Net Present Value

Net Present Value

Net Present Value (NPV) measures the value of an investment by summing all discounted cash flows, including the initial outlay.

$NPV = \sum_{t=0}^{n} \frac{CF_t}{(1+r)^t}$

Where:

• $CF_t$ is the cash flow at time $t$
• $CF_0$ is typically negative (initial investment)
• $r$ is the discount rate (required return)

Decision Rule

• NPV > 0: Investment creates value — accept
• NPV < 0: Investment destroys value — reject
• NPV = 0: Investment earns exactly the required return

Example

Project with initial cost $1000 and returns of$300, $400,$500 at 10%:

$NPV = -1000 + \frac{300}{1.1} + \frac{400}{1.1^2} + \frac{500}{1.1^3} = -21.04$

This project returns less than the 10% required rate, so it should be rejected.

Use Python's enumerate to iterate with index for the time periods.