net present value

Examples of net present value in the following topics:

• 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:

• Defining NPV

  • Net Present Value (NPV) is the sum of the present values of the cash inflows and outflows.
  • Since cash flows occur over a period of time, the investor knows that due to the time value of money, each cash flow has a certain value today .
  • 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.
  • There is no difference in value between the value of the money earned and the money invested.

• 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.

• Defining the IRR

  • 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.
  • In more specific terms, the IRR of an investment is the discount rate at which the net present value of costs (negative cash flows) of the investment equals the net present value of the benefits (positive cash flows) of the investment.

• Deciding to Refund Bonds

  • The decision of whether to refund a particular debt issue is usually based on a capital budgeting (present value) analysis.
  • The principal benefit, or cash inflow, is the present value of the after-tax interest savings over the life of the issue.
  • Step 1: Calculate the present value of interest savings (cash inflows):
  • Step 2: Calculate the net investment (net cash outflow at time 0).
  • Net present value of refunding = Present value of interest savings - Present value of net investment

• Defining the Payback Method

  • The payback method is considered a method of analysis with serious limitations and qualifications for its use, because it does not account for the time value of money, risk, financing or other important considerations, such as opportunity cost.
  • While the time value of money can be rectified by applying a weighted average cost of capital discount, it is generally agreed that this tool for investment decisions should not be used in isolation.
  • Alternative measures of "return" preferred by economists are net present value and internal rate of return.
  • Start by calculating net cash flow for each year: net cash flow year one = cash inflow year one - cash outflow year one.
  • Then cumulative cash flow = (net cash flow year one + net cash flow year two + net cash flow year three).

• Discounted Cash Flow Approach

  • This finds discounted present values (DPV).
  • These present values are summed to give the net present value (NPV) of the asset.
  • -- To find the discounted present value of an asset, it is necessary to sum the discounted present value of each future cash flow (FV) at any time period (t) in years from the present time, using the appropriate interest rate (i).
  • -- Use this equation to find the present value of a future terminal value.
  • To find the discounted present value of an asset, it is necessary to sum the discounted present value of each future cash flow (FV) at any time period (t) in years from the present time, using the appropriate interest rate (i).

• MVA and EVA

  • where: MVA is market value added, V is the market value of the firm, including the value of the firm's equity and debt, and K is the capital invested in the firm.
  • EVA is net operating profit after taxes (or NOPAT) less a capital charge, the latter being the product of the cost of capital and the economic capital.
  • where r is the return on investment capital (ROIC); c is the weighted average of cost of capital (WACC); K is the economic capital employed; NOPAT is the net operating profit after tax.
  • The firm's market value added, or MVA, is the discounted sum (present value) of all future expected economic value added: MVA = Present Value of a series of EVA values.
  • MVA is the present value of a series of EVA values.

• Dollar-Value LIFO

  • However, because it does occur and thus costs change over time, the dollar-value method presents data that show an increased cost of goods sold (COGS) when prices are rising, and a lower net income.
  • This can, in turn, reduce a company's taxes, but can make shareholders unhappy due to a lower net income on reports.
  • Managers apply the concepts of interest, future value, and present value in making business decisions.
  • That is, the dollars held now must be accumulated or rolled forward, or future dollars must be discounted or brought back to the present dollar value, before comparisons are valid.
  • Such comparisons involve future value and present value concepts.

• Cost of Goods Sold and Gross Profit

  • The various deductions leading from net sales to net income are as follows:
  • Net income (or Net profit) = Operating profit – taxes – interest
  • Costs include all costs of purchase, costs of conversion and other costs incurred in bringing the inventories to their present location and condition.
  • The costs of those goods not yet sold are deferred as costs of inventory until the inventory is sold or written down in value.