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| In [[finance]], the '''net present value''' ('''NPV''') or '''net present worth''' ('''NPW''')<ref name=netpresworth>{{cite book | author=Lin, Grier C. I.; Nagalingam, Sev V. | authorlink= | coauthors= | title=CIM justification and optimisation | year=2000 | publisher=Taylor & Francis | location=London | isbn=0-7484-0858-4 | pages=36}}</ref> of a [[time series]] of [[cash flow]]s, both incoming and outgoing, is defined as the sum of the [[present value]]s (PVs) of the individual cash flows of the same entity.
| | Last but not least, make sure you have enough shingles to finish the job and to cover the bare minimum of repairs. The chance of a minor repair becoming a major problem can be mitigated just by the homeowner taking advantage of available resources. This is a simple process and will keep you from costly and time-consuming roof shingle repairs. At the end of the day, the right roofing job for your Portland home should fall within your budget. There are several ways to install green roof systems, largely depending on where you want to place the insulation layer. <br><br>To strengthen the roof, roofing contractors would advise getting it checked every year. When the roof cement has dried, the fiberglass tape prevents cracking on the edges. For example, for the roof repair of thermoplastic systems, duct tapes & sealants are the best suited repair materials, whereas fully developed roof systems can be repaired effectively with the help of plastic roof cement. When you adored this information in addition to you would want to get details with regards to [http://houstonroofingcontractors.net Woodlands commercial roofing] i implore you to check out the site. If your metal roof has larger holes, clean and sand the area before spreading roofing cement over the damaged area. You just need to help him or her with the inputs that are required to make a plan or an estimate. <br><br>Professional contractors state that colors do not really matter as much in differing types of weather. Their expansive knowledge in various types of roofs and materials makes them an necessitous tool for your roof repair. does not mean you have to replace your entire roof. No matter what your living situation is, you can make your surrounding more green. Starting with a fresh surface will make it easy to install a new underlayment where needed, a new leak barrier membrane, metal flashings, and vent covers. <br><br>One of the materials which will need this by default is that of the wooden roofing systems. There are limitless advantages of this revolutionary product, but to enjoy them all, you need to be extra careful in order to handle it with ease. Now, when it comes to fixing your damaged roof you are also presented with an eco friendly option, and that is to choose Rubber Roofing Material. Once the moss is scrubbed off, a strip of zinc or copper should be nailed to the affected area. It's not impossible for a homeowner to reroof his own home, but most roofing jobs are done by professionals. <br><br>Water can travel significantly along the insides of the house before it finally creates the tell-tale stain. By spending a bit more money you can be sure that the job will be done properly and last another five to ten years. Cedar's insulative quality, artistic appeal, and wind and shock resistance makes the cedar shakes and shingle the best choice for your roofing. Screw the wire brush cleaning head onto the first rod, and push the head upwards through the inspection hatch while rotating the rod counterclockwise. ll need longer nails to get through their extra material. |
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| In the 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 used throughout [[economics]], [[finance]], and [[accounting]], it measures the excess or shortfall of cash flows, in present value terms, above the cost of funds.
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| NPV can be described as the “difference amount” between the sums of discounted: cash inflows and cash outflows. It compares the present value of money today to the present value of money in the future, taking inflation and returns into account
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| The NPV of a sequence of cash flows takes as input the cash flows and a discount rate or discount curve and outputs a price; the converse process in DCF analysis — taking a sequence of cash flows and a price as input and inferring as output a discount rate (the discount rate which would yield the given price as NPV) — is called the [[yield (finance)|yield]] and is more widely used in bond trading.
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| == Formula ==
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| Each cash inflow/outflow is [[discounted]] back to its present value (PV). Then they are summed. Therefore NPV is the sum of all terms,
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| :<math>\frac{R_t}{(1+i)^{t}}</math>
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| where
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| :<math>t</math> – the time of the cash flow
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| :<math>i</math> – the [[discount window|discount rate]] (the [[rate of return]] that could be earned on an investment in the financial markets with similar risk.); the [[opportunity cost]] of capital
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| :<math>R_t</math> – the net cash flow i.e. cash inflow – cash outflow, at time ''t'' . For educational purposes, <math>R_0</math> is commonly placed to the left of the sum to emphasize its role as (minus) the investment.
