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NPV Calculations

NPV Calculations

Net Present Value (NPV) is a central tool in discounted cash flow (DCF) analysis, and is a standard method for using the time value of money to appraise long-term projects. It is a time series of cash flows, both incoming and outgoing, including initial cash flows such as the cost of purchasing an asset. Each cash inflow/outflow is discounted back to its present value (PV), the results of which are summed. NPV is a desirable investment decision rule as it measures value creation. If positive, it creates value, if negative, it destroys value. Further advantages are that it considers the timing of the project's expected cash flows and the risk of the investment through the discount rate.
NPV is calculated using a financial calculator, or by a spreadsheet analysis.

The underlying formula is:
NPV = -CFo + (sum of N, t-1) CFt/(1+k) t
Where: t - the time of the cash flow
CF - the net cash flow (the amount of cash, inflow minus outflow) at time t
CFo - initial investment
k - cost of capital (discount rate or rate of return that could be earned on an investment in the financial markets with similar risk).

Cash flow estimates are often projected to five or ten years. The rate used to discount future cash flows (k) to the present value is a key variable of this process. A firm's weighted average cost of capital (WACC) is often used, but many people believe that it is appropriate to use higher discount rates to adjust for risk or other factors. A variable discount rate with higher rates applied to cash flows occurring further along the time span might be used to reflect the yield curve premium for long-term debt.

NPV is an indicator of how much value an investment or project adds to the firm as outlined in the table below.
NPV NPV > 0 Investment would create value Project may be accepted
NPV NPV < 0 Investment would destroy value Project should be rejected
NPV NPV= 0 Investment would neither gain nor lose value Indifferent if accept or reject

NPV can be used to choose between projects of different life spans or sizes. Appropriately risked projects with a positive NPV could be accepted. This does not necessarily mean that they should be undertaken since NPV at the cost of capital may not account for the opportunity i.e. comparison with other available investments. In theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected.

Using the NPV for investment decisions is more reliable than many other methods, such as ROI, however it is not without drawbacks. The calculation is very sensitive to the discount rate: a small change in the discount rates causes a large change in the NPV. As the estimate of the appropriate discount rate is uncertain, this makes NPV numbers very uncertain. An NPV also often relies on uncertain forecasts of future cash flows. One solution to both problems is to calculate a range of NPV numbers using different discount rates and forecasts, so that one can generate, for example, best, worst and median case NPV numbers, or even a probability distribution for the NPV (possibly using for example a Monte Carlo approach).