1907:
direct comparison to be made between
Project A and the alternative. Related to this concept is to use the firm's reinvestment rate. Re-investment 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.
4210:. The ARR is a percentage return. Say, if ARR = 7%, then it means that the project is expected to earn seven cents out of each dollar invested (yearly). If the ARR is equal to or greater than the required rate of return, the project is acceptable. If it is less than the desired rate, it should be rejected. When comparing investments, the higher the ARR, the more attractive the investment. More than half of large firms calculate ARR when appraising projects.
2019:, if there is a choice between two mutually exclusive alternatives, the one yielding the higher NPV should be selected. A positive net present value indicates that the projected earnings generated by a project or investment (in present dollars) exceeds the anticipated costs (also in present dollars). This concept is the basis for the Net Present Value Rule, which dictates that the only investments that should be made are those with positive NPVs.
4231:(CBA), sometimes also called benefitâcost analysis, is a systematic approach to estimating the strengths and weaknesses of alternatives. It is used to determine options which provide the best approach to achieving benefits while preserving savings in, for example, transactions, activities, and functional business requirements. A CBA may be used to compare completed or potential courses of action, and to estimate or evaluate the value against the
4015:
3835:
3756:) appear to exceed the outgoing cash flow (100,000), the future cash flows are not adjusted using the discount rate. Thus, the project appears misleadingly profitable. When the cash flows are discounted however, it indicates the project would result in a net loss of 31,863.09. Thus, the NPV calculation indicates that this project should be disregarded because investing in this project is the equivalent of a loss of 31,863.09 at
6155:
6145:
3909:, 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.
25:
181:) 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 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
3913:
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 effect of such losses below their true financial cost. A rigorous approach to risk requires identifying and valuing risks explicitly,
3948:
based on the cash flow that is being discounted. The second item is that the function will assume the item in the first position of the array is period 1 not period zero. This then results in incorrectly discounting all array items by one extra period. The easiest fix to both of these errors is to use the "=XNPV(...)" formula.
2139:. The discount rate is assumed to be constant over the life of an investment; however, discount rates can change over time. For example, discount rates can change as the cost of capital changes. There are other drawbacks to the NPV method, such as the fact that it displays a lack of consideration for a projectâs size and the
3912:
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
1914:
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
1746:
Over a project's lifecycle, cash flows are typically spread across each period (for example spread across each year), and as such the middle of the year represents the average point in time in which these cash flows occur. Hence mid period discounting typically provides a more accurate, although less
2122:
The NPV is heavily dependent on knowledge of future cash flows, their timing, the length of a project, the initial investment required, and the discount rate. Hence, it can only be accurate if these input parameters are correct; although, sensitivity analyzes can be undertaken to examine how the NPV
1933:
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
1906:
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
141:
Because of its simplicity, NPV is a useful tool to determine whether a project or investment will result in a net profit or a loss. A positive NPV results in profit, while a negative NPV results in a loss. The NPV measures the excess or shortfall of cash flows, in present value terms, above the cost
129:
of identical cash flows, the cash flow in the present is the most valuable, with each future cash flow becoming less valuable than the previous cash flow. A cash flow today is more valuable than an identical cash flow in the future because a present flow can be invested immediately and begin earning
3947:
When using
Microsoft's Excel, the "=NPV(...)" formula makes two assumptions that result in an incorrect solution. The first is that the amount of time between each item in the input array is constant and equidistant (e.g., 30 days of time between item 1 and item 2) which may not always be correct
3784:
The shareholders cannot 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
3789:
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
120:
dictates that time affects the value of cash flows. For example, a lender may offer 99 cents for the promise of receiving $ 1.00 a month from now, but the promise to receive that same dollar 20 years in the future would be worth much less today to that same person (lender), even if the payback in
411:
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, the previous formula will be used to determine the present value of each cash flow separately. Any cash flow
2102:
The NPV can be easily calculated using modern spreadsheets, under the assumption that the discount rate and future cash flows are known. For a firm considering investing in multiple projects, the NPV has the benefit of being additive. That is, the NPVs of different projects may be aggregated to
1918:
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
1910:
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 for more detailed
1899:(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
1246:
146:, a company should pursue every investment with a positive NPV. However, in practical terms a company's capital constraints limit investments to projects with the highest NPV whose cost cash flows, or initial cash investment, do not exceed the company's capital. NPV is a central tool in
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1490:
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cashflow (the initial investment) with positive future cashflows (the return on the investment). A key assessment is whether, for a given discount rate, the NPV is positive (profitable) or negative (loss-making). The IRR is the discount rate for which the NPV is exactly 0.
133:
NPV is determined by calculating the costs (negative cash flows) and benefits (positive cash flows) for each period of an investment. After the cash flow for each period is calculated, the present value (PV) of each one is achieved by discounting its future value (see
771:
1313:
The NPV method can be slightly adjusted to calculate how much money is contributed to a project's investment per dollar invested. This is known as the capital efficiency ratio. The formula for the net present value per dollar investment (NPVI) is given below:
2068:
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.
1873:
1625:
The NPV formula assumes that the benefits and costs occur at the end of each period, resulting in a more conservative NPV. However, it may be that the cash inflows and outflows occur at the beginning of the period or in the middle of the period.
3708:
3770:). It is the present value of each future cash flow that must be determined in order to provide any meaningful comparison between cash flows at different periods of time. There are a few inherent assumptions in this type of analysis:
2159:
Comparing mutually exclusive projects with different investment horizons can be difficult. Since unequal projects are all assumed to have duplicate investment horizons, the NPV approach can be used to compare the optimal duration NPV.
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1090:
4577:
tend to prefer net present value (NPV) analysis. Such preference has been described as being a matter of professional education, as opposed to an assessment of the actual merits of either method. In the latter group, however, the
3981:
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
3763:. The concept of time value of money indicates that cash flows in different periods of time cannot be accurately compared unless they have been adjusted to reflect their value at the same period of time (in this instance,
2621:. For simplicity, assume the company will have no outgoing cash flows after the initial 100,000 cost. This also makes the simplifying assumption that the net cash received or paid is lumped into a single transaction occurring
1741:
2388:
2274:
2022:
An investment with a positive NPV is profitable, but one with a negative NPV will not necessarily result in a net loss: it is just that the internal rate of return of the project falls below the required rate of return.
983:
3943:
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
3616:
3935:
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,
2614:. Recall, a cost is a negative for outgoing cash flow, thus this cash flow is represented as â100,000. The company assumes the product will provide equal benefits of 10,000 for each of 12 years beginning at
4465:
491:
4549:
1320:
276:
4239:), commercial transactions, and project investments. For example, the U.S. Securities and Exchange Commission must conduct cost-benefit analyses before instituting regulations or deregulations.
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2714:
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of each year. At the end of the 12 years the product no longer provides any cash flow and is discontinued without any additional costs. Assume that the effective annual discount rate is 10%.
3924:
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
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2011:. 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
5559:
1756:
3781:
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.
3928:
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
1079:
601:
4717:
3627:
4395:(EAC) is the cost per year of owning and operating an asset over its entire lifespan. It is calculated by dividing the negative NPV of a project by the "present value of
405:
1047:
878:
4079:(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.
2005:
1974:
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1523:
1302:
1275:
837:
804:
569:
542:
356:
325:
883:
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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.)
1009:
1937:
An alternative to using discount factor to adjust for risk is to explicitly correct the cash flows for the risk elements using risk-adjusted net present value (
5552:
2450:
5223:
5212:
Myers, S.C. (1974), âInteractions of
Corporate Financing and Investment Decisions â Implications for Capital Budgetingâ, Journal of Finance (March), pp. 1â25
2114:
The NPV approach does not consider hidden costs and project size. Thus, investment decisions on projects with substantial hidden costs may not be accurate.
188:
The NPV of a sequence of cash flows takes as input the cash flows and a discount rate or discount curve and outputs a present value, which is the current
3540:
The total present value of the incoming cash flows is 68,136.91. The total present value of the outgoing cash flows is simply the 100,000 at time
1635:
192:. The converse process in discounted cash flow (DCF) analysis takes a sequence of cash flows and a price as input and as output the discount rate, or
5545:
5016:"Economic multi-objective approach to design off-grid microgrids: A support for business decision making (comparison of different economic criteria)"
4567:
when comparing investment projects of unequal lifespans. However, the projects being compared must have equal risk: otherwise, EAC must not be used.
2285:
2174:
2099:
timing patterns and size differences for each project, and provides an easy, unambiguous dollar value comparison of different investment options.
1241:{\displaystyle \mathrm {NPV} (i,N,R)=R\left({\frac {1-\left({\frac {1}{1+i}}\right)^{N+1}}{1-\left({\frac {1}{1+i}}\right)}}\right),\quad i\neq 0}
5378:
4103:(MIRR): similar to IRR, but it makes explicit assumptions about the reinvestment of the cash flows. Sometimes it is called Growth Rate of Return.
4569:
The technique was first discussed in 1923 in engineering literature, and, as a consequence, EAC appears to be a favoured technique employed by
4246:
To provide a basis for comparing investments (or decisions), comparing the total expected cost of each option with its total expected benefits.
422:
The NPV can also be thought of as the difference between the discounted benefits and costs over time. As such, the NPV can also be written as:
215:
3553:
2595:
between commodity price and supply offer) whereas real parts are responsible for representing the effect of compound interest (compare with
4579:
2151:
The NPV calculation is purely financial and thus does not consider non-financial metrics that may be relevant to an investment decision.
3801:
A more simple example of the net present value of incoming cash flow over a set period of time, would be winning a
Powerball lottery of
3735:) of 3,186.31. The opposite of discounting is compounding. Taking the example in reverse, it is the equivalent of investing 3,186.31 at
90:
that asset will generate. The present value of a cash flow depends on the interval of time between now and the cash flow because of the
4405:
5178:
428:
42:
4470:
138:) at a periodic rate of return (the rate of return dictated by the market). NPV is the sum of all the discounted future cash flows.
1485:{\displaystyle \mathrm {NPVI} (i,N)={\frac {\sum _{t=1}^{N}{\frac {R_{t}}{(1+i)^{t}}}}{\sum _{t=1}^{N}{\frac {C_{t}}{(1+i)^{t}}}}}}
1049:
and so on. Furthermore, all future cash flows during a period are assumed to be at the end of each period. For constant cash flow
34:
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5479:
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5404:
5083:
4921:
4718:"Proposed Modifications to the Cost-Benefit Analysis Decision Criteria for Road Project Evaluation to Improve Decisionmaking"
4675:
2607:
A corporation must decide whether to introduce a new product line. The company will have immediate costs of 100,000 at
1919:
investments in order to maximize the value of the firm, the corporate reinvestment rate would probably be a better choice.