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| The result of this formula is multiplied with the Annual Net cash in-flows and reduced by Initial Cash outlay the present value but in cases 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, nevertheless the usual initial investments during the first year ''R<sub>0</sub>'' are summed up a negative cash flow.<ref>{{cite book | last = Khan | first = M.Y. | title = Theory & Problems in Financial Management | publisher = McGraw Hill Higher Education | location = Boston | year = 1993| isbn = 978-0-07-463683-1 }}</ref>
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| Given the (period, cash flow) pairs (<math>t</math>, <math>R_t</math>) where <math>N</math> is the total number of periods, the net present value <math>\mathrm{NPV}</math> is given by:
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| : <math>\mathrm{NPV}(i, N) = \sum_{t=0}^{N} \frac{R_t}{(1+i)^{t}}</math>
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| == The discount rate ==
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| {{Main|Annual effective discount rate}}
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| The rate used to discount future cash flows to the present value is a key variable of this process.
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| A firm's [[weighted average cost of capital]] (after tax) is often used, but many people believe that it is appropriate to use higher discount rates to adjust for risk, opportunity cost, 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.
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| 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 5% 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 possibly lower cost of capital.
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| An NPV calculated using variable discount rates (if they are known for the duration of the investment) may better reflect the situation than one calculated from a constant discount rate for the entire investment duration. Refer to the tutorial article written by Samuel Baker<ref name="slbaker">{{cite web | last = Baker | first = Samuel L. | coauthors = | title = Perils of the Internal Rate of Return | publisher = | year= 2000 | url = http://sambaker.com/econ/invest/invest.html | accessdate = January 12, 2007}}</ref> for more detailed relationship between the NPV value and the discount rate.
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| 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.
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| 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.
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| Using variable rates over time, or discounting "guaranteed" cash flows differently 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 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 using [[rNPV]] or a similar method, then discount at the firm's rate.
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| == Use in decision making ==
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| NPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if <math>R_t</math> is a positive value, the project is in the status of positive cash inflow in the time of ''t''. If <math>R_t</math> 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.
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| {| class="wikitable" align="center" font-size="120%" border:"2px solid black;"
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| |-
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| ! width="70" | If...
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| ! width="250" | It means...
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| ! width="350" | Then...
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| | NPV > 0 || the investment would add value to the firm || the project may be accepted
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| |-
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| | NPV < 0 || the investment would subtract value from the firm || the project should be rejected
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| | 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.
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| |}
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| == Interpretation as integral transform ==
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| The time-discrete formula of the net present value
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| : <math>\mathrm{NPV}(i) = \sum_{t=0}^{N} \frac{R_t}{(1+i)^{t}}</math>
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| can also be written in a continuous variation
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| : <math>\mathrm{NPV}(i) = \int_{t=0}^{\infty} (1+i)^{-t} \cdot r(t) \, dt</math>
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| where
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| :''r(t)'' is the rate of flowing cash given in money per time, and ''r(t)'' = 0 when the investment is over.
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| Net present value can be regarded as [[Laplace transform#Formal definition|Laplace-]]<ref>{{cite journal
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| | last1 = Grubbström | first1 = Robert W.
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| | doi = 10.1287/mnsc.13.7.558
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| | title = On the Application of the Laplace Transform to Certain Economic Problems
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| | journal = Management Science
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| | volume = 13
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| | pages = 558–567
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| | year = 1967}}</ref><ref>Steven Buser: [http://universalknowledge.weebly.com/uploads/2/6/4/6/2646484/laplace_transforms_as_present_value_rules_--_stephen_buser.pdf LaPlace Transforms as Present Value Rules: A Note], ''The Journal of Finance'', Vol. 41, No. 1, March, 1986, pp. 243-247.</ref> respectively [[Z-transform#Definition|Z-transformed]] cash flow with the [[integral operator]] including the complex number ''s'' which resembles to the interest rate ''i'' from the real number space or more precisely ''s = ln(1 + i)''.
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| : <math>F(s) = \mathcal{L} \left\{f(t)\right\}=\int_0^{\infty} e^{-st} f(t) \,dt </math>
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| From this follow simplifications known from [[cybernetics]], [[control theory]] and [[system dynamics]]. Imaginary parts of the [[complex number]] ''s'' describe the oscillating behaviour (compare with the [[pork cycle]], [[cobweb theorem]], and [[phase shift]] between commodity price and supply offer) whereas real parts are responsible for representing the effect of compound interest (compare with [[damping]]).
