Information about Net Present Value
Net present value (NPV) is a standard method for the financial appraisal of long-term projects. Used for capital budgeting, and widely throughout economics, it measures the excess or shortfall of cash flows, in present value (PV) terms, once financing charges are met. By definition,
NPV = Present value of net cash flows. For its expression, see the formula section below.
Where
For more information on how to calculate the PV of a dollar or of a stream of payments, see time value of money.
Another approach to choosing the discount rate factor is to decide the rate which the capital needed for the project could return if invested in an alternative venture. If, for example, the capital required for Project A can earn five percent elsewhere, use this discount rate in the NPV calculation to allow a direct comparison to be made between Project A and the alternative. Related to this concept is to use the firm's Reinvestment Rate. Reinvestment rate can be defined as the rate of return for the firm's investments on average. When analyzing projects in a capital constrained environment, it may be appropriate to use the reinvestment rate rather than the firm's weighted average cost of capital as the discount factor. It reflects opportunity cost of investment, rather than the (typically) lower cost of capital.
NPV value obtained using variable discount rates (if they are known) with the years of the investment duration better reflects the real situation than that calculated from a constant discount rate for the entire investment duration. Refer to the tutorial article written by Samuel Baker[1] for more detailed relationship between the NPV value and the discount rate.
For some professional investors, their investment funds are committed to target a specified rate of return. In such cases, that rate of return should be selected as the discount rate for the NPV calculation. In this way, a direct comparison can be made between the profitability of the project and the desired rate of return.
To some extent, the selection of the discount rate is dependent on the use to which it will be put. If the intent is simply to determine whether a project will add value to the company, using the firm's weighted average cost of capital may be appropriate. If trying to decide between alternative investments in order to maximize the value of the firm, the corporate reinvestment rate would probably be a better choice.
Using variable rates over time, or discounting "guaranteed" cash flows different from "at risk" cash flows may be a superior methodology, but is seldom used in practice. Using the discount rate to adjust for risk is often difficult to do in practice (especially internationally), and is really difficult to do well. An alternative to using discount factor to adjust for risk is to explicitly correct the cash flows for the risk elements, then discount at the firm's rate.
is a positive value, the project is in the status of discounted cash inflow in the time of t. If 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 may 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.
However, NPV = 0 does not mean that a project is only expected to break even, in the sense of undiscounted profit or loss (earnings). It will show net total positive cash flow and earnings over its life.
The sum of all these present values is the net present value, which equals $8,881. Since the NPV is greater than zero, the corporation should invest in the project.
The same example in an Excel formulae:
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. have a negative value, then paradoxical results are possible. For example, if the are generally negative late in the project (eg, an industrial or mining project might have clean-up and restoration costs), then an increase in the discount rate can make the project appear more favourable. 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, ie, 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. by 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.
NPV = Present value of net cash flows. For its expression, see the formula section below.
Formula
Each cash inflow/outflow is discounted back to its PV. Then they are summed. Therefore
Where
- t - the time of the cash flow
- n - the total time of the project
- r - the discount rate
- - the net cash flow (the amount of cash) at time t.
- the capital outlay at the beginning of the investment time ( 
= 0 )
For more information on how to calculate the PV of a dollar or of a stream of payments, see time value of money.
The Discount Rate
The rate used to discount future cash flows to their present values is a key variable of this process. Most firms have a well defined policy regarding their capital structure, so the weighted average cost of capital (after tax) is used with all projects. Some people believe that it is appropriate to use higher discount rates to adjust for risk for riskier projects. Another method is to use a variable discount rate with higher rates applied to cash flows occurring further along the time span, (reflecting the yield curve premium for long-term debt).Another approach to choosing the discount rate factor is to decide the rate which the capital needed for the project could return if invested in an alternative venture. If, for example, the capital required for Project A can earn five percent elsewhere, use this discount rate in the NPV calculation to allow a direct comparison to be made between Project A and the alternative. Related to this concept is to use the firm's Reinvestment Rate. Reinvestment rate can be defined as the rate of return for the firm's investments on average. When analyzing projects in a capital constrained environment, it may be appropriate to use the reinvestment rate rather than the firm's weighted average cost of capital as the discount factor. It reflects opportunity cost of investment, rather than the (typically) lower cost of capital.
NPV value obtained using variable discount rates (if they are known) with the years of the investment duration better reflects the real situation than that calculated from a constant discount rate for the entire investment duration. Refer to the tutorial article written by Samuel Baker[1] for more detailed relationship between the NPV value and the discount rate.
For some professional investors, their investment funds are committed to target a specified rate of return. In such cases, that rate of return should be selected as the discount rate for the NPV calculation. In this way, a direct comparison can be made between the profitability of the project and the desired rate of return.
To some extent, the selection of the discount rate is dependent on the use to which it will be put. If the intent is simply to determine whether a project will add value to the company, using the firm's weighted average cost of capital may be appropriate. If trying to decide between alternative investments in order to maximize the value of the firm, the corporate reinvestment rate would probably be a better choice.
Using variable rates over time, or discounting "guaranteed" cash flows different from "at risk" cash flows may be a superior methodology, but is seldom used in practice. Using the discount rate to adjust for risk is often difficult to do in practice (especially internationally), and is really difficult to do well. An alternative to using discount factor to adjust for risk is to explicitly correct the cash flows for the risk elements, then discount at the firm's rate.
What NPV tells
NPV is an indicator of how much value an investment or project adds to the value of the firm. With a particular project, if is a positive value, the project is in the status of discounted cash inflow in the time of t. If 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 may 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. |
However, NPV = 0 does not mean that a project is only expected to break even, in the sense of undiscounted profit or loss (earnings). It will show net total positive cash flow and earnings over its life.
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 /
= -$100,000 PV.