5339:
Beaves, Robert G. (January 1988). "Net
Present Value and Rate of Return: Implicit and Explicit Reinvestment Assumptions".
4243:
To determine if an investment (or decision) is sound, ascertaining if â and by how much â its benefits outweigh its costs.
412:
within 12 months will not be discounted for NPV purpose, nevertheless the usual initial investments during the first year
4036:
3856:
766:{\displaystyle \mathrm {NPV} (i,N)=\sum _{t=0}^{N}{\frac {B_{t}}{(1+i)^{t}}}-\sum _{t=0}^{N}{\frac {C_{t}}{(1+i)^{t}}}}
2660:
5374:
5262:"A costâbenefit analysis of document management strategies used at a financial institution in Zimbabwe: A case study"
5186:, Jerusalem and Montreal: bnarchives.net, pp. 8â11 (for discussion of history of use of NPV as "capitalisation")
4845:
4625:
4097:(IRR): which calculates the rate of return of a project while disregarding the absolute amount of money to be gained.
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3479:
3411:
3343:
4044:
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3275:
3207:
3139:
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3003:
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2799:
2731:
6026:
5050:
4314:
4307:
4109:: which measures the time required for the cash inflows to equal the original outlay. It measures risk, not return.
4100:
3821:
paid over time. See "other factors" above that could affect the payment amount. Both scenarios are before taxes.
1896:
3742:(the present value) at an interest rate of 10% compounded for 12 years, which results in a cash flow of 10,000 at
5126:
Grubbström, Robert W. (March 1967). "On The
Application of the Laplace Transform to Certain Economic Problems".
3813:, however, if one does select the "CASH" option, they will receive a one-time lump sum payment of approximately
6194:
6189:
5939:
4986:
4121:(EAC): a capital budgeting technique that is useful in comparing two or more projects with different lifespans.
4040:
3860:
2080:
NPV is an indicator for project investments, and has several advantages and disadvantages for decision-making.
1949:
NPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if
1887:
95:
4235:
of a decision, project, or policy. It is commonly used to evaluate business or policy decisions (particularly
6179:
6085:
121:
both cases was equally certain. This decrease in the current value of future cash flows is based on a chosen
2092:, which is consistent with the goal of wealth maximization by creating the highest wealth for shareholders.
1868:{\displaystyle \mathrm {NPV} (i,N)=-{\text{Initial Investment}}+\sum _{t=1}^{N}{\frac {R_{t}}{(1+i)^{t-1}}}}
6204:
5879:
5603:
5996:
4560:
Alternatively, EAC can be obtained by multiplying the NPV of the project by the "loan repayment factor".
6199:
5959:
2417:
2103:
calculate the highest wealth creation, based on the available capital that can be invested by a firm.
6130:
6115:
6105:
5944:
5759:
4228:
4221:
4183:
4176:
4082:
3703:{\displaystyle {\begin{aligned}\mathrm {NPV} &=68,136.91-100,000\\&=-31,863.09\end{aligned}}}
4692:
4150:
1892:
The rate used to discount future cash flows to the present value is a key variable of this process.
1056:
578:
6148:
6125:
6063:
5889:
5814:
5774:
5754:
5312:
Lin, Steven A. Y. (January 1976). "The
Modified Internal Rate of Return and Investment Criterion".
4961:
4396:
4025:
3845:
4888:
4329:
to rank alternative investments of equal size. As the name implies, MIRR is a modification of the
4162:
3932:
model can be used to account for the risk premium without compounding its effect on present value.
5859:
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5819:
5789:
5729:
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4265:
4259:
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3990:
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2007:
is a negative value, the project is in the status of discounted cash outflow in the time of
363:
193:
5250:
Arnold, G. (2007). Essentials of corporate financial management. London: Pearson
Education, Ltd.
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4693:"Net present value (NPV) method - explanation, example, assumptions, advantages, disadvantages"
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is a positive value, the project is in the status of positive cash inflow in the time of
6016:
5239:
5076:
Introduction to Cost-Benefit Analysis: Looking for Reasonable Shortcuts. Second edition, 2021
4088:
1277:
term is important in the above formulae. A typical capital project involves a large negative
850:
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3929:
1983:
1952:
1534:
1501:
1280:
1253:
815:
782:
547:
520:
334:
303:
212:
back to its present value (PV). Then all are summed such that NPV is the sum of all terms:
163:
147:
46:
358:
is commonly placed to the left of the sum to emphasize its role as (minus) the investment.
8:
6184:
5988:
5419:
5381:
endorses the definitions, purposes, and constructs of classes of measures that appear in
5294:
5161:
4596:
4195:
4142:
2554:{\displaystyle F(s)=\left\{{\mathcal {L}}f\right\}(s)=\int _{0}^{\infty }e^{-st}f(t)\,dt}
2131:
The accuracy of the NPV method relies heavily on the choice of a discount rate and hence
2089:
988:
170:
151:
117:
91:
3752:
The importance of NPV becomes clear in this instance. Although the incoming cash flows (
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5712:
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5143:
5112:
5031:
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3918:
159:
111:
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2123:
changes as the input variables are changed, thus reducing the uncertainty of the NPV.
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5839:
5829:
5739:
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5643:
5638:
5598:
5593:
5580:
5568:
5500:
5429:
5370:
5099:
Buser, Stephen A. (March 1986). "LaPlace Transforms as Present Value Rules: A Note".
5079:
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5015:
4917:
4841:
4749:
4737:
4671:
4621:
4564:
4354:
4326:
4191:
3721:
decreases. For example, the final incoming cash flow has a future value of 10,000 at
2425:
2088:
The NPV includes all relevant time and cash flows for the project by considering the
143:
99:
4001:
and became included in textbooks from the 1950s onwards, starting in finance texts.
2421:
2117:
6048:
6043:
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5809:
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5628:
5613:
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5273:
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5108:
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5014:
Fioriti, Davide; Pintus, Salvatore; Lutzemberger, Giovanni; Poli, D. (2020-06-01).
4729:
2016:
2012:
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296:
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5692:
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5027:
4289:
4187:
3969:
Net present value as a valuation methodology dates at least to the 19th century.
3921:
techniques, and explicitly calculating the cost of financing any losses incurred.
2573:
2140:
1736:{\displaystyle \mathrm {NPV} (i,N)=\sum _{t=0}^{N}{\frac {R_{t}}{(1+i)^{t-0.5}}}}
197:
82:) is a way of measuring the value of an asset that has cashflow by adding up the
5365:
Farris, Paul W.; Neil T. Bendle; Phillip E. Pfeifer; David J. Reibstein (2010).
6058:
5969:
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refers to the fact that the calculation excludes external factors, such as the
4273:
4199:
4106:
3925:
2588:
2577:
2569:
2383:{\displaystyle \mathrm {NPV} (i)=\int _{t=0}^{\infty }(1+i)^{-t}\cdot r(t)\,dt}
292:
178:
122:
5352:
5325:
4812:
169:
In the case when all future cash flows are positive, or incoming (such as the
6173:
5677:
4741:
4644:
4236:
4154:
4146:
4115:: which attempts to value managerial flexibility that is assumed away in NPV.
3994:
3795:
2596:
2269:{\displaystyle \mathrm {NPV} (i,N)=\sum _{t=0}^{N}{\frac {R_{t}}{(1+i)^{t}}}}
978:{\displaystyle \mathrm {NPV} (i,N)=\sum _{t=0}^{N}{\frac {R_{t}}{(1+i)^{t}}}}
174:
83:
5508:
5278:
5261:
5916:
5764:
5749:
5623:
5367:
Marketing Metrics: The Definitive Guide to Measuring Marketing Performance.
4586:(which was a year before the first mention of NPV in accounting textbooks).
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2075:
5874:
5844:
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5618:
5425:
5201:, RIPE Series in Global Political Economy, New York and London: Routledge
4112:
3958:
2592:
2565:
2132:
1900:
126:
98:). It provides a method for evaluating and comparing capital projects or
2126:
6120:
6080:
5884:
5834:
5804:
5682:
5433:
5299:
The Harvard Law School Program on Corporate Governance Discussion Paper
5147:
4574:
4366:
4358:
4322:
4269:
4207:
4203:
4158:
3611:{\displaystyle \mathrm {NPV} =PV({\text{benefits}})-PV({\text{costs}})}
2584:
209:
189:
107:
2154:
196:(IRR) which would yield the given price as NPV. This rate, called the
5854:
5717:
4583:
4285:
3970:
3791:
2096:
182:
155:
87:
4014:
3834:
1613:
That is for every dollar invested in the project, a contribution of
5904:
5799:
5784:
4787:
4570:
1750:
The NPV formula using beginning of period discounting is given by:
1525:
is the net cash flow i.e. cash inflow â cash outflow, at time
327:
is the net cash flow i.e. cash inflow â cash outflow, at time
4865:"Net Present Value (NPV): What It Means and Steps to Calculate It"
4615:
4582:
endorses EAC, having discussed it as early as 1959 in a published
1011:, where cash flows in successive periods are then discounted from
5734:
5227:
4460:{\displaystyle \mathrm {EAC} =-{\frac {\mathrm {NPV} }{A_{t,r}}}}
4318:
2146:
2118:
Relies on input parameters such as knowledge of future cash flows
5359:
486:{\displaystyle \mathrm {NPV} =\mathrm {PV} (B)-\mathrm {PV} (C)}
4544:{\displaystyle {A_{t,r}}={\frac {1-{\frac {1}{(1+r)^{t}}}}{r}}}
407:
is the discount factor, also known as the present value factor.
5260:
David, Rodreck; Ngulube, Patrick; Dube, Adock (16 July 2013).
4091:: which includes issues other than cash, such as time savings.
3805:. If one does not select the "CASH" option they will be paid
1575:
and the discounted net costs across the life of a project are
5633:
5013:
4362:
4333:(IRR) and as such aims to resolve some problems with the IRR.
3940:
or other efficiency measures are used as a complement to NPV.
