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 principal repayment on a bond) have a positive sign, while cash outflows (such as the money used to purchase the investment) have a negative sign.

\( NPV(i, N) = \Sigma ^N _ {t=1} \dfrac{R}{1+i)^t} \)


Net Present Value (NPV) Formula NPV is the sum 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 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 bond cost.

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 and 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 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 at 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 the use of the firm's reinvestment rate. The 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 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.

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