Net present value

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The net present value (NPV) or net present worth (NPW) [1] applies to a series of cash flows occurring at different times. The present value of a cash flow depends on the interval of time between now and the cash flow. It also depends on the annual effective discount rate. NPV accounts for the time value of money. It provides a method for evaluating and comparing capital projects or financial products with cash flows spread over time, as in loans, investments, payouts from insurance contracts plus many other applications.

Contents

Time value of money 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 both cases was equally certain. This decrease in the current value of future cash flows is based on a chosen rate of return (or discount rate). If for example there exists a time series 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 [2] because a present flow can be invested immediately and begin earning returns, while a future flow cannot.

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 Formula) 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.

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 of funds. [3] In a theoretical situation of unlimited capital budgeting, 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 discounted cash flow (DCF) analysis and is a standard method for using the time value of money to appraise long-term projects. It is widely used throughout economics, financial analysis, and financial accounting.

In the case when all future cash flows are positive, or incoming (such as the principal and coupon payment of a bond) 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 inflation and returns into account.

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 fair price. 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 internal rate of return (IRR) which would yield the given price as NPV. This rate, called the yield, is widely used in bond trading.

Formula

Each cash inflow/outflow is discounted back to its present value (PV). Then all are summed such that NPV is the sum of all terms:

where:

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 within 12 months will not be discounted for NPV purpose, nevertheless the usual initial investments during the first year R0 are summed up a negative cash flow. [4]

The NPV can also be thought of as the difference between the discounted benefits and costs over time. As such, the NPV can be also be written as:

where:

Given the (period, cash inflows, cash outflows) shown by (, , ) where is the total number of periods, the net present value is given by:

where:

The NPV can be rewritten using the net cash flow in each time period as:

By convention, the initial period occurs at time , where cash flows in successive periods are then discounted from and so on. Furthermore, all future cash flows during a period are assumed to be at the end of each period. [5] For constant cash flow , the net present value is a finite geometric series and is given by:

Inclusion of the term is important in the above formulae. A typical capital project involves a large negative 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.

Capital efficiency

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:

where:

Example

If the discounted benefits across the life of a project are $100 million and the discounted net costs across the life of a project are $60 million then the NPVI is:

That is for every dollar invested in the project, a contribution of $0.6667 is made to the project's NPV. [6]

Alternative discounting frequencies

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.

The NPV formula for mid period discounting is given by:

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 conservative NPV. [7] [8]

The NPV formula using beginning of period discounting is given by:

This results in the least conservative NPV.

The discount rate

The rate used to discount future cash flows to the present value is a key variable of this process.

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.

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. 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.

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 [9] for more detailed relationship between the NPV and the discount rate.

For some professional investors, their investment funds are committed to target a specified rate of return. In such cases, that rate of return should be selected as the discount rate for the NPV calculation. In this way, a direct comparison can be made between the profitability of the project and the desired rate of return.

To some extent, the selection of the discount rate is dependent on the use to which it will be put. If the intent is simply to determine whether a project will add value to the company, using the firm's weighted average cost of capital may be appropriate. If trying to decide between alternative investments in order to maximize the value of the firm, the corporate reinvestment rate would probably be a better choice.

Risk-adjusted net present value (rNPV)

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 risk-adjusted net present value (rNPV) or a similar method, then discount at the firm's rate.

Use in decision making

NPV is an indicator of how much value an investment or project adds to the firm. With a particular project, if is a positive value, the project is in the status of positive cash inflow in the time of t. If is a negative value, the project is in the status of discounted cash outflow in the time of t. Appropriately risked projects with a positive NPV 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. 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.

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.

If...It means...Then...
NPV > 0the investment would add value to the firmthe project may be accepted
NPV < 0the investment would subtract value from the firmthe project may be rejected
NPV = 0the investment would neither gain nor lose value for the firmWe 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.

Advantages and disadvantages of using Net Present Value

NPV is an indicator for project investments, and has several advantages and disadvantages for decision-making.

Advantages

The NPV includes all relevant time and cash flows for the project by considering the time value of money, which is consistent with the goal of wealth maximization by creating the highest wealth for shareholders.

The NPV formula accounts for cash flow timing patterns and size differences for each project, and provides an easy, unambiguous dollar value comparison of different investment options. [10] [11]

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 calculate the highest wealth creation, based on the available capital that can be invested by a firm. [12]

Disadvantages

The NPV method has several disadvantages.