2065:
the investment would neither gain nor lose value for the firm
154:
to appraise long-term projects. It is widely used throughout
5567:
5392:
1571:
If the discounted benefits across the life of a project are
4232:
2404:) is the rate of flowing cash given in money per time, and
1938:
1928:
103:
5180:
Systemic Fear, Modern Finance and the Future of Capitalism
4962:"Disadvantages of Net Present Value (NPV) for Investments"
513:
Given the (period, cash inflows, cash outflows) shown by (
5515:
5467:
5448:
5387:
Common Language: Marketing Activities and Metrics Project
1941:) or a similar method, then discount at the firm's rate.
1922:
5369:
Upper Saddle River, New Jersey: Pearson Education, Inc.
4004:
2015:, i.e., comparison with other available investments. In
1629:
The NPV formula for mid period discounting is given by:
271:{\displaystyle \mathrm {PV} ={\frac {R_{t}}{(1+i)^{t}}}}
2163:
2076:
Advantages and disadvantages of using Net Present Value
4194:. The ratio does not take into account the concept of
1620:
575:
is the total number of periods, the net present value
150:(DCF) analysis and is a standard method for using the
4639:
4637:
4473:
4408:
4186:, also known as average rate of return, or ARR, is a
4149:. The idea is to value the project as if it were all
3630:
3556:
3482:
3414:
3346:
3278:
3210:
3142:
3074:
3006:
2938:
2870:
2802:
2734:
2663:
2583:
describe the oscillating behaviour (compare with the
2453:
2288:
2177:
2127:
Relies on choice of discount rate and discount factor
1986:
1955:
1759:
1638:
1537:
1504:
1323:
1283:
1256:
1093:
1059:
1017:
991:
886:
853:
818:
785:
612:
581:
550:
523:
431:
366:
337:
306:
218:
1911:
relationship between the NPV and the discount rate.
4300:
2168:The time-discrete formula of the net present value
2155:
Difficulty in comparing mutually exclusive projects
125:(or discount rate). If for example there exists a
4838:Cognitive Biases in the Capital Investment Context
4788:"NPV Method - NPV and Risk Modelling for Projects"
4764:"Mid Period Definition, Calculation, Applications"
4634:
4543:
4459:
3977:, and the calculation as "capitalising," writing:
3702:
3610:
3524:
3456:
3388:
3320:
3252:
3184:
3116:
3048:
2980:
2912:
2844:
2776:
2708:
2553:
2382:
2268:
1999:
1968:
1867:
1735:
1550:
1517:
1484:
1296:
1269:
1240:
1073:
1041:
1003:
977:
872:
831:
798:
765:
595:
563:
536:
485:
399:
350:
319:
270:
142:of funds. In a theoretical situation of unlimited
5403:sfn error: no target: CITEREFCopelandWeston1988 (
5177:Bichler, Shimshon; Nitzan, Jonathan (July 2010),
3717:increases the present value of each cash flow at
2054:the investment would subtract value from the firm
985:By convention, the initial period occurs at time
847:The NPV can be rewritten using the net cash flow
6171:
5259:
5199:Capital as Power. A Study of Order and Creorder.
5051:"Pros and Cons of Using Net Present Value (NPV)"
3961:programs have built-in formulae for PV and NPV.
2709:{\displaystyle {\frac {-100,000}{(1+0.10)^{0}}}}
5503:: Society of Industrial Accountants of Canada.
5379:Marketing Accountability Standards Board (MASB)
4563:EAC is often used as a decision-making tool in
3525:{\displaystyle {\frac {10,000}{(1+0.10)^{12}}}}
3457:{\displaystyle {\frac {10,000}{(1+0.10)^{11}}}}
3389:{\displaystyle {\frac {10,000}{(1+0.10)^{10}}}}
5398:
3321:{\displaystyle {\frac {10,000}{(1+0.10)^{9}}}}
3253:{\displaystyle {\frac {10,000}{(1+0.10)^{8}}}}
3185:{\displaystyle {\frac {10,000}{(1+0.10)^{7}}}}
3117:{\displaystyle {\frac {10,000}{(1+0.10)^{6}}}}
3049:{\displaystyle {\frac {10,000}{(1+0.10)^{5}}}}
2981:{\displaystyle {\frac {10,000}{(1+0.10)^{4}}}}
2913:{\displaystyle {\frac {10,000}{(1+0.10)^{3}}}}
2845:{\displaystyle {\frac {10,000}{(1+0.10)^{2}}}}
2777:{\displaystyle {\frac {10,000}{(1+0.10)^{1}}}}
2279:can also be written in a continuous variation
2147:Lack of consideration of non-financial metrics
5553:
5526:sfn error: no target: CITEREFJonesSmith1982 (
5478:sfn error: no target: CITEREFJonesSmith1982 (
5459:sfn error: no target: CITEREFJonesSmith1982 (
5196:
5176:
4668:Theory & Problems in Financial Management
4616:Lin, Grier C. I.; Nagalingam, Sev V. (2000).
3790:competitive factors, uneven or unpredictable
2436:from the real number space or more precisely
5197:Nitzan, Jonathan; Bichler, Shimshon (2009),
4911:
4620:. London: Taylor & Francis. p. 36.
4169:
3905:are generally negative late in the project (
2564:From this follow simplifications known from
2412:) = 0 when the investment is over.
1878:This results in the least conservative NPV.
295:that could be earned per unit of time on an
4840:. Germany: Cabler Verlag. pp. 30â255.
4609:
4580:Society of Management Accountants of Canada
4043:. Unsourced material may be challenged and
3863:. Unsourced material may be challenged and
6154:
6144:
5560:
5546:
5521:
5473:
5454:
5125:
4252:
2111:The NPV method has several disadvantages.
2043:the investment would add value to the firm
5277:
4984:
4916:. UK: Wiley-Blackwell. pp. 115â193.
4377:
4125:
4063:Learn how and when to remove this message
3883:Learn how and when to remove this message
2544:
2373:
1944:
806:are the benefits or cash inflows at time
4670:. Boston: McGraw Hill Higher Education.
4554:where r is the annual interest rate and
4214:
3993:, NPV was formalized and popularized by
102:with cash flows spread over time, as in
5048:
4914:Public Sector Property Asset Management
4813:"Perils of the Internal Rate of Return"
839:are the costs or cash outflows at time
6172:
5338:
5078:. UK: Edward Elgar. pp. 136â245.
5073:
4912:Ngwira, Malawi; Manase, David (2016).
4835:
4804:
4715:
4085:(ARR): a ratio similar to IRR and MIRR
1923:Risk-adjusted net present value (rNPV)
5541:
5496:The appraisal of capital expenditures
5439:
5418:Fish, John Charles Lounsbury (1923).
5292:
5098:
4859:
4857:
4831:
4829:
4810:
4690:
4383:These paragraphs are an excerpt from
4153:("unleveraged"), and to then add the
4005:Alternative capital budgeting methods
2432:which resembles to the interest rate
2416:Net present value can be regarded as
1308:
130:returns, while a future flow cannot.
5492:
5417:
5266:SA Journal of Information Management
4665:
4656:erk, DeMarzo, and Stangeland, p. 64.
4268:(IRR) is a method of calculating an
4041:adding citations to reliable sources
4008:
3861:adding citations to reliable sources
3828:
3798:assumption, as well as many others.
2164:Interpretation as integral transform
1881:
419:are summed up a negative cash flow.
47:move details into the article's body
18:
5311:
4985:Damodaran, Aswath (21 April 2023).
4889:"Some Alternative Investment Rules"
3952:
2635:) can be calculated for each year:
1621:Alternative discounting frequencies
1558:are the net cash outflows, at time
13:
5113:10.1111/j.1540-6261.1986.tb04502.x
4854:
4826:
4618:CIM justification and optimisation
4435:
4432:
4429:
4416:
4413:
4410:
4343:This paragraph is an excerpt from
4175:This paragraph is an excerpt from
4131:This paragraph is an excerpt from
3824:
3809:per year for 20 years, a total of
3642:
3639:
3636:
3564:
3561:
3558:
2511:
2476:
2328:
2296:
2293:
2290:
2185:
2182:
2179:
1767:
1764:
1761:
1646:
1643:
1640:
1334:
1331:
1328:
1325:
1101:
1098:
1095:
1067:
1064:
1061:
894:
891:
888:
620:
617:
614:
589:
586:
583:
470:
467:
450:
447:
439:
436:
433:
223:
220:
200:, is widely used in bond trading.
14:
6216:
5442:Principles of Engineering Economy
4938:"Sensitivity Analysis Definition"
4734:10.5325/transportationj.51.4.0473
4337:
4325:'s attractiveness. It is used in
3728:but has a present value (at
2628:The present value (value at
6153:
6143:
5295:"The Case for Investor Ordering"
4315:modified internal rate of return
4308:Modified internal rate of return
4306:This section is an excerpt from
4301:Modified internal rate of return
4258:This section is an excerpt from
4220:This section is an excerpt from
4101:Modified internal rate of return
4013:
3833:
2106:
1897:weighted average cost of capital
503:are the benefits or cash inflows
23:
5486:
5411:
5332:
5305:
5286:
5253:
5244:
5240:Accounting Rate of Return - ARR
5233:
5216:
5205:
5190:
5170:
5154:
5119:
5092:
5067:
5042:
5007:
4978:
4954:
4930:
4905:
4881:
4357:refers to the time required to
2637:
2025:
1228:
291:is the discount rate, i.e. the
5940:Debtor-in-possession financing
5049:Mendell, Brooks (2020-05-31).
4987:"Cash Flow and Discount Rates"
4780:
4756:
4709:
4684:
4659:
4650:
4523:
4510:
3605:
3597:
3585:
3577:
3510:
3497:
3442:
3429:
3374:
3361:
3306:
3293:
3238:
3225:
3170:
3157:
3102:
3089:
3034:
3021:
2966:
2953:
2898:
2885:
2830:
2817:
2762:
2749:
2694:
2681:
2541:
2535:
2495:
2489:
2463:
2457:
2440: = ln(1 +
2370:
2364:
2346:
2333:
2306:
2300:
2254:
2241:
2201:
2189:
1888:Annual effective discount rate
1847:
1834:
1783:
1771:
1715:
1702:
1662:
1650:
1617:is made to the project's NPV.
