## Net Present Value

Read this section that discusses Net Present Values (NPV), calculating and interpreting NP, and the advantages and disadvantages of using NPV. It also gives examples of how these concepts are implemented in practical applications.

### Defining NPV

Net Present Value (NPV) is the sum of the present values of the cash inflows and outflows.

#### LEARNING OBJECTIVE

• Define Net Present Value

#### 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

Any 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.

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

In order 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, in order to sum the cash inflows and outflows, each cash flow must be discounted to a common point in time.

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 = PVInflows+ PVOutflows

Don't forget that inflows and outflows have opposite signs; outflows are negative.

Also recall that $PV$ is found by the formula $PV=\dfrac{FV}{(1+i)^t}$ 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 simply 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.

Source: Boundless