Calculating the NPV
The NPV is found by summing the present values of each individual cash flow.
Learning Objective

Calculate a project's Net Present Value.
Key Points
 Cash inflows have a positive sign, while cash outflows are negative.
 To find the NPV accurately, the investor must know the exact size and time of occurrence of each cash flow. This is easy to find for some investments (like bonds), but more difficult for others (like industrial machinery).
 Investors use different rates for their discount rate such as using the weighted average cost of capital, variable rates, and reinvestment rate.
Terms

cash flow
The sum of cash revenues and expenditures over a period of time.

variable
something whose value may be dictated or discovered.

discount rate
The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.
Full Text
Calculating the NPV
The NPV of an investment is calculated by adding the PVs (present values) of all of the cash inflows and outflows . Cash inflows (such as coupon payments or the repayment of principal on a bond) have a positive sign while cash outflows (such as the money used to purchase the investment) have a negative sign.
Net Present Value (NPV) Formula
NPV is the sum of of the present values of all cash flows associated with a project. The business will receive regular payments, represented by variable R, for a period of time. This period of time is expressed in variable t. The payments are discounted using a selected interest rate, signified by the i variable.
The accurate calculation of NPV relies on knowing the amount of each cash flow and when each will occur. For securities like bonds, this is an easy requirement to meet. The bond clearly states when each coupon payment will occur, the size of each payment, when the principal will be repaid, and the cost of the bond. For other investments, this is not so simple to determine. When a new piece of machinery is purchased, for example, the investor (the purchasing company) has to estimate the size and occurrence of maintenance costs as well as the size and occurrence of the revenues generated by the machine.
The other integral input variable for calculating NPV is the discount rate. There are many methods for calculating the appropriate discount rate. A firm's weighted average cost of capital after tax (WACC) is often used. Since many people believe that it is appropriate to use higher discount rates to adjust for risk or other factors, they may choose to use a variable discount rate.
Another approach to selecting the discount rate factor is to decide the rate that 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. Reinvestment rate can be defined as the rate of return for the firm's investments on average, which can also be used as the discount rate.
Key Term Reference
 bond
 Appears in these related concepts: Factors Affecting the Price of a Bond, Current Maturities of LongTerm Debt, and Preferred Stock
 capital
 Appears in these related concepts: Temple Architecture in the Greek Orientalizing Period, Minoan Architecture, and The Acropolis
 cash inflow
 Appears in these related concepts: Reporting Financing Activities, Defining NPV, and The Financial Statements
 cash outflow
 Appears in these related concepts: Managing Disbursements, Advantages of the NPV method, and Selected Financial Ratios and Analyses
 cost of capital
 Appears in these related concepts: Advantages of the Payback Method, Calculating the IRR, and Cost of Capital Considerations
 coupon payment
 Appears in these related concepts: Reinvestment Risk, The "Bond Yield Plus Risk Premium" Approach, and Evaluating Currency Swaps
 discount
 Appears in these related concepts: The Discount Rate, Par Value at Maturity, and Present Value, Multiple Flows
 investment
 Appears in these related concepts: Functions of Corporate Finance, The Role of the Financial System, and GDP Equation in Depth (C+I+G+X)
 investor
 Appears in these related concepts: Advantages of Private Financing, Seasoned Equity Offering, and Agency
 present value
 Appears in these related concepts: Capital Leases vs. Operating Leases, Calculating Values for Different Durations of Compounding Periods, and Present Value and the Time Value of Money
 principal
 Appears in these related concepts: MultiPeriod Investment, Types of Bonds, and Formulas and ProblemSolving
 reinvestment rate
 Appears in these related concepts: Disadvantages of the IRR Method, The Yield Curve, and Modified IRR
 return
 Appears in these related concepts: Dollar Returns, Comparing the Fields of Finance, Economics, and Accounting, and Disadvantages of the Payback Method
 risk
 Appears in these related concepts: The ExportImport Bank of the United States, Approaches to Assessing Risk, and Risks Involved in Capital Budgeting
 securities
 Appears in these related concepts: Secondary Market Organizations, Types of Market Organizations, and Financial Instruments
 security
 Appears in these related concepts: Advantages of Public Financing, Pricing a Security, and Underwriter
 weighted average
 Appears in these related concepts: Average Cost Method, Market Reporting, and Expected Value
Sources
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