1467:
1454:
1406:
1393:
1350:
1338:
1123:
1105:
1074:{\displaystyle \mathrm {NPV} }
963:
950:
910:
898:
867:
854:
751:
738:
689:
676:
636:
624:
596:{\displaystyle \mathrm {NPV} }
509:are the costs or cash outflows
480:
474:
460:
454:
388:
375:
256:
243:
114:plus many other applications.
96:annual effective discount rate
1:
4602:
2428:including the complex number
2137:nvestment's true risk premium
2095:The NPV formula accounts for
2083:
5880:Staggered board of directors
5028:10.1016/j.renene.2020.05.154
4716:Davies, Wayne (2012-10-01).
4691:Javed, Rashid (2016-12-28).
2602:
2057:the project may be rejected
2046:the project may be accepted
1903:premium for long-term debt.
331:. For educational purposes,
297:investment with similar risk
285:is the time of the cash flow
208:Each cash inflow/outflow is
135:
7:
5997:Accretion/dilution analysis
5293:Hirst, Scott (2018-07-01).
4590:
400:{\displaystyle 1/(1+i)^{t}}
10:
6221:
5960:Leveraged recapitalization
5493:Edge, C. Geoffrey (1959).
5424:(2nd ed.). New York:
5399:Copeland & Weston 1988
4836:Serfas, Sebastian (2011).
4557:t is the number of years.
4382:
4342:
4305:
4257:
4219:
4174:
4130:
3964:
1926:
1885:
1566:
1042:{\displaystyle t=1,2,3...}
203:
185:and returns into account.
6139:
6131:Valuation using multiples
6116:Sum-of-the-parts analysis
6086:ModiglianiâMiller theorem
5987:
5945:Dividend recapitalization
5925:
5773:
5760:Secondary market offering
5663:
5652:
5579:
5444:. New York: Ronald Press.
5440:Grant, Eugene L. (1930).
5353:10.1080/00137918808966958
5341:The Engineering Economist
5326:10.1080/00137917608902796
5314:The Engineering Economist
4811:Baker, Samuel L. (2000).
4697:Accounting For Management
4184:accounting rate of return
4177:Accounting rate of return
4170:Accounting rate of return
4165:â and other side effects.
4083:Accounting rate of return
2576:. Imaginary parts of the
2034:
2031:
6149:List of investment banks
6064:Free cash flow to equity
5890:Super-majority amendment
5815:Management due diligence
5755:Seasoned equity offering
4647:, and Stangeland, p. 94.
4206:of the proposed capital
2028:
1915:desired rate of return.
1053:, the net present value
5860:Shareholder rights plan
5850:Post-merger integration
5820:Managerial entrenchment
5790:Contingent value rights
5730:Initial public offering
5438:, and expanded upon in
5385:as part of its ongoing
5279:10.4102/sajim.v15i2.540
4331:internal rate of return
4266:Internal rate of return
4260:Internal rate of return
4253:Internal rate of return
4095:Internal rate of return
3991:neo-classical economics
3938:Internal rate of return
3794:, and a more realistic
880:in each time period as:
873:{\displaystyle (R_{t})}
194:internal rate of return
6002:Adjusted present value
5865:Special-purpose entity
5703:Direct public offering
5673:At-the-market offering
5522:Jones & Smith 1982
5474:Jones & Smith 1982
5455:Jones & Smith 1982
5167:, 1909 edition, p. 548
5101:The Journal of Finance
5074:de Rus, Ginés (2021).
4722:Transportation Journal
4545:
4461:
4393:equivalent annual cost
4385:Equivalent annual cost
4378:Equivalent annual cost
4145:introduced in 1974 by
4139:Adjusted present value
4133:Adjusted present value
4126:Adjusted present value
4119:Equivalent annual cost
4077:Adjusted present value
3984:
3704:
3612:
3526:
3458:
3390:
3322:
3254:
3186:
3118:
3050:
2982:
2914:
2846:
2778:
2710:
2555:
2384:
2270:
2227:
2001:
1970:
1945:Use in decision making
1869:
1820:
1737:
1688:
1552:
1519:
1486:
1440:
1379:
1298:
1271:
1242:
1075:
1043:
1005:
979:
936:
874:
833:
800:
767:
724:
662:
597:
565:
538:
487:
401:
352:
321:
272:
6195:Management accounting
6190:Engineering economics
6017:Conglomerate discount
5421:Engineering Economics
5140:10.1287/mnsc.13.7.558
4546:
4462:
4229:Costâbenefit analysis
4222:Costâbenefit analysis
4215:Cost-benefit analysis
4198:. ARR calculates the
4089:Cost-benefit analysis
3979:
3896:If, for example, the
3754:10,000 Ă 12 = 120,000
3705:
3613:
3527:
3459:
3391:
3323:
3255:
3187:
3119:
3051:
2983:
2915:
2847:
2779:
2711:
2556:
2385:
2271:
2207:
2002:
2000:{\displaystyle R_{t}}
1971:
1969:{\displaystyle R_{t}}
1870:
1800:
1738:
1668:
1553:
1551:{\displaystyle C_{t}}
1520:
1518:{\displaystyle R_{t}}
1487:
1420:
1359:
1299:
1297:{\displaystyle R_{0}}
1272:
1270:{\displaystyle R_{0}}
1243:
1076:
1044:
1006:
980:
916:
875:
834:
832:{\displaystyle C_{t}}
801:
799:{\displaystyle B_{t}}
768:
704:
642:
598:
566:
564:{\displaystyle C_{t}}
539:
537:{\displaystyle B_{t}}
488:
402:
353:
351:{\displaystyle R_{0}}
322:
320:{\displaystyle R_{t}}
273:
6180:Mathematical finance
6039:Economic value added
6034:Discounted cash flow
5222:Dirk Jenter (2003).
4471:
4406:
4037:improve this section
3999:The Rate of Interest
3957:Many computer-based
3930:certainty equivalent
3857:improve this section
3749:(the future value).
3628:
3554:
3480:
3412:
3344:
3276:
3208:
3140:
3072:
3004:
2936:
2868:
2800:
2732:
2661:
2451:
2286:
2175:
1984:
1953:
1757:
1636:
1535:
1502:
1321:
1281:
1254:
1091:
1057:
1015:
989:
884:
851:
816:
783:
610:
579:
548:
521:
429:
364:
335:
304:
216:
164:financial accounting
148:discounted cash flow
94:(which includes the
16:Valuation in finance
6205:Valuation (finance)
5624:Senior secured debt
4994:New York University
4666:Khan, M.Y. (1993).
4597:Profitability index
4196:time value of money
3785:stock repurchases.)
2515:
2424:cash flow with the
2332:
2135:, representing an i
2090:time value of money
1004:{\displaystyle t=0}
152:time value of money
118:Time value of money
112:insurance contracts
92:Time value of money
6159:Outline of finance
6071:Market value added
6054:Financial modeling
6012:Business valuation
5935:Debt restructuring
5713:Follow-on offering
5698:Corporate spin-off
5656:(terms/conditions)
5573:investment banking
5128:Management Science
4792:www.projectnpv.com
4541:
4457:
4369:, or to reach the
3975:fictitious capital
3917:, by actuarial or
3776:investment horizon
3700:
3698:
3608:
3522:
3454:
3386:
3318:
3250:
3182:
3114:
3046:
2978:
2910:
2842:
2774:
2706:
2551:
2501:
2380:
2312:
2266:
1997:
1966:
1865:
1794:Initial Investment
1747:conservative NPV.
