Net present value

From Free net encyclopedia

Net present value (or NPV) is a standard method in finance of capital budgeting – the planning of long-term investments. Using the NPV method a potential investment project should be undertaken if the present value of all cash inflows minus the present value of all cash outflows (which equals the net present value) is greater than zero.

A key input into this process is the interest rate or “discount rate” which is used to discount future cash flows to their present values. If the discount rate is equal to the shareholder’s required rate of return, any NPV > 0 means that the required return has been exceeded, and the shareholders will expect an additional profit that has a present value equal to the NPV. Thus if the goal of the corporation is to maximize shareholders’ wealth, managers should undertake all projects that have an NPV > 0, or if two projects are mutually exclusive, they should choose the one with the highest positive NPV.

1 Example
2 Formula
3 See also
4 External links

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Example

X corporation must decide whether to introduce a new product line. The new product will have startup costs, operational costs, and incoming cash flows over six years. This project will have an immediate (t=0) cash outflow of $100,000 (which might include machinery, and employee training costs). Other cash outflows for years 1-6 are expected to be $5,000 per year. Cash inflows are expected to be $30,000 per year for years 1-6. All cash flows are after-tax, and there are no cash flows expected after year 6. The required rate of return is 10%. The present value (PV) can be calculated for each year:

T=0 -$100,000 / 1.10^0 = -$100,000 PV.

T=1 ($30,000 - $5,000)/ 1.10^1 = $22,727 PV.

T=2 ($30,000 - $5,000)/ 1.10^2 = $20,661 PV.

T=3 ($30,000 - $5,000)/ 1.10^3 = $18,783 PV.

T=4 ($30,000 - $5,000)/ 1.10^4 = $17,075 PV.

T=5 ($30,000 - $5,000)/ 1.10^5 = $15,523 PV.

T=6 ($30,000 - $5,000)/ 1.10^6 = $14,112 PV.

The sum of all these present values is the net present value, which equals $8,882. Since the NPV is greater than zero, the corporation should invest in the project.

More realistic problems would need to consider other factor, generally including the calculation of taxes, uneven cash flows, and salvage values.

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Formula

Net Present Value can thus be calculated by the following formula, where t is the amount of time (usually in years) that cash has been invested in the project, N the total length of the project (in this case, five years), i the cost of capital and C the cash flow at that point in time.

if the only cash outflow is the initial investment, then the formula may be written:

<math>\mbox{NPV} = \sum_{t=1}^N \frac{C_t}{(1+i)^t} - Initial Investment</math>

The above example is based on a constant rate being used for future interest rate predictions and works very well for small amounts of money or short time horizons. Any calculations which involve large amounts or protracted time spans will use a yield curve to give different rates for the various time points on the calculation. So, the rate for 1 year may be the 10% - the (money market) rate while the rate for 2 years may be 11% and that for 3 years 11.5%, and so on.

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