Net present value

Overview

Net present value (NPV), also known as net present worth (NPW) is a method for assessing whether future amounts of money are worth more or less than the cost of an investment made today. It is widely used in finance, economics, and project evaluation to judge whether a planned activity is expected to create value. NPV works by converting future cash flows into their “present value,” recognising that money available now is more valuable than the same amount received later. This adjustment reflects factors such as interest rates, inflation, and the opportunity to use money for other purposes. An investment typically has a positive NPV when the present value of its expected future benefits exceeds its initial cost, indicating that it is likely to be financially worthwhile. A negative NPV suggests the opposite. Because it summarises expected gains and losses in a single figure, NPV is a central tool for comparing alternative projects and making informed financial and economic decisions. Net Present Value measures the value of an asset that has cashflow by adding up the present value of all future cash flows 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 time value of money (which includes the annual effective discount rate). 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. 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 because a present flow can be invested immediately and begin earning returns, while a future flow cannot.

How NPV is determined

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. 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:

P V

=

R

t

( 1 + i

)

t

{\displaystyle \mathrm {PV} ={\frac {R_{t}}{(1+i)^{t}}}}

where:

t is the time of the cash flow i is the discount rate, i.e. the return that could be earned per unit of time on an investment with similar risk

R

t

{\displaystyle R_{t}}

is the net cash flow i.e. cash inflow − cash outflow, at time t. For educational purposes,

R

0

{\displaystyle R_{0}}

is commonly placed to the left of the sum to emphasize its role as (minus) the investment.

1

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:

N P V I

( i , N ) =

∑

t = 1

N

R

t

( 1 + i

)

t

∑

t = 1

N

C

t

( 1 + i

)

t

{\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}}}}}}

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:

NPVI= ⁠$100M-$60M/$60M⁠ ≈ 0.6667 That is for every dollar invested in the project, a contribution of $0.6667 is made to the project's NPV.

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:

N P V

( i , N ) =

∑

t = 0

N

R

t

( 1 + i

)

t − 0.5

{\displaystyle \mathrm {NPV} (i,N)=\sum _{t=0}^{N}{\frac {R_{t}}{(1+i)^{t-0.5}}}}

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

N P V

( i , N ) = −

Initial Investment

+

∑

t = 1

N

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 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

R

t

{\displaystyle R_{t}}

is a positive value, the project is in the status of positive cash inflow in the time of t. If

R

t

{\displaystyle R_{t}}

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.

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 periods 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 greatest 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. 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.

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.