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| == Example ==
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| <!-- People like to mess with this example. Please be 100% sure you are correct before you make a change to it!-->
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| A corporation must decide whether to introduce a new product line. The new product will have start-up expenditures, operational expenditures, and then it will have associated incoming cash receipts (sales) and disbursements (Cash paid for materials, supplies, direct labor, maintenance, repairs, and direct overhead) over 12 years. This project will have an immediate (t=0) cash outflow of 100,000 (which might include all cash paid for the machinery, transportation-in and set-up expenditures, and initial employee training disbursements.) The annual net cash flow (receipts less disbursements) from this new line for years 1-12 is forecast as follows: -54672, -39161, 3054, 7128, 25927, 28838, 46088, 77076, 46726, 76852, 132332, 166047, reflecting two years of running deficits as experience and sales are built up, with net cash receipts forecast positive after that. At the end of the 12 years it's estimated that the entire line becomes obsolete and its scrap value just covers all the removal and disposal expenditures. All values are after-tax, and the required rate of return is given to be 10%. (This also makes the simplifying assumption that the net cash received or paid is lumped into a single transaction occurring ''on the last day'' of each year.)
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| The present value (PV) can be calculated for each year:
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| {| class="wikitable" align="center" font-size="120%" border:"2px solid black;"
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| !Year!!Cash flow!!Present value
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| |-
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| |T=0||<math>\frac{-100,000}{(1+0.10)^0}</math>||-100,000
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| |T=1||<math>\frac{-54672}{(1+0.10)^1}</math>||-49701.8182
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| |-
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| |T=2||<math>\frac{-39161}{(1+0.10)^2}</math>||-32364.46281
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| |-
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| |T=3||<math>\frac{3054}{(1+0.10)^3}</math>||2294.515402
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| |-
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| |T=4||<math>\frac{7128}{(1+0.10)^4}</math>||4868.51991
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| |-
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| |T=5||<math>\frac{25927}{(1+0.10)^5}</math>||16098.62714
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| |-
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| |T=6||<math>\frac{28838}{(1+0.10)^6}</math>||16278.29919
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| |T=7||<math>\frac{46088}{(1+0.10)^7}</math>||23650.43135
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| |-
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| |T=8||<math>\frac{77076}{(1+0.10)^8}</math>||35956.52284
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| |T=9||<math>\frac{46726}{(1+0.10)^9}</math>||19816.38532
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| |T=10||<math>\frac{76852}{(1+0.10)^{10}}</math>||29629.77288
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| |-
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| |T=11||<math>\frac{132332}{(1+0.10)^{11}}</math>||46381.55871
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| |-
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| |T=12||<math>\frac{166047}{(1+0.10)^{12}}</math>||52907.69139
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| |}
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| The sum of all these present values is the net present value, which equals 65,816.04. 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. There are a few inherent assumptions in this type of discounted cash flow / net present value type analysis:
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| # The ''investment horizon'' of all possible investment projects considered are equally acceptable to the investor (e.g. a 3 year project is not necessarily preferable vs. a 20 year project.)
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| # The 10% discount rate is the appropriate (and stable) rate to discount the expected cash flows from each project being considered. Each project is assumed equally speculative.
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| # the shareholders can't get above a 10% return on their money if they were to directly assume an equivalent level of risk. (If the investor could do better elsewhere, no projects should be undertaken by the firm, and the excess capital should be turned over to the shareholder through dividends and stock repurchases.)
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| More realistic problems would also need to consider other factors, generally including: smaller time buckets, the calculation of taxes (including the cash flow timing), inflation, currency exchange fluctuations, hedged or unhedged commodity costs, risks of technical obsolescence, potential future competitive factors, uneven or unpredictable [[cash flows]], and a more realistic [[salvage value]] assumption, as well as many others.
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| == Common pitfalls ==
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| * If, for example, the <math>R_t</math> 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.
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| * 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 following: 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 method|Monte Carlo]] techniques, and explicitly calculating the cost of financing any losses incurred.
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| * 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|date=March 2007}}
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| * 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]] or other efficiency measures are used as a complement to NPV.
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| * Non-specialist users frequently make the error of computing NPV based on cash flows after interest. This is wrong because it double counts the time value of money. Free cash flow should be used as the basis for NPV computations.
