Net Present Value (NPV)

(noun)

The present value of a project or an investment decision determined by summing the discounted incoming and outgoing future cash flows resulting from the decision.

Related Terms

Examples of Net Present Value (NPV) in the following topics:

  • Defining NPV

    • Net Present Value (NPV) is the sum of the present values of the cash inflows and outflows.
    • The net present value (NPV) is simply the sum of the present values (PVs) and all the outflows and inflows:
    • Also recall that PV is found by the formula $PV=\frac { FV }{ { (1+i) }^{ t } }$ where FV is the future value (size of each cash flow), i is the discount rate, and t is the number of periods between the present and future.
    • NPV = 0: The PV of the inflows is equal to the PV of the outflows.
    • There is no difference in value between the value of the money earned and the money invested.

  • Calculating the NPV

    • The NPV is found by summing the present values of each individual cash flow.
    • The NPV of an investment is calculated by adding the PVs (present values) of all of the cash inflows and outflows .
    • The accurate calculation of NPV relies on knowing the amount of each cash flow and when each will occur.
    • The other integral input variable for calculating NPV is the discount rate.
    • NPV is the sum of of the present values of all cash flows associated with a project.

  • Foreign Investments

    • We can use the net present value (NPV) to calculate the monetary return to an investment in Equation 26.This equation is almost identical to the present value formula, except the PV0 is negative and located on the right-hand side while we add a new variable, NPV.If the net present value (NPV) equals zero, then this equation reduces to the present value formula.With the NPV formula, we could invest the amount PV0 today that generates the future cash flows, FVi, thatends at Time T.
    • If we calculate a positive, net present value, then our investment is paying off.Consequently, the investment is increasing the investor's wealth because more money flows in than out.Furthermore, investors would use the net present value formula to evaluate several investment projects.Then they select the project with the highest NPV, as long as the NPV is positive.An investor would never choose a project with a negative NPV because the project's return would be negative.Over time, more money flows out than in, creating a net loss.
    • We calculated a net present value of -$82.64 in Equation 27.Unfortunately, you could earn more on the financial securities than your brother's business because the NPV is negative.
    • We calculate the net present value of your investment of $12,358.27 in Equation 29.The NPV is positive, and the investment increases your wealth.However, we must forecast the exchange rates, except today's exchange rate, E0.
    • We calculate the net present value of -$9,764.60 in Equation 30.Our investment became a disaster because we earned a negative return because the euro had depreciated.

  • NPV Profiles

    • The NPV calculation involves discounting all cash flows to the present based on an assumed discount rate.
    • When the discount rate is large, there are larger differences between PV and FV (present and future value) for each cash flow than when the discount rate is small.
    • When the value of the outflows is greater than the inflows, the NPV is negative.
    • And it is the discount rate at which the value of the cash inflows equals the value of the cash outflows.
    • Describe the relationship between a project's discount rate and its Net Present Value

  • Calculating the IRR

    • Given a collection of pairs (time, cash flow), a rate of return for which the net present value is zero is an internal rate of return.
    • Given a collection of pairs (time, cash flow) involved in a project, the internal rate of return follows from the net present value as a function of the rate of return.
    • Given the (period, cash flow) pairs (n, Cn) where n is a positive integer, the total number of periods N, and the net present value NPV, the internal rate of return is given by r in:
    • Any fixed time can be used in place of the present (e.g., the end of one interval of an annuity); the value obtained is zero if and only if the NPV is zero.
    • Because the internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value of all cash flows (both positive and negative) from a particular investment equal to zero, then the IRR r is given by the formula:

  • Calculating the Yield of an Annuity

    • The yield of an annuity is commonly found using either the percent change in the value from PV to FV, or the internal rate of return.
    • Since annuities include multiple payments over the lifetime of the investment, the PV (or V1 in is the present value of the entire investment, not just the first payment.
    • The IRR is the interest rate (or discount rate) that causes the Net Present Value (NPV) of the annuity to equal 0.
    • You plug the numbers into the NPV formula and set NPV equal to 0.
    • When r = 14.3%, NPV = 0, so therefore the IRR of the investment is 14.3%.

  • Ranking Investment Proposals

    • When NPV > 0, the investment would add value to the firm so the project may be accepted
    • When NPV < 0, the investment would subtract value from the firm so the project should be rejected
    • When NPV = 0, the investment would neither gain nor lose value for the firm.
    • The internal rate of return on an investment or project is the "annualized effective compounded return rate" or "rate of return" that makes the net present value (NPV as NET*1/(1+IRR)^year) of all cash flows (both positive and negative) from a particular investment equal to zero.
    • Each cash inflow/outflow is discounted back to its present value (PV).

  • Advantages of the NPV method

    • Since it essentially determines the present value of the gain or loss of an investment, it is easy to understand and is a great decision making tool.
    • When NPV is positive, the investment is worthwhile; On the other hand, when it is negative, it should not be undertaken; and when it is 0, there is no difference in the present values of the cash outflows and inflows.
    • When presented with the NPVs of multiple options, the investor will simply choose the option with the highest NPV because it will provide the most additional value for the firm.
    • NPV simply and clearly shows whether a project adds value to the firm or not.
    • Describe the advantages of using net present value to evaluate potential investments

  • Interpreting the NPV

    • A positive NPV means the investment makes sense financially, while the opposite is true for a negative NPV.
    • NPV is the present value (PV) of all the cash flows (with inflows being positive cash flows and outflows being negative), which means that the NPV can be considered a formula for revenues minus costs.
    • If NPV is positive, that means that the value of the revenues (cash inflows) is greater than the costs (cash outflows).
    • Similarly, an investor should refuse any option that has a negative NPV because it only subtracts from the value.
    • The NPV is only as good as the inputs.

  • Multiple IRRs

    • In the case of positive cash flows followed by negative ones and then by positive ones, the IRR may have multiple values.
    • It has been shown that with multiple internal rates of return, the IRR approach can still be interpreted in a way that is consistent with the present value approach provided that the underlying investment stream is correctly identified as net investment or net borrowing.
    • Despite a strong academic preference for NPV, surveys indicate that executives prefer IRR over NPV.
    • However, NPV remains the "more accurate" reflection of value to the business.
    • NPV is a preferable metric in these cases.