# How to calculate NPV

/Net present value (NPV) analysis is useful for determining the current value of a stream of cash flows that extend out into the future. To calculate net present value, we use the following formula:

NPV = X * [(1+r)^n - 1]/[r * (1+r)^n]

Where:

X = The amount received per period

n = The number of periods

r = The rate of return

As an example of how to calculate net present value, the CFO of Smith Company is interested in the NPV associated with a production facility that the CEO wants to acquire. In exchange for an initial $10 million payment, Smith should receive payments of $1.2 million at the end of each of the next 15 years. Smith has a corporate cost of capital of 9%. To calculate the NPV, we insert the cash flow information into the NPV formula:

1,200,000*((1+0.09)^15-1)/(0.09*(1+0.09)^15) = $9,672,826

The present value of the cash flows associated with the investment is $327,174 lower than the initial investment in the facility, so Smith should not proceed with the investment.

It is not that difficult to estimate the amount of cash received per period, as well as the number of periods over which cash will be received. The difficult inclusion in the formula is the rate of return. This is generally considered to be a company's cost of capital, but can also be considered its incremental cost of capital, or a risk-adjusted cost of capital. In the latter case, this means that several extra percentage points are added to the corporate cost of capital for those cash flow situations considered to be unusually risky.

The NPV calculation can be massively more complicated than the simplified example just shown. In reality, you may need to include the cash flows related to the following additional items:

- Ongoing expenditures related to the investment
- Variable amounts of cash flow being received over time, rather than the same amount every time
- Variable timing for the receipt of cash, rather than the consistent receipt of a payment on the same date
- The amount of working capital required for the project, as well as the release of working capital at the end of the project
- The amount at which the investment can be resold at the end of its useful life
- The tax value of depreciation on the fixed asset that was purchased

All of the preceding factors should be considered when evaluating NPV for an investment proposal. In addition, consider generating several models to account for the worst case, most likely, and best case scenarios for cash flows.

NPV can also be used to compare several cash flows to decide which has the largest current value. NPV is commonly used in the analysis of capital purchasing requests, to see if an initial payment for fixed assets and other expenditures will generate positive cash flows in the future. If so, NPV becomes the basis for a decision to buy a fixed asset.

Net present value should not be the only method used to evaluate the need for a fixed asset. It may be more important to acquire fixed assets that can improve the capacity of a bottleneck operation, and in some cases there are regulatory or legal reasons why an asset must be acquired, irrespective of its NPV. Thus, net present value is only one of several tools that should be used to evaluate a purchasing decision.

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