Net Present Value

Defining NPV

Read this section on net present values (NPV). How do investors calculate and interpret NPV? What are the advantages and disadvantages of using NPV? Pay attention to the examples of how investors use these concepts in practical applications.

Every investment includes cash outflows and cash inflows. There is the cash required to invest and (hopefully) the return.

To see whether the cash outflows are less than the cash inflows (i.e., the investment earns a positive return), the investor aggregates the cash flows. 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. Thus, to sum the cash inflows and outflows, each flow must be discounted to a common point.

Airplane

Airplane Before purchasing a new airplane, airlines evaluate the NPV of the plan by calculating the PV of the revenue it can earn from it and the PV of its cost (e.g., purchase cost, maintenance, fuel, etc.).

The net present value (NPV) is simply the sum of the present values (PVs) and all the outflows and inflows:

NPV = PV_Inflows+ PV_Outflows

Do not forget that inflows and outflows have opposite signs; outflows are negative.

Also, recall that PV is found by the formula \(PVdfrac{FV}{(1+i)^t}\) 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. The PV of multiple cash flows is the sum of the PVs for each cash flow.

The sign of NPV can explain a lot about whether the investment is good or not:

NPV > 0: The PV of the inflows is greater than the PV of the outflows. The money earned on the investment is worth more today than the costs. Therefore, it is a good investment.
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.
NPV < 0: The PV of the inflows is less than the PV of the outflows. The money earned on the investment is worth less today than the costs. Therefore, it is a bad investment.

Key Points

Because of the time value of money, cash inflows and outflows only can be compared at the same point in time.
NPV discounts each inflow and outflow to the present, and then sums them to see how the value of the inflows compares to the other.
A positive NPV means the investment is worthwhile, an NPV of 0 means the inflows equal the outflows, and a negative NPV means the investment is not good for the investor.

Terms

Cash Outflow – cash that is spent or invested by the investor.
Cash Inflow – cash that is received by the investor. For example, dividends paid on a stock owned by the investor is a cash inflow.

Source: Boundless Finance, https://ftp.worldpossible.org/endless/eos-rachel/RACHEL/RACHEL/modules/en-boundless-static/www.boundless.com/finance/textbooks/boundless-finance-textbook/capital-budgeting-11/net-present-value-94/index.html
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