Comparing two projects of different life spans

Introduction to Financial Concepts in Python

Dakota Wixom

Quantitative Finance Analyst

Different NPVs and IRRs

Year Project 1 Project 2
1 -$100 -$125
2 $200 $100
3 $300 $100
4 N / A $100
5 N / A $100
6 N / A $100
7 N / A $100
8 N / A $100

Assume a 5% discount rate for both projects

Project comparison

NPV IRR Length
#1 362.58 200% 3
#2 453.64 78.62% 8

Notice how you could undertake multiple Project 1's over 8 years? Are the NPVs fair to compare?

Introduction to Financial Concepts in Python

Equivalent Annual Annuity (EAA) can be used to compare two projects of different lifespans in present value terms.

Apply the EAA method to the previous two projects using the computed NPVs * -1:

import numpy as np
npv_project1 = 362.58
npv_project2 = 453.64
np.pmt(rate=0.05, nper=3, pv=-1*npv_project1, fv=0)

133.14

np.pmt(rate=0.05, nper=8, pv=-1*npv_project2, fv=0)

70.18

Project 1 has the highest EAA

Introduction to Financial Concepts in Python

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Introduction to Financial Concepts in Python

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