The NPV approach does not consider hidden costs and project size. Thus, investment decisions on projects with substantial hidden costs may not be accurate. [13]

Relies on input parameters such as knowledge of future cash flows

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 changes as the input variables are changed, thus reducing the uncertainty of the NPV. [14]

Relies on choice of discount rate and discount factor

The accuracy of the NPV method relies heavily on the choice of a discount rate and hence discount factor, representing an investment's true risk premium. [15] 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. [16] [10] There are other drawbacks to the NPV method, such as the fact that it displays a lack of consideration for a project’s size and the cost of capital. [17] [11]

Lack of consideration of non-financial metrics

The NPV calculation is purely financial and thus does not consider non-financial metrics that may be relevant to an investment decision. [18]

Difficulty in comparing mutually exclusive projects

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. [19]

Interpretation as integral transform

The time-discrete formula of the net present value

can also be written in a continuous variation

where

r(t) is the rate of flowing cash given in money per time, and r(t) = 0 when the investment is over.

Net present value can be regarded as Laplace- [20] [21] respectively 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).

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).

Example

A corporation must decide whether to introduce a new product line. The company will have immediate costs of 100,000 at t = 0. Recall, a cost is a negative for outgoing cash flow, thus this cash flow is represented as −100,000. The company assumes the product will provide equal benefits of 10,000 for each of 12 years beginning at t = 1. 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 on the last day 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%.

The present value (value at t = 0) can be calculated for each year:

YearCash flowPresent value
T = 0−100,000
T = 19,090.91
T = 28,264.46
T = 37,513.15
T = 46,830.13
T = 56,209.21
T = 65,644.74
T = 75,131.58
T = 84,665.07
T = 94,240.98
T = 103,855.43
T = 113,504.94
T = 123,186.31

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 t = 0. Thus:

In this example:

Observe that as t increases the present value of each cash flow at t decreases. For example, the final incoming cash flow has a future value of 10,000 at t = 12 but has a present value (at t = 0) 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 t = 0 (the present value) at an interest rate of 10% compounded for 12 years, which results in a cash flow of 10,000 at t = 12 (the future value).

The importance of NPV becomes clear in this instance. Although the incoming cash flows (10,000 × 12 = 120,000) 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 t = 0. 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, t = 0). [2] 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:

  1. 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.)
  2. 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.
  3. 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 stock repurchases.)

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.

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 $500 million. If one does not select the "CASH" option they will be paid $25,000,000 per year for 20 years, a total of $500,000,000, however, if one does select the "CASH" option, they will receive a one-time lump sum payment of approximately $285 million, the NPV of $500,000,000 paid over time. See "other factors" above that could affect the payment amount. Both scenarios are before taxes.

Common pitfalls

Software support

Many computer-based spreadsheet programs have built-in formulae for PV and NPV.

History

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: [22]

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.

In 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. [23] [24]

Alternative capital budgeting methods

Adjusted present value

Adjusted present value (APV) is a valuation method introduced in 1974 by Stewart Myers. [25] The idea is to value the project as if it were all equity financed ("unleveraged"), and to then add the present value of the tax shield of debt – and other side effects. [26]

Accounting rate of return

The accounting rate of return, also known as average rate of return, or ARR, is a financial ratio used in capital budgeting. [27] The ratio does not take into account the concept of time value of money. ARR calculates the return, generated from net income of the proposed capital investment. 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. [28]

Cost-benefit analysis

Cost–benefit analysis (CBA), sometimes also called benefit–cost 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. [29] A CBA may be used to compare completed or potential courses of action, and to estimate or evaluate the value against the cost of a decision, project, or policy. It is commonly used to evaluate business or policy decisions (particularly public policy), commercial transactions, and project investments. For example, the U.S. Securities and Exchange Commission must conduct cost-benefit analyses before instituting regulations or deregulations. [30] :6

  1. To determine if an investment (or decision) is sound, ascertaining if – and by how much – its benefits outweigh its costs.
  2. To provide a basis for comparing investments (or decisions), comparing the total expected cost of each option with its total expected benefits.

Internal rate of return

Internal rate of return (IRR) is a method of quantifying the merits of a project or investment opportunity. The calculation is termed internal because it depends only on the cash flows of the investment being analyzed and excludes external factors, such as returns available elsewhere, the risk-free rate, inflation, the cost of capital, or financial risk. [31]

Modified internal rate of return

The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. [32] [33] It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR.

