## Net Present Value in Finance.

NPV in finance analysis is the result of calculations used to find today’s value of a future stream of payments.

Actually Net present value is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

Required TVM calculations can be easily realised with Python.

There is a Simple Decision Rule after NPV is known:

• Accept the Project if NPV > 0

• Reject the Project if NPV < 0

Interpretation of NPV:

• Pursue the Project: Increase Today´s Company Value by NPV

• Total Company Value is the sum of all Projects´ NPVs

#### Net Present Value (NPV) formula:

**$$NPV = 𝐼𝑜 + \sum_{t = 1}^n \frac { CFt }{ (1 + r)^t }$$**

Where:

NPV: Net Present Value

Io: Initial Investment (negative)

CFt: cashflow @ timestamp t

N: Total number of periods

r: required rate of return

t = timestamp (0, 1, …, N)

```
cf = [-180, 30, 50, 70, 80, 70]
f = 1.08
NPV = 0
for i in range(6):
NPV += cf[i] / f**(i)
print(NPV)
```

You can also calculate NPV using NUMPY library which is much more simple way to do it.

```
import numpy as np
import numpy_financial as npf
cf = np.array([-200, 20, 50, 70, 100, 50])
r = 0.06
npf.npv(r, cf)
```

Intuition behind the Required Rate of Return:

• Opportunity Costs: (Expected) Return of comparable / alternative
Projects

• Weighted Average Costs to fund Capital Outflow Io

− Cost of Debt (Interest Rate charged by Bondholders / Banks)

− Cost of Equity (Required Return by Shareholders)