- T=1 ($30,000 - $5,000) /
= $22,727 PV.
- T=2 ($30,000 - $5,000) /
= $20,661 PV.
- T=3 ($30,000 - $5,000) /
= $18,783 PV.
- T=4 ($30,000 - $5,000) /
= $17,075 PV.
- T=5 ($30,000 - $5,000) /
= $15,523 PV.
- T=6 ($30,000 - $5,000) /
= $14,112 PV.
The sum of all these present values is the net present value, which equals $8,881. Since the NPV is greater than zero, the corporation should invest in the project.
The same example in an 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 some (or all) of the have a negative value, then paradoxical results are possible. For example, if the are generally negative late in the project (eg, an industrial or mining project might have clean-up and restoration costs), then an increase in the discount rate can make the project appear more favourable. 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, ie, 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. by 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.
Influence of currency system
Currency systems that include demurrage alter the effective cost of capital and lead to an increased NPV emphasis on long term returns. While such currency systems are atypical in the modern world they were prevalent in earlier eras when commodities formed the basis of private currencies.Alternative capital budgeting methods
- payback period: which measures the time required for the cash inflows to equal the original outlay. It measures risk, not return.
- cost-benefit analysis: which includes issues other than cash, such as time savings.
- real option method: which attempts to value managerial flexibility that is assumed away in NPV.
- internal rate of return (IRR): which calculates the rate of return of a project without making assumptions about the reinvestment of the cash flows (hence internal)
- modified internal rate of return (MIRR): similar to IRR, but it makes explicit assumptions about the reinvestment of the cash flows. Sometimes it is called Growth Rate of Return.
Applications of NPV
- NPV Methodology, Examples, Limitations.
- Using NPV to calculate share prices.
- Calculating Net Present Value.
See also
- Rate of return on investment
- Capital budgeting
- Cost of capital
- Debt overhang
- Discounted cash flow
- Internal rate of return
- Real versus nominal value
References
Capital budgeting (or investment appraisal) is the planning process used to determine a firm's long term investments such as new machinery, replacement machinery, new plants, new products, and research and development projects.
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Economics is the social science that studies the production, distribution, and consumption of goods and services. The term economics comes from the Greek for oikos (house) and nomos (custom or law), hence "rules of the house(hold).
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Present value is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk.
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Present value is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk.
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The time value of money is based on the premise that an investor prefers to receive a payment of a fixed amount of money today, rather than an equal amount in the future, all else being equal.
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The weighted average cost of capital (WACC) is used in finance to measure a firm's cost of capital. This has been used by many firms in the past as a discount rate for financed projects, as the cost of financing (capital) is regarded by some as a logical discount rate (required
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In economics, opportunity cost, or economic cost, is the cost of something in terms of an opportunity forgone (and the benefits which could be received from that opportunity), or the most valuable forgone alternative (or highest-valued option forgone), i.e.
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The cost of capital for a firm is a weighted sum of the cost of equity and the cost of debt (see the financing decision). It is also known as the "Hurdle Rate" or "Discount Rate".
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Present value is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk.
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Cash flow is a term that refers to the amount of cash being received and spent by a business during a defined period of time, sometimes tied to a specific project. Measurement of cash flow can be used
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- to evaluate the state or performance of a business or project.
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Demurrage is a cost associated with owning or holding currency over a given period of time. It is sometimes referred to as a carrying cost of money. For commodity money such as gold, demurrage is in practice nothing more than the cost of storing and securing the gold.
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Payback period in business and economics refers to the period of time required for the return on an investment to "repay" the sum of the original investment. For example, a $1000 investment which returned $500 per year would have a two year payback period.
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Cost-benefit analysis is a term that refers both to:
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- a formal discipline used to help appraise, or assess, the case for a project or proposal, which itself is a process known as project appraisal; and
- an informal approach to making decisions of any kind.
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Real Options Analysis involves applying the mathematical techniques found in financial options to assess the best course of action to be taken when faced with a real-life decision.
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The internal rate of return (IRR) is a capital budgeting method used by firms to decide whether they should make long-term investments.
The IRR is the annualized effective compounded return rate which can be earned on the invested capital, i.e. the yield on the investment.
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The IRR is the annualized effective compounded return rate which can be earned on the invested capital, i.e. the yield on the investment.
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Modified Internal Rate of Return (MIRR) is a financial measure used to determine the attractiveness of an investment. It is generally used as part of a capital budgeting process to rank various alternative choices.
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In finance, rate of return (ROR) or return on investment (ROI), or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested.
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Capital budgeting (or investment appraisal) is the planning process used to determine a firm's long term investments such as new machinery, replacement machinery, new plants, new products, and research and development projects.
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The cost of capital for a firm is a weighted sum of the cost of equity and the cost of debt (see the financing decision). It is also known as the "Hurdle Rate" or "Discount Rate".
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Debt overhang is a fiscal situation of a government, predominantly in developing countries. It describes a situation where the debt of a country exceeds its future capacity to pay it.
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In finance, the discounted cash flow (or DCF) approach describes a method to value a project, company, or financial asset using the concepts of the time value of money. All future cash flows are estimated and discounted to give them a present value.
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The internal rate of return (IRR) is a capital budgeting method used by firms to decide whether they should make long-term investments.
The IRR is the annualized effective compounded return rate which can be earned on the invested capital, i.e. the yield on the investment.
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The IRR is the annualized effective compounded return rate which can be earned on the invested capital, i.e. the yield on the investment.
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In economics, the nominal values of something are its money values in different years. Real values adjust for differences in the price level in those years. Examples include a bundle of commodities, such as gross domestic product, and income.
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January 12 is the 1st day of the year (2nd in leap years) in the Gregorian calendar. There are 0 days remaining.
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