Net present value In finance, the net present value (NPV) or net present worth (NPW) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (PVs) of the individual cash flows. In case when all future cash flows are incoming (such as coupons and principal of a bond) and the only outflow of cash is the purchase price, the NPV is simply the PV of future cash flows minus the purchase price (which is its own PV). 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.

Used for capital budgeting, and widely throughout economics, finance, and accounting, it measures the excess or shortfall of cash flows, in present value terms, once financing charges are met. The NPV of a sequence of cash flows takes as input the cash flows and a discount rate or discount curve and outputting a price; the converse process in DCF analysis, taking as input a sequence of cash flows and a price and inferring as output a discount rate (the discount rate which would yield the given price as NPV) is called the yield, and is more widely used in bond trading.

Formula Each cash inflow/outflow is discounted back to its present value (PV). Then they are summed. Therefore NPV is the sum of all terms, , where t – the time of the cash flow i – the discount rate (the rate of return that could be earned on an investment in the financial markets with similar risk. ) Rt – the net cash flow (the amount of cash, inflow minus outflow) at time t (for educational purposes, R0 is commonly placed to the left of the sum to emphasize its role as (minus the) investment.

The result of this formula if multiplied with the Annual Net cash in-flows and reduced by Initial Cash outlay will be the present value but in case where the cash flows are not equal in amount then the previous formula will be used to determine the present value of each cash flow separately. Any cash flow within 12 months will not be discounted for NPV purpose. What NPV Means NPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if Rt is a positive value, the project is in the status of discounted cash inflow in the time of t.

If Rt is a negative value, the project is in the status of discounted cash outflow in the time of t. 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 opportunity cost, i. e. comparison with other available investments. In financial theory, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected. The following sums up the NPVs in various situations. If… | It means… | Then… |

NPV > 0| the investment would add value to the firm| the project may be accepted| NPV < 0| the investment would subtract value from the firm| the project should be rejected| NPV = 0| the investment would neither gain nor lose value for the firm| We should be indifferent in the decision whether to accept or reject the project. This project adds no monetary value. Decision should be based on other criteria, e. g. strategic positioning or other factors not explicitly included in the calculation. | Example A 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 each 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: Year| Cashflow| Present Value| T=0| | -$100,000| T=1| | $22,727| T=2| | $20,661| T=3| | $18,783| T=4| | $17,075|

T=5| | $15,523| T=6| | $14,112| The sum of all these present values is the net present value, which equals $8,881. 52. Since the NPV is greater than zero, it would be better to invest in the project than to do nothing, and the corporation should invest in this project if there is no alternative with a higher NPV. The same example in Excel formulae: * NPV(rate,net_inflow)+initial_investment * PV(rate,year_number,yearly_net_inflow) | | More realistic problems would need to consider other factors, generally including the calculation of taxes, uneven cash flows, and salvage values as well as the availability of alternate investment opportunities.

Common pitfalls * If for example the Rt are generally negative late in the project (e. g. , an industrial or mining project might have clean-up and restoration costs), then at that stage the company owes money, so a high discount rate is not cautious but too optimistic. Some people see this as a problem with NPV. A way to avoid this problem is to include explicit provision for financing any losses after the initial investment, that is, explicitly calculate the cost of financing such losses. * Another common pitfall is to adjust for risk by adding a premium to the discount rate.

Whilst a bank might charge a higher rate of interest for a risky project, that does not mean that this is a valid approach to adjusting a net present value for risk, although it can be a reasonable approximation in some specific cases. One reason such an approach may not work well can be seen from the foregoing: if some risk is incurred resulting in some losses, then a discount rate in the NPV will reduce the impact of such losses below their true financial cost. A rigorous approach to risk requires identifying and valuing risks explicitly, e. g. y actuarial or Monte Carlo techniques, and explicitly calculating the cost of financing any losses incurred. * Yet another issue can result from the compounding of the risk premium. R is a composite of the risk free rate and the risk premium. As a result, future cash flows are discounted by both the risk-free rate as well as the risk premium and this effect is compounded by each subsequent cash flow. This compounding results in a much lower NPV than might be otherwise calculated. The certainty equivalent model can be used to account for the risk premium without compounding its effect on present value. citation needed] * If NPV is less than 0, which is to say, negative, the project should not be immediately rejected. Sometimes companies have to execute an NPV-negative project if not executing it creates even more value destruction. * Another issue with relying on NPV is that it does not provide an overall picture of the gain or loss of executing a certain project. To see a percentage gain relative to the investments for the project, usually, Internal rate of return is used complimented to the NPV method.