Payback period

Payback period in capital budgeting refers to the time required to recoup the funds expended in an investment, or to reach the break-even point. [34]

Equivalent annual cost

In finance, the equivalent annual cost (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 annuity factor":

, where

where r is the annual interest rate and

t is the number of years.

Alternatively, EAC can be obtained by multiplying the NPV of the project by the "loan repayment factor".

EAC is often used as a decision-making tool in capital budgeting when comparing investment projects of unequal lifespans. However, the projects being compared must have equal risk: otherwise, EAC must not be used. [35]

The technique was first discussed in 1923 in engineering literature, [36] and, as a consequence, EAC appears to be a favoured technique employed by engineers, while accountants tend to prefer net present value (NPV) analysis. [37] Such preference has been described as being a matter of professional education, as opposed to an assessment of the actual merits of either method. [38] In the latter group, however, the Society of Management Accountants of Canada endorses EAC, having discussed it as early as 1959 in a published monograph [39] (which was a year before the first mention of NPV in accounting textbooks). [40]

See also

Related Research Articles

The discounted cash flow (DCF) analysis, in financial analysis, is a method used to value a security, project, company, or asset, that incorporates the time value of money. Discounted cash flow analysis is widely used in investment finance, real estate development, corporate financial management, and patent valuation. Used in industry as early as the 1700s or 1800s, it was widely discussed in financial economics in the 1960s, and U.S. courts began employing the concept in the 1980s and 1990s.

<span class="mw-page-title-main">Discounting</span> When a creditor delays payments from a debtor in exchange for a fee

In finance, discounting is a mechanism in which a debtor obtains the right to delay payments to a creditor, for a defined period of time, in exchange for a charge or fee. Essentially, the party that owes money in the present purchases the right to delay the payment until some future date. This transaction is based on the fact that most people prefer current interest to delayed interest because of mortality effects, impatience effects, and salience effects. The discount, or charge, is the difference between the original amount owed in the present and the amount that has to be paid in the future to settle the debt.

Internal rate of return (IRR) is a method of quantifying the merits of a project or investment opportunity. The calculation is termed internal because it depends only on the cash flows of the investment being analyzed and excludes external factors, such as returns available elsewhere, the risk-free rate, inflation, the cost of capital, or financial risk.

In economics and finance, present value (PV), also known as present discounted value, is the value of an expected income stream determined as of the date of valuation. The present value is usually less than the future value because money has interest-earning potential, a characteristic referred to as the time value of money, except during times of negative interest rates, when the present value will be equal or more than the future value. Time value can be described with the simplified phrase, "A dollar today is worth more than a dollar tomorrow". Here, 'worth more' means that its value is greater than tomorrow. A dollar today is worth more than a dollar tomorrow because the dollar can be invested and earn a day's worth of interest, making the total accumulate to a value more than a dollar by tomorrow. Interest can be compared to rent. Just as rent is paid to a landlord by a tenant without the ownership of the asset being transferred, interest is paid to a lender by a borrower who gains access to the money for a time before paying it back. By letting the borrower have access to the money, the lender has sacrificed the exchange value of this money, and is compensated for it in the form of interest. The initial amount of borrowed funds is less than the total amount of money paid to the lender.

<span class="mw-page-title-main">Time value of money</span> Conjecture that there is greater benefit to receiving a sum of money now rather than later

The time value of money is the widely accepted conjecture that there is greater benefit to receiving a sum of money now rather than an identical sum later. It may be seen as an implication of the later-developed concept of time preference.

The weighted average cost of capital (WACC) is the rate that a company is expected to pay on average to all its security holders to finance its assets. The WACC is commonly referred to as the firm's cost of capital. Importantly, it is dictated by the external market and not by management. The WACC represents the minimum return that a company must earn on an existing asset base to satisfy its creditors, owners, and other providers of capital, or they will invest elsewhere.

<span class="mw-page-title-main">Economic value added</span> Value of a firms profit after deduction of capital costs

In accounting, as part of financial statements analysis, economic value added is an estimate of a firm's economic profit, or the value created in excess of the required return of the company's shareholders. EVA is the net profit less the capital charge ($) for raising the firm's capital. The idea is that value is created when the return on the firm's economic capital employed exceeds the cost of that capital. This amount can be determined by making adjustments to GAAP accounting. There are potentially over 160 adjustments but in practice, only several key ones are made, depending on the company and its industry.