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| == History ==
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| Net present value as a valuation methodology dates at least to the 19th century. [[Karl Marx]] refers to NPV as [[fictitious capital]], and the calculation as "capitalising," writing:<ref>Karl Marx, [[Capital, Volume III|''Capital,'' Volume 3]], 1909 edition, p. 548</ref>
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| {{quotation|The forming of a fictitious capital is called capitalising. Every periodically repeated income is capitalised by calculating it on the average rate of interest, as an income which would be realised by a capital at this rate of interest.}}
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| In [[mainstream economics|mainstream]] [[neo-classical economics]], NPV was formalized and popularized by [[Irving Fisher]], in his 1907 ''The Rate of Interest'' and became included in textbooks from the 1950s onwards, starting in finance texts.<ref>{{citation | title = Systemic Fear, Modern Finance and the Future of Capitalism | first1 = Shimshon | last1 = Bichler | first2 = Jonathan | last2 = Nitzan | location = Jerusalem and Montreal | date = July 2010 | url = http://bnarchives.yorku.ca/289/03/20100700_bn_systemic_fear_modern_finance_future_of_capitalism.pdf | pages = 8–11 (for discussion of history of use of NPV as "capitalisation")}}</ref><ref>{{citation | title = Capital as Power. A Study of Order and Creorder. | first2 = Shimshon | last2 = Bichler | first1 = Jonathan | last1 = Nitzan | year = 2009 | series = RIPE Series in Global Political Economy | location = New York and London | publisher = Routledge}}</ref>
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| == Alternative capital budgeting methods ==
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| * [[Adjusted present value]] (APV): adjusted present value, is the net present value of a project if financed solely by ownership equity plus the present value of all the benefits of financing.
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| * [[Accounting rate of return]] (ARR): a ratio similar to IRR and MIRR
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| * [[Cost-benefit analysis]]: which includes issues other than cash, such as time savings.
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| * [[Internal rate of return]] (IRR): which calculates the rate of return of a project while disregarding the absolute amount of money to be gained.
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| * [[Modified Internal Rate of Return|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.
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| * [[Payback period]]: which measures the time required for the cash inflows to equal the original outlay. It measures risk, not return.
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| * [[Real option]]: which attempts to value managerial flexibility that is assumed away in NPV.
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| == See also ==
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| * [[Profitability index]]
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| == References ==
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| {{Reflist}}
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| {{Corporate finance and investment banking}}
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| {{DEFAULTSORT:Net Present Value (NPV)}}
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| [[Category:Basic financial concepts]]
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| [[Category:Mathematical finance]]
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| [[Category:Investment]]
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| [[Category:Management accounting]]
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| [[nl:Contante waarde#Netto contante waarde]]
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Last but not least, make sure you have enough shingles to finish the job and to cover the bare minimum of repairs. The chance of a minor repair becoming a major problem can be mitigated just by the homeowner taking advantage of available resources. This is a simple process and will keep you from costly and time-consuming roof shingle repairs. At the end of the day, the right roofing job for your Portland home should fall within your budget. There are several ways to install green roof systems, largely depending on where you want to place the insulation layer.
To strengthen the roof, roofing contractors would advise getting it checked every year. When the roof cement has dried, the fiberglass tape prevents cracking on the edges. For example, for the roof repair of thermoplastic systems, duct tapes & sealants are the best suited repair materials, whereas fully developed roof systems can be repaired effectively with the help of plastic roof cement. When you adored this information in addition to you would want to get details with regards to Woodlands commercial roofing i implore you to check out the site. If your metal roof has larger holes, clean and sand the area before spreading roofing cement over the damaged area. You just need to help him or her with the inputs that are required to make a plan or an estimate.
Professional contractors state that colors do not really matter as much in differing types of weather. Their expansive knowledge in various types of roofs and materials makes them an necessitous tool for your roof repair. does not mean you have to replace your entire roof. No matter what your living situation is, you can make your surrounding more green. Starting with a fresh surface will make it easy to install a new underlayment where needed, a new leak barrier membrane, metal flashings, and vent covers.
One of the materials which will need this by default is that of the wooden roofing systems. There are limitless advantages of this revolutionary product, but to enjoy them all, you need to be extra careful in order to handle it with ease. Now, when it comes to fixing your damaged roof you are also presented with an eco friendly option, and that is to choose Rubber Roofing Material. Once the moss is scrubbed off, a strip of zinc or copper should be nailed to the affected area. It's not impossible for a homeowner to reroof his own home, but most roofing jobs are done by professionals.
Water can travel significantly along the insides of the house before it finally creates the tell-tale stain. By spending a bit more money you can be sure that the job will be done properly and last another five to ten years. Cedar's insulative quality, artistic appeal, and wind and shock resistance makes the cedar shakes and shingle the best choice for your roofing. Screw the wire brush cleaning head onto the first rod, and push the head upwards through the inspection hatch while rotating the rod counterclockwise. ll need longer nails to get through their extra material.