# NPV and Taxes

The NPV (net present value) of an investment is calculated by adding together the present value of each of the individual cash flows associated with the investment. This technique is more fully discussed in our net present value tutorial.

The purpose of this tutorial is to discuss the effect of taxation on each of the investment cash flows and, as a result, on the NPV of the investment itself.

## Impact of NPV and Taxes

Taxation will impact each type of cash flow from the investment in different ways, in any calculations the after tax cash flow should be used when solving time value of money problems. Typical cash flows which might occur for an investment in a project include the following:

Initial Investment
The initial investment is a cash flow out of the business, the amount before tax is used as the tax effect is taken care of using the depreciation / tax allowances (see below).

Depreciation and Tax Allowances
Tax allowances on the initial investment are normally given over a number of years. Often straight line depreciation is used as an estimate of the tax allowances. The effect of this tax allowance is to reduce the tax paid by the business, and this reduction can be viewed as a cash flow into the business. Salvage values on equipment used within the project are normally not taken into account when calculating the straight line depreciation or tax allowances.

Operating Income
Operating income is subject to tax and the cash flow after tax is used in calculations

Operating Expenses
Operating expenses are tax allowable and therefore reduce the tax paid by the business. This reduction in tax is viewed as a cash flow into the business.

Working Capital
Working capital increases needed for the project are normally returned after the project and there is no tax effect to consider.

Salvage Value
Salvage values on equipment used within the project are normally seen as a cash flow into the business at the end of the project. The salvage value is subject to tax, and the after tax cash flow should be used.

One off costs
One off costs such as maintenance charges are treated like operating expenses and are tax allowable, and therefore reduce the tax paid by the business. This reduction in tax is viewed as a cash flow into the business.

## NPV and Taxes Example

To demonstrate the effect of tax on the net present value we will look at a simple example. Suppose a business invests 20,000 in an asset which will reduce costs by 9,000 a year for 4 years. For tax purposes the asset is depreciated on a straight line basis over 4 years. The business has a tax rate of 20% and uses an after tax discount rate of 6% to evaluate investments.

The cash flows from the project are as follows:

1. The initial investment in the project is 20,000 at the start of year 1.
2. The initial investment of 20,000 is depreciated over 4 years and results in a tax allowance of 20,000/4 = 5,000 a year. This allowance gives a tax saving of 5,000 x 20% = 1,000 a year for 4 years.
3. The reduction in costs increases the net income of the business by 9,000 a year. However, this is subject to tax of 9,000 x 20% = 1,800, resulting in an increase of 7,200 a year for 4 years.

The cash flows from the investment in the asset can be seen in the cash flow diagram below.

Dealing with each of the cash flows in turn, the net present value of the project is calculated as follows:

Preset Value of the Tax Savings due to Depreciation
The present value of the tax saving due to the tax allowance based on depreciation is given by the present value of an annuity formula as follows:

```PV = Pmt x (1 - 1 / (1 + i)n) / i
PV = 1000 x (1 - 1 / (1 + 6%)4) / 6%
PV = 3,465
```

Preset Value of the Reduction in Costs
The present value of the reduction in costs is also given by the present value of an annuity formula as follows:

```PV = Pmt x (1 - 1 / (1 + i)n) / i
PV = 7,200 x (1 - 1 / (1 + 6%)4) / 6%
PV = 24,949
```

NPV of the Investment
The NPV of the investment in the asset is the sum of the present values of each of the cash flows.

```NPV = PV investment + PV depreciation + PV reduced costs
NPV = -20,000 + 3,465 + 24,949
NPV = 8,414
```

The positive NPV means that the investment in the project should be undertaken.

## NPV and Taxes Example with a Salvage Value

Consider now a second example where the project equipment has a salvage value at the end of its useful life.

Suppose a business is considering a 4 year investment project with the following cash flows:

Equipment Cost = 120,000
Annual income = 90,000
Annual expenses = 50,000
Maintenance after 2 years = 8,000
Salvage value of equipment = 25,000

The business uses the straight line method of depreciation and excludes salvage value when calculating tax allowances for depreciation. The tax rate of the company is 20%, and the after tax discount rate used by the business is 5%.

The cash flows from the project can be summarized as follows:

1. The initial investment in the equipment is 120,000 at the start of year 1.
2. As before, the depreciation on the equipment is 120,000/4 = 30,000 a year, which gives a tax saving of 30,000 x 20% = 6,000 a year for 4 years.
3. The annual net operating income from the project is 90,000 – 50,000 = 40,000. The tax on the income is 40,000 x 20% = 8,000, giving an after tax net cash flow each year of 32,000 for 4 years.
4. The one off maintenance cost after 2 years is 8,000, after allowing for tax of 8,000 x 20% = 1,600, the cash flow is 6,400.
5. The equipment is sold after 4 years for 25,000, after tax of 25,000 x 20% = 5,000, the lump sum cash flow from the sale is 20,000.

The cash flow diagram for the project is as follows:

Dealing with each cash flow in turn, the net present value of the project is calculated as follows:

Preset Value of the Tax Savings due to Depreciation
The present value of the tax saving due to the tax allowance based on depreciation is given by the present value of an annuity formula as follows

```PV = Pmt x (1 - 1 / (1 + i)n) / i
PV = 6000 x (1 - 1 / (1 + 5%)4) / 5%
PV = 21,276
```

Preset Value of the Net Income from the Project
The present value of the net operating cash flow is also given by the present value of an annuity formula as follows

```PV = Pmt x (1 - 1 / (1 + i)n) / i
PV = 32,000 x (1 - 1 / (1 + 5%)3) / 5%
PV = 113,470
```

Preset Value of the Maintenance Cost
The present value of the one off maintenance cost is given by the present value of a lump sum formula as follows:

```PV = FV / (1 + i)n
PV = 6,400 / (1 + 5%)2
PV = 5,805
```

Preset Value of the Salvage Value
The present value of the salvage value of the equipment is also given by the present value of a lump sum formula as follows:

```PV = FV / (1 + i)n
PV = 20,000 / (1 + 5%)4
PV = 16,454
```

NPV of the Investment
Finally, the NPV of the investment in the project is the sum of the present values of each cash flow as calculated above.

```NPV = -120,000 + 21,276 + 113,470 - 5,805 + 16,454
NPV = 25,395
```

The positive NPV means that the investment in the project should be undertaken.