A tale of two project proposals

Introduzione ai concetti finanziari in Python

Dakota Wixom

Quantitative Finance Analyst

Common profitability analysis methods

  • Net Present Value (NPV)
  • Internal Rate of Return (IRR)
  • Equivalent Annual Annuity (EAA)
Introduzione ai concetti finanziari in Python

Net Present Value (NPV)

NPV is equal to the sum of all discounted cash flows:

$ NPV = \sum_{t=1}^{T} \frac{C_t}{(1+r)^t} - C_0$

  • $C_t$: Cash flow C at time t
  • r: Discount rate

NPV is a simple cash flow valuation measure that does not allow for the comparison of different sized projects or lengths.

Introduzione ai concetti finanziari in Python

Internal Rate of Return (IRR)

The internal rate of return must be computed by solving for IRR in the NPV equation when set equal to 0.

$ NPV = \sum_{t=1}^{T} \frac{C_t}{(1+IRR)^t} - C_0 = 0$

  • $C_t$: Cash flow C at time t
  • IRR: Internal Rate of Return

IRR can be used to compare projects of different sizes and lengths but requires an algorithmic solution and does not measure total value.

Introduzione ai concetti finanziari in Python

IRR in NumPy

You can use the NumPy function .irr(values) to compute the internal rate of return of an array of values.

Example:

import numpy as np
project_1 = np.array([-100,150,200])
np.irr(project_1)

1.35

Project 1 has an IRR of 135%

Introduzione ai concetti finanziari in Python

Let's practice!

Introduzione ai concetti finanziari in Python

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