 1.4 | |

Depreciation | + | 18.0 | 18.0 | 18.0 | 18.0 | 18.0 |

After-tax cash flows | 33.4 | 32.7 | 33.4 | 29.2 | 19.4 | |

After-tax salvage value | + | 24.0 | ||||

After-tax total net cash flows | 33.4 | 32.7 | 33.4 | 29.2 | 43.4 | |

Discount rate @ 8% | × | 0.926 | 0.857 | 0.794 | 0.735 | 0.681 |

Present value of cash flows | 30.9 | 28.0 | 26.5 | 21.5 | 29.5 | |

Total present value | 136.5 |

After-tax salvage value included in the schedule above

= $30 million – ($30 million – $10 million) × 30%

= $24 million

Net present value

= present value of cash flows – initial outlay

= $136.5 million – $100 million

= $36.5 million.

Since the NPV is positive, the company should go ahead with the setup of paper mill.

Please note that we will get the same after-tax total net cash flows if we subtract taxes from before-tax cash flows directly (instead of finding net income and then adding non-cash items to arrive at after-tax cash flows). Calculation for Year 1 is illustrated below.

After-tax cash flows in Year 1

= before-tax cash flows – taxes

= $40 million – $6.6 million

= $33.4 million

Written by Obaidullah Jan, ACA, CFA <--- Hire me on Upwork