1733:
1579:then the NPVI is:
1548:
1515:
1482:
1309:Capital efficiency
1294:
1267:
1238:
1071:
1039:
1001:
975:
870:
829:
796:
763:
593:
561:
534:
483:
397:
348:
317:
268:
160:financial analysis
100:financial products
86:of all the future
6200:Capital budgeting
6167:
6166:
6091:Net present value
6076:Minority interest
6007:Associate company
5983:
5982:
5950:Financial sponsor
5870:Special situation
5840:Pre-emption right
5830:Minority discount
5740:Private placement
5639:Subordinated debt
5594:Exchangeable debt
5581:Capital structure
5569:Corporate finance
5383:Marketing Metrics
5085:978-1-83910-374-2
4923:978-1-118-34658-7
4677:978-0-07-463683-1
4565:capital budgeting
4539:
4533:
4455:
4355:capital budgeting
4327:capital budgeting
4202:, generated from
4192:capital budgeting
4073:
4072:
4065:
3973:refers to NPV as
3893:
3892:
3885:
3621:In this example:
3603:
3583:
3538:
3537:
3520:
3452:
3384:
3316:
3248:
3180:
3112:
3044:
2976:
2908:
2840:
2772:
2704:
2426:integral operator
2264:
2073:
2072:
1882:The discount rate
1863:
1795:
1731:
1480:
1477:
1416:
1250:Inclusion of the
1219:
1212:
1166:
1085:and is given by:
973:
761:
699:
266:
144:capital budgeting
76:net present worth
68:net present value
64:
63:
43:length guidelines
6212:
6157:
6156:
6147:
6146:
6049:Fairness opinion
6044:Enterprise value
6027:Weighted average
5955:Leveraged buyout
5810:Drag-along right
5708:Equity carve-out
5665:Equity offerings
5661:
5660:
5657:
5629:Shareholder loan
5614:Second lien debt
5609:Preferred equity
5589:Convertible debt
5562:
5555:
5548:
5539:
5538:
5532:
5531:
5519:
5513:
5512:
5490:
5484:
5483:
5471:
5465:
5464:
5452:
5446:
5445:
5437:
5415:
5409:
5408:
5396:
5390:
5363:
5357:
5356:
5336:
5330:
5329:
5309:
5303:
5302:
5290:
5284:
5283:
5281:
5257:
5251:
5248:
5242:
5237:
5231:
5220:
5214:
5209:
5203:
5202:
5194:
5188:
5187:
5185:
5174:
5168:
5158:
5152:
5151:
5123:
5117:
5116:
5096:
5090:
5089:
5071:
5065:
5064:
5062:
5061:
5046:
5040:
5039:
5020:Renewable Energy
5011:
5005:
5004:
5002:
5000:
4991:
4982:
4976:
4975:
4973:
4972:
4958:
4952:
4951:
4949:
4948:
4934:
4928:
4927:
4909:
4903:
4902:
4900:
4899:
4893:webpage.pace.edu
4885:
4879:
4878:
4876:
4875:
4861:
4852:
4851:
4833:
4824:
4823:
4821:
4819:
4808:
4802:
4801:
4799:
4798:
4784:
4778:
4777:
4775:
4774:
4760:
4754:
4753:
4713:
4707:
4706:
4704:
4703:
4688:
4682:
4681:
4663:
4657:
4654:
4648:
4641:
4632:
4631:
4613:
4550:
4548:
4547:
4542:
4540:
4535:
4534:
4532:
4531:
4530:
4505:
4496:
4491:
4490:
4489:
4466:
4464:
4463:
4458:
4456:
4454:
4453:
4438:
4427:
4419:
4391:In finance, the
4371:break-even point
4143:valuation method
4068:
4061:
4057:
4054:
4048:
4017:
4009:
3953:Software support
3888:
3881:
3877:
3874:
3868:
3837:
3829:
3820:
3816:
3812:
3808:
3804:
3769:
3762:
3755:
3748:
3741:
3734:
3727:
3713:Observe that as
3709:
3707:
3706:
3701:
3699:
3677:
3645:
3617:
3615:
3614:
3609:
3604:
3601:
3584:
3581:
3567:
3546:
3531:
3529:
3528:
3523:
3521:
3519:
3518:
3517:
3495:
3484:
3463:
3461:
3460:
3455:
3453:
3451:
3450:
3449:
3427:
3416:
3395:
3393:
3392:
3387:
3385:
3383:
3382:
3381:
3359:
3348:
3327:
3325:
3324:
3319:
3317:
3315:
3314:
3313:
3291:
3280:
3259:
3257:
3256:
3251:
3249:
3247:
3246:
3245:
3223:
3212:
3191:
3189:
3188:
3183:
3181:
3179:
3178:
3177:
3155:
3144:
3123:
3121:
3120:
3115:
3113:
3111:
3110:
3109:
3087:
3076:
3055:
3053:
3052:
3047:
3045:
3043:
3042:
3041:
3019:
3008:
2987:
2985:
2984:
2979:
2977:
2975:
2974:
2973:
2951:
2940:
2919:
2917:
2916:
2911:
2909:
2907:
2906:
2905:
2883:
2872:
2851:
2849:
2848:
2843:
2841:
2839:
2838:
2837:
2815:
2804:
2783:
2781:
2780:
2775:
2773:
2771:
2770:
2769:
2747:
2736:
2715:
2713:
2712:
2707:
2705:
2703:
2702:
2701:
2679:
2665:
2638:
2634:
2620:
2613:
2560:
2558:
2557:
2552:
2531:
2530:
2514:
2509:
2488:
2484:
2480:
2479:
2389:
2387:
2386:
2381:
2357:
2356:
2331:
2326:
2299:
2275:
2273:
2272:
2267:
2265:
2263:
2262:
2261:
2239:
2238:
2229:
2226:
2221:
2188:
2026:
2017:financial theory
2013:opportunity cost
2006:
2004:
2003:
1998:
1996:
1995:
1975:
1973:
1972:
1967:
1965:
1964:
1874:
1872:
1871:
1866:
1864:
1862:
1861:
1860:
1832:
1831:
1822:
1819:
1814:
1796:
1793:
1770:
1742:
1740:
1739:
1734:
1732:
1730:
1729:
1728:
1700:
1699:
1690:
1687:
1682:
1649:
1616:
1609:
1607:
1605:
1604:
1603:
1599:
1596:
1595:
1591:
1578:
1574:
1557:
1555:
1554:
1549:
1547:
1546:
1524:
1522:
1521:
1516:
1514:
1513:
1491:
1489:
1488:
1483:
1481:
1479:
1478:
1476:
1475:
1474:
1452:
1451:
1442:
1439:
1434:
1418:
1417:
1415:
1414:
1413:
1391:
1390:
1381:
1378:
1373:
1357:
1337:
1303:
1301:
1300:
1295:
1293:
1292:
1276:
1274:
1273:
1268:
1266:
1265:
1247:
1245:
1244:
1239:
1224:
1220:
1218:
1217:
1213:
1211:
1197:
1184:
1183:
1182:
1171:
1167:
1165:
1151:
1137:
1104:
1083:geometric series
1080:
1078:
1077:
1072:
1070:
1052:
1048:
1046:
1045:
1040:
1010:
1008:
1007:
1002:
984:
982:
981:
976:
974:
972:
971:
970:
948:
947:
938:
935:
930:
897:
879:
877:
876:
871:
866:
865:
842:
838:
836:
835:
830:
828:
827:
809:
805:
803:
802:
797:
795:
794:
772:
770:
769:
764:
762:
760:
759:
758:
736:
735:
726:
723:
718:
700:
698:
697:
696:
674:
673:
664:
661:
656:
623:
602:
600:
599:
594:
592:
574:
570:
568:
567:
562:
560:
559:
543:
541:
540:
535:
533:
532:
516:
508:
502:
492:
490:
489:
484:
473:
453:
442:
406:
404:
403:
398:
396:
395:
374:
357:
355:
354:
349:
347:
346:
326:
324:
323:
318:
316:
315:
290:
284:
277:
275:
274:
269:
267:
265:
264:
263:
241:
240:
231:
226:
59:
56:
50:
41:Please read the
27:
26:
19:
6220:
6219:
6215:
6214:
6213:
6211:
6210:
6209:
6170:
6169:
6168:
6163:
6135:
6111:Stock valuation
6106:Residual income
6022:Cost of capital
5979:
5975:Project finance
5965:High-yield debt
5921:
5900:Tag-along right
5825:Mandatory offer
5795:Control premium
5776:
5769:
5745:Public offering
5693:Bought out deal
5655:
5654:
5648:
5575:
5566:
5536:
5535:
5525:
5520:
5516:
5491:
5487:
5477:
5472:
5468:
5458:
5453:
5449:
5416:
5412:
5402:
5397:
5393:
5364:
5360:
5337:
5333:
5310:
5306:
5291:
5287:
5258:
5254:
5249:
5245:
5238:
5234:
5221:
5217:
5210:
5206:
5195:
5191:
5183:
5175:
5171:
5159:
5155:
5124:
5120:
5097:
5093:
5086:
5072:
5068:
5059:
5057:
5047:
5043:
5012:
5008:
4998:
4996:
4989:
4983:
4979:
4970:
4968:
4960:
4959:
4955:
4946:
4944:
4936:
4935:
4931:
4924:
4910:
4906:
4897:
4895:
4887:
4886:
4882:
4873:
4871:
4863:
4862:
4855:
4848:
4834:
4827:
4817:
4815:
4809:
4805:
4796:
4794:
4786:
4785:
4781:
4772:
4770:
4762:
4761:
4757:
4714:
4710:
4701:
4699:
4689:
4685:
4678:
4664:
4660:
4655:
4651:
4642:
4635:
4628:
4614:
4610:
4605:
4593:
4588:
4587:
4526:
4522:
4509:
4504:
4497:
4495:
4479:
4475:
4474:
4472:
4469:
4468:
4443:
4439:
4428:
4426:
4409:
4407:
4404:
4403:
4388:
4380:
4375:
4374:
4365:expended in an
4348:
4340:
4335:
4334:
4311:
4303:
4298:
4297:
4290:cost of capital
4263:
4255:
4250:
4249:
4225:
4217:
4212:
4211:
4188:financial ratio
4180:
4172:
4167:
4166:
4151:equity financed
4136:
4128:
4069:
4058:
4052:
4049:
4034:
4018:
4007:
3967:
3955:
3904:
3889:
3878:
3872:
3869:
3854:
3838:
3827:
3825:Common pitfalls
3818:
3814:
3810:
3806:
3802:
3764:
3757:
3753:
3743:
3736:
3729:
3722:
3697:
3696:
3675:
3674:
3646:
3635:
3631:
3629:
3626:
3625:
3600:
3580:
3557:
3555:
3552:
3551:
3541:
3513:
3509:
3496:
3485:
3483:
3481:
3478:
3477:
3445:
3441:
3428:
3417:
3415:
3413:
3410:
3409:
3377:
3373:
3360:
3349:
3347:
3345:
3342:
3341:
3309:
3305:
3292:
3281:
3279:
3277:
3274:
3273:
3241:
3237:
3224:
3213:
3211:
3209:
3206:
3205:
3173:
3169:
3156:
3145:
3143:
3141:
3138:
3137:
3105:
3101:
3088:
3077:
3075:
3073:
3070:
3069:
3037:
3033:
3020:
3009:
3007:
3005:
3002:
3001:
2969:
2965:
2952:
2941:
2939:
2937:
2934:
2933:
2901:
2897:
2884:
2873:
2871:
2869:
2866:
2865:
2833:
2829:
2816:
2805:
2803:
2801:
2798:
2797:
2765:
2761:
2748:
2737:
2735:
2733:
2730:
2729:
2697:
2693:
2680:
2666:
2664:
2662:
2659:
2658:
2629:
2623:on the last day
2615:
2608:
2605:
2574:system dynamics
2520:
2516:
2510:
2505:
2475:
2474:
2473:
2469:
2452:
2449:
2448:
2349:
2345:
2327:
2316:
2289:
2287:
2284:
2283:
2257:
2253:
2240:
2234:
2230:
2228:
2222:
2211:
2178:
2176:
2173:
2172:
2166:
2157:
2149:
2141:cost of capital
2133:discount factor
2129:
2120:
2109:
2086:
2078:
1991:
1987:
1985:
1982:
1981:
1960:
1956:
1954:
1951:
1950:
1947:
1931:
1925:
1890:
1884:
1850:
1846:
1833:
1827:
1823:
1821:
1815:
1804:
1792:
1760:
1758:
1755:
1754:
1718:
1714:
1701:
1695:
1691:
1689:
1683:
1672:
1639:
1637:
1634:
1633:
1623:
1614:
1601:
1600:
1597:
1593:
1589:
1588:
1587:
1585:
1583:
1576:
1572:
1569:
1542:
1538:
1536:
1533:
1532:
1509:
1505:
1503:
1500:
1499:
1470:
1466:
1453:
1447:
1443:
1441:
1435:
1424:
1419:
1409:
1405:
1392:
1386:
1382:
1380:
1374:
1363:
1358:
1356:
1324:
1322:
1319:
1318:
1311:
1288:
1284:
1282:
1279:
1278:
1261:
1257:
1255:
1252:
1251:
1201:
1196:
1192:
1185:
1172:
1155:
1150:
1146:
1145:
1138:
1136:
1132:
1094:
1092:
1089:
1088:
1060:
1058:
1055:
1054:
1050:
1016:
1013:
1012:
990:
987:
986:
966:
962:
949:
943:
939:
937:
931:
920:
887:
885:
882:
881:
861:
857:
852:
849:
848:
840:
823:
819:
817:
814:
813:
807:
790:
786:
784:
781:
780:
754:
750:
737:
731:
727:
725:
719:
708:
692:
688:
675:
669:
665:
663:
657:
646:
613:
611:
608:
607:
582:
580:
577:
576:
572:
555:
551:
549:
546:
545:
528:
524:
522:
519:
518:
514:
506:
500:
466:
446:
432:
430:
427:
426:
418:
391:
387:
370:
365:
362:
361:
342:
338:
336:
333:
332:
311:
307:
305:
302:
301:
288:
282:
259:
255:
242:
236:
232:
230:
219:
217:
214:
213:
206:
110:, payouts from
60:
54:
51:
40:
37:may be too long
32:This article's
28:
24:
17:
12:
11:
5:
6218:
6208:
6207:
6202:
6197:
6192:
6187:
6182:
6165:
6164:
6162:
6161:
6151:
6140:
6137:
6136:
6134:
6133:
6128:
6126:Terminal value
6123:
6118:
6113:
6108:
6103:
6098:
6093:
6088:
6083:
6078:
6073:
6068:
6067:
6066:
6059:Free cash flow
6056:
6051:
6046:
6041:
6036:
6031:
6030:
6029:
6019:
6014:
6009:
6004:
5999:
5993:
5991:
5985:
5984:
5981:
5980:
5978:
5977:
5972:
5970:Private equity
5967:
5962:
5957:
5952:
5947:
5942:
5937:
5931:
5929:
5923:
5922:
5920:
5919:
5914:
5913:
5912:
5902:
5897:
5892:
5887:
5882:
5877:
5872:
5867:
5862:
5857:
5852:
5847:
5842:
5837:
5832:
5827:
5822:
5817:
5812:
5807:
5802:
5797:
5792:
5787:
5781:
5779:
5771:
5770:
5768:
5767:
5762:
5757:
5752:
5747:
5742:
5737:
5732:
5727:
5726:
5725:
5715:
5710:
5705:
5700:
5695:
5690:
5685:
5680:
5675:
5669:
5667:
5658:
5650:
5649:
5647:
5646:
5641:
5636:
5631:
5626:
5621:
5616:
5611:
5606:
5601:
5599:Mezzanine debt
5596:
5591:
5585:
5583:
5577:
5576:
5565:
5564:
5557:
5550:
5542:
5534:
5533:
5524:, p. 106.