Rational pricing is the assumption in financial economics that asset prices – and hence asset pricing models – will reflect the arbitrage-free price of the asset as any deviation from this price will be "arbitraged away". This assumption is useful in pricing fixed income securities, particularly bonds, and is fundamental to the pricing of derivative instruments.

Bond valuation is the process by which an investor arrives at an estimate of the theoretical fair value, or intrinsic worth, of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate.

In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received. When the price of an asset is considered as a function of yield, duration also measures the price sensitivity to yield, the rate of change of price with respect to yield, or the percentage change in price for a parallel shift in yields.

In finance, the terminal value of a security is the present value at a future point in time of all future cash flows when we expect stable growth rate forever. It is most often used in multi-stage discounted cash flow analysis, and allows for the limitation of cash flow projections to a several-year period; see Forecast period (finance). Forecasting results beyond such a period is impractical and exposes such projections to a variety of risks limiting their validity, primarily the great uncertainty involved in predicting industry and macroeconomic conditions beyond a few years.

<span class="mw-page-title-main">Capital budgeting</span> How an organization allocates its cash and resources

Capital budgeting in corporate finance, corporate planning and accounting is an area of capital management that concerns the planning process used to determine whether an organization's long term capital investments such as new machinery, replacement of machinery, new plants, new products, and research development projects are worth the funding of cash through the firm's capitalization structures. It is the process of allocating resources for major capital, or investment, expenditures. An underlying goal, consistent with the overall approach in corporate finance, is to increase the value of the firm to the shareholders.

In finance, return is a profit on an investment. It comprises any change in value of the investment, and/or cash flows which the investor receives from that investment over a specified time period, such as interest payments, coupons, cash dividends and stock dividends. It may be measured either in absolute terms or as a percentage of the amount invested. The latter is also called the holding period return.

The modified internal rate of return (MIRR) is a financial measure of an investment's attractiveness. It is used in capital budgeting to rank alternative investments of equal size. As the name implies, MIRR is a modification of the internal rate of return (IRR) and as such aims to resolve some problems with the IRR.

The Z-spread, ZSPRD, zero-volatility spread, or yield curve spread of a bond is the parallel shift or spread over the zero-coupon Treasury yield curve required for discounting a pre-determined cash flow schedule to arrive at its present market price. The Z-spread is also widely used in the credit default swap (CDS) market as a measure of credit spread that is relatively insensitive to the particulars of specific corporate or government bonds.

Valuation using discounted cash flows is a method of estimating the current value of a company based on projected future cash flows adjusted for the time value of money. The cash flows are made up of those within the “explicit” forecast period, together with a continuing or terminal value that represents the cash flow stream after the forecast period. In several contexts, DCF valuation is referred to as the "income approach".

<span class="mw-page-title-main">Profitability index</span> Mathematical economic formula

Profitability index (PI), also known as profit investment ratio (PIR) and value investment ratio (VIR), is the ratio of payoff to investment of a proposed project. It is a useful tool for ranking projects because it allows you to quantify the amount of value created per unit of investment. Under capital rationing, PI method is suitable because PI method indicates relative figure i.e. ratio instead of absolute figure.

A benefit–cost ratio (BCR) is an indicator, used in cost–benefit analysis, that attempts to summarize the overall value for money of a project or proposal. A BCR is the ratio of the benefits of a project or proposal, expressed in monetary terms, relative to its costs, also expressed in monetary terms. All benefits and costs should be expressed in discounted present values. A BCR can be a profitability index in for-profit contexts. A BCR takes into account the amount of monetary gain realized by performing a project versus the amount it costs to execute the project. The higher the BCR the better the investment. The general rule of thumb is that if the benefit is higher than the cost the project is a good investment.

The Penalized Present Value (PPV) is a method of capital budgeting under risk, where the value of the investment is "penalized" as a function of its risk. It was developed by Fernando Gómez-Bezares in the 1980s.

<span class="mw-page-title-main">Corporate finance</span> Framework for corporate funding, capital structure, and investments

Corporate finance is the area of finance that deals with the sources of funding, and the capital structure of corporations, the actions that managers take to increase the value of the firm to the shareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is to maximize or increase shareholder value.

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