5514:
5485:
5476:, p. 108.
5466:
5457:, p. 103.
5447:
5410:
5391:
5358:
5347:(4): 275â302.
5331:
5320:(4): 237â247.
5304:
5285:
5252:
5243:
5232:
5215:
5204:
5189:
5169:
5153:
5134:(7): 558â567.
5118:
5107:(1): 243â247.
5091:
5084:
5066:
5041:
5006:
4977:
4953:
4929:
4922:
4904:
4880:
4853:
4846:
4825:
4803:
4779:
4768:Financial Edge
4755:
4728:(4): 473â487.
4708:
4683:
4676:
4658:
4649:
4633:
4626:
4607:
4606:
4604:
4601:
4600:
4599:
4592:
4589:
4552:
4551:
4538:
4529:
4525:
4521:
4518:
4515:
4512:
4508:
4503:
4500:
4494:
4488:
4485:
4482:
4478:
4452:
4449:
4446:
4442:
4437:
4434:
4431:
4425:
4422:
4418:
4415:
4412:
4389:
4381:
4379:
4376:
4351:Payback period
4349:
4345:Payback period
4341:
4339:
4338:Payback period
4336:
4321:measure of an
4312:
4304:
4302:
4299:
4294:financial risk
4282:risk-free rate
4274:rate of return
4264:
4256:
4254:
4251:
4248:
4247:
4244:
4226:
4218:
4216:
4213:
4181:
4173:
4171:
4168:
4137:
4129:
4127:
4124:
4123:
4122:
4116:
4110:
4107:Payback period
4104:
4098:
4092:
4086:
4080:
4071:
4070:
4021:
4019:
4012:
4006:
4003:
3997:, in his 1907
3966:
3963:
3954:
3951:
3950:
3949:
3945:
3941:
3933:
3926:risk-free rate
3922:
3910:
3900:
3891:
3890:
3841:
3839:
3832:
3826:
3823:
3787:
3786:
3782:
3779:
3711:
3710:
3695:
3692:
3689:
3686:
3683:
3680:
3678:
3676:
3673:
3670:
3667:
3664:
3661:
3658:
3655:
3652:
3649:
3647:
3644:
3641:
3638:
3634:
3633:
3619:
3618:
3607:
3599:
3596:
3593:
3590:
3587:
3579:
3576:
3573:
3570:
3566:
3563:
3560:
3536:
3535:
3532:
3516:
3512:
3508:
3505:
3502:
3499:
3494:
3491:
3488:
3475:
3468:
3467:
3464:
3448:
3444:
3440:
3437:
3434:
3431:
3426:
3423:
3420:
3407:
3400:
3399:
3396:
3380:
3376:
3372:
3369:
3366:
3363:
3358:
3355:
3352:
3339:
3332:
3331:
3328:
3312:
3308:
3304:
3301:
3298:
3295:
3290:
3287:
3284:
3271:
3264:
3263:
3260:
3244:
3240:
3236:
3233:
3230:
3227:
3222:
3219:
3216:
3203:
3196:
3195:
3192:
3176:
3172:
3168:
3165:
3162:
3159:
3154:
3151:
3148:
3135:
3128:
3127:
3124:
3108:
3104:
3100:
3097:
3094:
3091:
3086:
3083:
3080:
3067:
3060:
3059:
3056:
3040:
3036:
3032:
3029:
3026:
3023:
3018:
3015:
3012:
2999:
2992:
2991:
2988:
2972:
2968:
2964:
2961:
2958:
2955:
2950:
2947:
2944:
2931:
2924:
2923:
2920:
2904:
2900:
2896:
2893:
2890:
2887:
2882:
2879:
2876:
2863:
2856:
2855:
2852:
2836:
2832:
2828:
2825:
2822:
2819:
2814:
2811:
2808:
2795:
2788:
2787:
2784:
2768:
2764:
2760:
2757:
2754:
2751:
2746:
2743:
2740:
2727:
2720:
2719:
2716:
2700:
2696:
2692:
2689:
2686:
2683:
2678:
2675:
2672:
2669:
2656:
2649:
2648:
2647:Present value
2645:
2642:
2604:
2601:
2589:cobweb theorem
2578:complex number
2570:control theory
2562:
2561:
2550:
2547:
2543:
2540:
2537:
2534:
2529:
2526:
2523:
2519:
2513:
2508:
2504:
2500:
2497:
2494:
2491:
2487:
2483:
2478:
2472:
2468:
2465:
2462:
2459:
2456:
2414:
2413:
2391:
2390:
2379:
2376:
2372:
2369:
2366:
2363:
2360:
2355:
2352:
2348:
2344:
2341:
2338:
2335:
2330:
2325:
2322:
2319:
2315:
2311:
2308:
2305:
2302:
2298:
2295:
2292:
2277:
2276:
2260:
2256:
2252:
2249:
2246:
2243:
2237:
2233:
2225:
2220:
2217:
2214:
2210:
2206:
2203:
2200:
2197:
2194:
2191:
2187:
2184:
2181:
2165:
2162:
2156:
2153:
2148:
2145:
2128:
2125:
2119:
2116:
2108:
2105:
2085:
2082:
2077:
2074:
2071:
2070:
2066:
2063:
2059:
2058:
2055:
2052:
2048:
2047:
2044:
2041:
2037:
2036:
2033:
2030:
1994:
1990:
1963:
1959:
1946:
1943:
1927:Main article:
1924:
1921:
1886:Main article:
1883:
1880:
1876:
1875:
1859:
1856:
1853:
1849:
1845:
1842:
1839:
1836:
1830:
1826:
1818:
1813:
1810:
1807:
1803:
1799:
1791:
1788:
1785:
1782:
1779:
1776:
1773:
1769:
1766:
1763:
1744:
1743:
1727:
1724:
1721:
1717:
1713:
1710:
1707:
1704:
1698:
1694:
1686:
1681:
1678:
1675:
1671:
1667:
1664:
1661:
1658:
1655:
1652:
1648:
1645:
1642:
1622:
1619:
1611:
1610:
1568:
1565:
1564:
1563:
1545:
1541:
1530:
1512:
1508:
1493:
1492:
1473:
1469:
1465:
1462:
1459:
1456:
1450:
1446:
1438:
1433:
1430:
1427:
1423:
1412:
1408:
1404:
1401:
1398:
1395:
1389:
1385:
1377:
1372:
1369:
1366:
1362:
1355:
1352:
1349:
1346:
1343:
1340:
1336:
1333:
1330:
1327:
1310:
1307:
1291:
1287:
1264:
1260:
1237:
1234:
1231:
1227:
1223:
1216:
1210:
1207:
1204:
1200:
1195:
1191:
1188:
1181:
1178:
1175:
1170:
1164:
1161:
1158:
1154:
1149:
1144:
1141:
1135:
1131:
1128:
1125:
1122:
1119:
1116:
1113:
1110:
1107:
1103:
1100:
1097:
1069:
1066:
1063:
1038:
1035:
1032:
1029:
1026:
1023:
1020:
1000:
997:
994:
969:
965:
961:
958:
955:
952:
946:
942:
934:
929:
926:
923:
919:
915:
912:
909:
906:
903:
900:
896:
893:
890:
869:
864:
860:
856:
845:
844:
826:
822:
811:
793:
789:
774:
773:
757:
753:
749:
746:
743:
740:
734:
730:
722:
717:
714:
711:
707:
703:
695:
691:
687:
684:
681:
678:
672:
668:
660:
655:
652:
649:
645:
641:
638:
635:
632:
629:
626:
622:
619:
616:
591:
588:
585:
558:
554:
531:
527:
511:
510:
504:
494:
493:
482:
479:
476:
472:
469:
465:
462:
459:
456:
452:
449:
445:
441:
438:
435:
416:
409:
408:
394:
390:
386:
383:
380:
377:
373:
369:
359:
345:
341:
314:
310:
299:
286:
262:
258:
254:
251:
248:
245:
239:
235:
229:
225:
222:
205:
202:
175:coupon payment
123:rate of return
62:
61:
55:September 2022
31:
29:
22:
15:
9:
6:
4:
3:
2:
6217:
6206:
6203:
6201:
6198:
6196:
6193:
6191:
6188:
6186:
6183:
6181:
6178:
6177:
6175:
6160:
6152:
6150:
6142:
6141:
6138:
6132:
6129:
6127:
6124:
6122:
6119:
6117:
6114:
6112:
6109:
6107:
6104:
6102:
6099:
6097:
6094:
6092:
6089:
6087:
6084:
6082:
6079:
6077:
6074:
6072:
6069:
6065:
6062:
6061:
6060:
6057:
6055:
6052:
6050:
6047:
6045:
6042:
6040:
6037:
6035:
6032:
6028:
6025:
6024:
6023:
6020:
6018:
6015:
6013:
6010:
6008:
6005:
6003:
6000:
5998:
5995:
5994:
5992:
5990:
5986:
5976:
5973:
5971:
5968:
5966:
5963:
5961:
5958:
5956:
5953:
5951:
5948:
5946:
5943:
5941:
5938:
5936:
5933:
5932:
5930:
5928:
5924:
5918:
5915:
5911:
5908:
5907:
5906:
5903:
5901:
5898:
5896:
5893:
5891:
5888:
5886:
5883:
5881:
5878:
5876:
5873:
5871:
5868:
5866:
5863:
5861:
5858:
5856:
5853:
5851:
5848:
5846:
5843:
5841:
5838:
5836:
5833:
5831:
5828:
5826:
5823:
5821:
5818:
5816:
5813:
5811:
5808:
5806:
5803:
5801:
5798:
5796:
5793:
5791:
5788:
5786:
5783:
5782:
5780:
5778:
5772:
5766:
5763:
5761:
5758:
5756:
5753:
5751:
5748:
5746:
5743:
5741:
5738:
5736:
5733:
5731:
5728:
5724:
5721:
5720:
5719:
5716:
5714:
5711:
5709:
5706:
5704:
5701:
5699:
5696:
5694:
5691:
5689:
5686:
5684:
5681:
5679:
5678:Book building
5676:
5674:
5671:
5670:
5668:
5666:
5662:
5659:
5651:
5645:
5642:
5640:
5637:
5635:
5632:
5630:
5627:
5625:
5622:
5620:
5617:
5615:
5612:
5610:
5607:
5605:
5602:
5600:
5597:
5595:
5592:
5590:
5587:
5586:
5584:
5582:
5578:
5574:
5570:
5563:
5558:
5556:
5551:
5549:
5544:
5543:
5540:
5529:
5523:
5518:
5510:
5506:
5502:
5498:
5497:
5489:
5481:
5475:
5470:
5462:
5456:
5451:
5443:
5435:
5431:
5427:
5423:
5422:
5414:
5406:
5401:, p. 51.
5400:
5395:
5388:
5384:
5380:
5376:
5375:0-13-705829-2
5372:
5368:
5362:
5354:
5350:
5346:
5342:
5335:
5327:
5323:
5319:
5315:
5308:
5300:
5296:
5289:
5280:
5275:
5271:
5267:
5263:
5256:
5247:
5241:
5236:
5229:
5225:
5219:
5213:
5208:
5200:
5193:
5182:
5181:
5173:
5166:
5164:
5157:
5149:
5145:
5141:
5137:
5133:
5129:
5122:
5114:
5110:
5106:
5102:
5095:
5087:
5081:
5077:
5070:
5056:
5052:
5045:
5037:
5033:
5029:
5025:
5021:
5017:
5010:
4995:
4988:
4981:
4967:
4963:
4957:
4943:
4939:
4933:
4925:
4919:
4915:
4908:
4894:
4890:
4884:
4870:
4866:
4860:
4858:
4849:
4847:9783834926432
4843:
4839:
4832:
4830:
4814:
4807:
4793:
4789:
4783:
4769:
4765:
4759:
4751:
4747:
4743:
4739:
4735:
4731:
4727:
4723:
4719:
4712:
4698:
4694:
4687:
4679:
4673:
4669:
4662:
4653:
4646:
4640:
4638:
4629:
4627:0-7484-0858-4
4623:
4619:
4612:
4608:
4598:
4595:
4594:
4585:
4581:
4576:
4572:
4568:
4566:
4561:
4558:
4555:
4536:
4527:
4519:
4516:
4513:
4506:
4501:
4498:
4492:
4486:
4483:
4480:
4476:
4450:
4447:
4444:
4440:
4423:
4420:
4402:
4401:
4400:
4398:
4394:
4386:
4372:
4368:
4364:
4360:
4356:
4352:
4346:
4332:
4328:
4324:
4320:
4316:
4309:
4295:
4291:
4287:
4283:
4279:
4275:
4271:
4267:
4261:
4245:
4242:
4241:
4240:
4238:
4237:public policy
4234:
4230:
4223:
4209:
4205:
4201:
4197:
4193:
4189:
4185:
4178:
4164:
4160:
4156:
4155:present value
4152:
4148:
4147:Stewart Myers
4144:
4140:
4134:
4120:
4117:
4114:
4111:
4108:
4105:
4102:
4099:
4096:
4093:
4090:
4087:
4084:
4081:
4078:
4075:
4074:
4067:
4064:
4056:
4046:
4042:
4038:
4032:
4031:
4027:
4022:This section
4020:
4016:
4011:
4010:
4002:
4000:
3996:
3995:Irving Fisher
3992:
3989:
3983:
3978:
3976:
3972:
3962:
3960:
3946:
3944:computations.
3942:
3939:
3934:
3931:
3927:
3923:
3920:
3916:
3911:
3908:
3903:
3899:
3895:
3894:
3887:
3884:
3876:
3866:
3862:
3858:
3852:
3851:
3847:
3842:This section
3840:
3836:
3831:
3830:
3822:
3819:$ 500,000,000
3817:, the NPV of
3815:$ 285 million
3811:$ 500,000,000
3803:$ 500 million
3799:
3797:
3796:salvage value
3793:
3783:
3780:
3777:
3773:
3772:
3771:
3767:
3760:
3750:
3746:
3739:
3732:
3725:
3720:
3716:
3693:
3690:
3687:
3684:
3681:
3679:
3671:
3668:
3665:
3662:
3659:
3656:
3653:
3650:
3648:
3624:
3623:
3622:
3594:
3591:
3588:
3574:
3571:
3568:
3550:
3549:
3548:
3544:
3533:
3514:
3506:
3503:
3500:
3492:
3489:
3486:
3476:
3473:
3470:
3469:
3465:
3446:
3438:
3435:
3432:
3424:
3421:
3418:
3408:
3405:
3402:
3401:
3397:
3378:
3370:
3367:
3364:
3356:
3353:
3350:
3340:
3337:
3334:
3333:
3329:
3310:
3302:
3299:
3296:
3288:
3285:
3282:
3272:
3269:
3266:
3265:
3261:
3242:
3234:
3231:
3228:
3220:
3217:
3214:
3204:
3201:
3198:
3197:
3193:
3174:
3166:
3163:
3160:
3152:
3149:
3146:
3136:
3133:
3130:
3129:
3125:
3106:
3098:
3095:
3092:
3084:
3081:
3078:
3068:
3065:
3062:
3061:
3057:
3038:
3030:
3027:
3024:
3016:
3013:
3010:
3000:
2997:
2994:
2993:
2989:
2970:
2962:
2959:
2956:
2948:
2945:
2942:
2932:
2929:
2926:
2925:
2921:
2902:
2894:
2891:
2888:
2880:
2877:
2874:
2864:
2861:
2858:
2857:
2853:
2834:
2826:
2823:
2820:
2812:
2809:
2806:
2796:
2793:
2790:
2789:
2785:
2766:
2758:
2755:
2752:
2744:
2741:
2738:
2728:
2725:
2722:
2721:
2717:
2698:
2690:
2687:
2684:
2676:
2673:
2670:
2667:
2657:
2654:
2651:
2650:
2646:
2643:
2640:
2639:
2636:
2632:
2626:
2624:
2618:
2611:
2600:
2598:
2594:
2590:
2586:
2582:
2579:
2575:
2571:
2567:
2548:
2545:
2538:
2532:
2527:
2524:
2521:
2517:
2506:
2502:
2498:
2492:
2485:
2481:
2470:
2466:
2460:
2454:
2447:
2446:
2445:
2443:
2439:
2435:
2431:
2427:
2423:
2422:Z-transformed
2420:respectively
2419:
2411:
2407:
2403:
2399:
2396:
2395:
2394:
2377:
2374:
2367:
2361:
2358:
2353:
2350:
2342:
2339:
2336:
2323:
2320:
2317:
2313:
2309:
2303:
2282:
2281:
2280:
2258:
2250:
2247:
2244:
2235:
2231:
2223:
2218:
2215:
2212:
2208:
2204:
2198:
2195:
2192:
2171:
2170:
2169:
2161:
2152:
2144:
2142:
2138:
2134:
2124:
2115:
2112:
2107:Disadvantages
2104:
2100:
2098:
2093:
2091:
2081:
2067:
2064:
2061:
2060:
2056:
2053:
2050:
2049:
2045:
2042:
2039:
2038:
2027:
2024:
2020:
2018:
2014:
2010:
1992:
1988:
1979:
1961:
1957:
1942:
1940:
1935:
1930:
1920:
1916:
1912:
1908:
1904:
1902:
1898:
1893:
1889:
1879:
1857:
1854:
1851:
1843:
1840:
1837:
1828:
1824:
1816:
1811:
1808:
1805:
1801:
1797:
1789:
1786:
1780:
1777:
1774:
1753:
1752:
1751:
1748:
1725:
1722:
1719:
1711:
1708:
1705:
1696:
1692:
1684:
1679:
1676:
1673:
1669:
1665:
1659:
1656:
1653:
1632:
1631:
1630:
1627:
1618:
1582:
1581:
1580:
1573:$ 100 million
1561:
1543:
1539:
1531:
1528:
1510:
1506:
1498:
1497:
1496:
1471:
1463:
1460:
1457:
1448:
1444:
1436:
1431:
1428:
1425:
1421:
1410:
1402:
1399:
1396:
1387:
1383:
1375:
1370:
1367:
1364:
1360:
1353:
1347:
1344:
1341:
1317:
1316:
1315:
1306:
1289:
1285:
1262:
1258:
1248:
1235:
1232:
1229:
1225:
1221:
1214:
1208:
1205:
1202:
1198:
1193:
1189:
1186:
1179:
1176:
1173:
1168:
1162:
1159:
1156:
1152:
1147:
1142:
1139:
1133:
1129:
1126:
1120:
1117:
1114:
1111:
1108:
1086:
1084:
1036:
1033:
1030:
1027:
1024:
1021:
1018:
998:
995:
992:
967:
959:
956:
953:
944:
940:
932:
927:
924:
921:
917:
913:
907:
904:
901:
862:
858:
824:
820:
812:
791:
787:
779:
778:
777:
755:
747:
744:
741:
732:
728:
720:
715:
712:
709:
705:
701:
693:
685:
682:
679:
670:
666:
658:
653:
650:
647:
643:
639:
633:
630:
627:
606:
605:
604:
603:is given by:
556:
552:
529:
525:
505:
499:
498:
497:
477:
463:
457:
443:
425:
424:
423:
420:
415:
392:
384:
381:
378:
371:
367:
360:
343:
339:
330:
312:
308:
300:
298:
294:
287:
281:
280:
279:
260:
252:
249:
246:
237:
233:
227:
211:
201:
199:
195:
191:
186:
184:
180:
176:
172:
167:
165:
161:
157:
153:
149:
145:
139:
137:
131:
128:
124:
119:
115:
113:
109:
105:
101:
97:
93:
89:
85:
84:present value
81:
77:
73:
69:
58:
48:
44:
38:
36:
30:
21:
20:
6101:Real options
6090:
5917:Tender offer
5777:acquisitions
5765:Underwriting
5750:Rights issue
5653:Transactions
5517:
5495:
5488:
5469:
5450:
5441:
5420:
5413:
5394:
5382:
5366:
5361:
5344:
5340:
5334:
5317:
5313:
5307:
5298:
5288:
5269:
5265:
5255:
5246:
5235:
5230:course-notes
5224:WACC and APV
5218:
5207:
5198:
5192:
5179:
5172:
5162:
5156:
5131:
5127:
5121:
5104:
5100:
5094:
5075:
5069:
5058:. Retrieved
5054:
5044:
5019:
5009:
4997:. Retrieved
4993:
4980:
4969:. Retrieved
4966:Investopedia
4965:
4956:
4945:. Retrieved
4942:Investopedia
4941:
4932:
4913:
4907:
4896:. Retrieved
4892:
4883:
4872:. Retrieved
4869:Investopedia
4868:
4837:
4816:. Retrieved
4806:
4795:. Retrieved
4791:
4782:
4771:. Retrieved
4767:
4758:
4725:
4721:
4711:
4700:. Retrieved
4696:
4686:
4667:
4661:
4652:
4617:
4611:
4562:
4559:
4556:
4553:
4390:
4317:(MIRR) is a
4277:
4227:
4059:
4050:
4035:Please help
4023:
3998:
3985:
3980:
3968:
3956:
3914:
3906:
3901:
3897:
3879:
3870:
3855:Please help
3843:
3807:$ 25,000,000
3800:
3788:
3775:
3765:
3758:
3751:
3744:
3737:
3730:
3723:
3718:
3714:
3712:
3620:
3542:
3539:
3471:
3403:
3335:
3267:
3199:
3131:
3063:
2995:
2927:
2859:
2791:
2723:
2652:
2630:
2627:
2622:
2616:
2609:
2606:
2580:
2563:
2441:
2437:
2433:
2429:
2415:
2409:
2405:
2401:
2397:
2392:
2278:
2167:
2158:
2150:
2130:
2121:
2113:
2110:
2101:
2094:
2087:
2079:
2032:It means...
2021:
2008:
1977:
1948:
1936:
1932:
1917:
1913:
1909:
1905:
1894:
1891:
1877:
1749:
1745:
1628:
1624:
1612:
1577:$ 60 million
1570:
1559:
1526:
1494:
1312:
1249:
1087:
1081:is a finite
846:
775:
512:
495:
421:
413:
410:
328:
207:
187:
168:
140:
132:
116:
79:
75:
71:
67:
65:
52:
35:lead section
33:
5875:Squeeze-out
5845:Proxy fight
5775:Mergers and
5688:Bought deal
5619:Senior debt
5426:McGraw-Hill
5160:Karl Marx,
4818:January 12,
4575:accountants
4276:. The term
4141:(APV) is a
4113:Real option
3959:spreadsheet
3919:Monte Carlo
2593:phase shift
2566:cybernetics
1901:yield curve
127:time series
108:investments
6185:Investment
6174:Categories
6121:Tax shield
6081:Mismarking
5885:Stock swap
5835:Pitch book
5805:Divestment
5683:Bookrunner
5604:Pari passu
5434:B001CZKN9K
5301:(2017â13).
5060:2023-04-21
4971:2022-04-30
4947:2023-04-21
4898:2023-04-21
4874:2023-04-21
4797:2023-04-21
4773:2023-04-21
4702:2023-04-21
4603:References
4367:investment
4323:investment
4270:investment
4208:investment
4204:net income
4159:tax shield
3988:mainstream
3792:cash flows
2585:pork cycle
2084:Advantages
2051:NPV < 0
2040:NPV > 0
210:discounted
190:fair price
88:cash flows
6096:Pure play
5989:Valuation
5855:Sell side
5718:Greenshoe
5509:16634923M
5036:224855745
4750:154096977
4742:0041-1612
4584:monograph
4571:engineers
4502:−
4424:−
4399:factor":
4319:financial
4286:inflation
4053:June 2023
4024:does not
3982:interest.
3971:Karl Marx
3873:June 2023
3844:does not
3685:−
3663:−
3589:−
3534:3,186.31
3466:3,504.94
3398:3,855.43
3330:4,240.98
3262:4,665.07
3194:5,131.58
3126:5,644.74
3058:6,209.21
2990:6,830.13
2922:7,513.15
2854:8,264.46
2786:9,090.91
2718:â100,000
2668:−
2644:Cash flow
2522:−
2512:∞
2503:∫
2359:⋅
2351:−
2329:∞
2314:∫
2209:∑
2097:cash flow
1934:do well.
1895:A firm's
1855:−
1802:∑
1790:−
1723:−
1670:∑
1422:∑
1361:∑
1233:≠
1190:−
1143:−
918:∑
706:∑
702:−
644:∑
464:−
183:inflation
171:principal
156:economics
45:and help
5927:Leverage
5905:Takeover
5800:Demerger
5785:Buy side
5501:Hamilton
5165:Volume 3
5163:Capital,
4999:21 April
4591:See also
4573:, while
4467:, where
4278:internal
4190:used in
3582:benefits
3547:. Thus:
2418:Laplace-
2035:Then...
1615:$ 0.6667
1608:â 0.6667
571:) where
5910:Reverse
5895:Synergy
5735:Pre-IPO
5723:Reverse
5644:Warrant
5228:MIT OCW
5148:2627695
4645:DeMarzo
4397:annuity
4157:of the
4045:removed
4030:sources
3965:History
3865:removed
3850:sources
2603:Example
2597:damping
2062:NPV = 0
1606:
1586:
1567:Example
1495:where:
776:where:
496:where:
278:where:
204:Formula
136:Formula
5507:
5432:
5377:. The
5373:
5146:
5082:
5055:Forisk
5034:
4920:
4844:
4748:
4740:
4674:
4643:Berk,
4624:
4359:recoup
4288:, the
4200:return
3694:863.09
3660:136.91
2591:, and
2393:where
2029:If...
1590:$ 100M
1584:NPVI=
293:return
162:, and
5634:Stock
5272:(2).
5184:(PDF)
5144:JSTOR
5032:S2CID
4990:(PDF)
4746:S2CID
4363:funds
4292:, or
3602:costs
1980:. If
1602:$ 60M
1594:$ 60M
198:yield
177:of a
104:loans
74:) or
5571:and
5528:help
5480:help
5461:help
5430:ASIN
5405:help
5371:ISBN
5080:ISBN
5001:2023
4918:ISBN
4842:ISBN
4820:2007
4738:ISSN
4672:ISBN
4622:ISBN
4361:the
4313:The
4233:cost
4182:The
4163:debt
4028:any
4026:cite
3915:e.g.
3907:e.g.
3848:any
3846:cite
3774:The
3747:= 12
3726:= 12
3507:0.10
3474:= 12
3439:0.10
3406:= 11
3371:0.10
3338:= 10
3303:0.10
3235:0.10
3167:0.10
3099:0.10
3031:0.10
2963:0.10
2895:0.10
2827:0.10
2759:0.10
2691:0.10
2641:Year
2572:and
1939:rNPV
1929:rNPV
1037:3...
179:bond
173:and
66:The
5349:doi
5322:doi
5274:doi
5136:doi
5109:doi
5024:doi
4730:doi
4353:in
4272:'s
4161:of
4039:by
3986:In
3859:by
3768:= 0
3761:= 0
3740:= 0
3733:= 0
3672:000
3666:100
3545:= 0
3493:000
3425:000
3357:000
3289:000
3270:= 9
3221:000
3202:= 8
3153:000
3134:= 7
3085:000
3066:= 6
3017:000
2998:= 5
2949:000
2930:= 4
2881:000
2862:= 3
2813:000
2794:= 2
2745:000
2726:= 1
2677:000
2671:100
2655:= 0
2633:= 0
2619:= 1
2612:= 0
2599:).
2444:).
1726:0.5
80:NPW
72:NPV
6176::
5505:OL
5499:.
5428:.
5345:33
5343:.
5318:21
5316:.
5297:.
5270:15
5268:.
5264:.
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5130:.
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5053:.
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4891:.
4867:.
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4828:^
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2807:10
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2190:(
2186:V
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2180:N
2009:t
1993:t
1989:R
1978:t
1962:t
1958:R
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1529:.
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1432:1
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1124:)
1121:R
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1109:i
1106:(
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1031:2
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1019:t
999:0
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957:+
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631:,
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615:N
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