Program to calculate NPV
Net present value, or NPV, is used to calculate the current total value of a future stream of payments.
If the NPV of a project or investment is positive, it means that the discounted present value of all future cash flows related to that project or investment will be positive, and therefore attractive.
To calculate NPV, you need to estimate future cash flows for each period and determine the correct discount rate.
where:
Rt = Net cash inflow/outflows during a single period
ti = Discount rate/return that could be earned in alternative investments
t = Number of timer periods
Calculating NPV with Python
let us consider project (X) with following specifications:
life time = 15 years
initail investments = 2000000 $
final project value = 1000000 $
project_cash_flow = [ - 2000000, 0 , 0 , 250000, 250000, 500000, 500000, 750000, 750000, 500000, 500000, 500000, 500000, 500000, 1000000]
discount_rate = [0.05, 0.055, 0.06, 0.065, 0.07, 0.075, 0.08, 0.085, 0.09, 0.095, 0.1, 0.105, 0.11, 0.115, 0.12, 0.125, 0.13, 0.135, 0.14, 0.145, 0.15]
we decide to perform a Net Present Value (NPV) analysis to determine the profitability of the project
Importing the python packages
import matplotlib.pyplot as plt
import matplotlib.pyplot as pltInput Data
project_cash_flow= [-2000000, 0, 0, 250000, 250000, 500000, 500000, 750000, 750000, 500000, 500000, 500000, 500000, 500000, 1000000]
discount_rate = [0.05, 0.055, 0.06, 0.065, 0.07, 0.075, 0.08, 0.085, 0.09, 0.095, 0.1, 0.105, 0.11, 0.115, 0.12, 0.125, 0.13, 0.135, 0.14, 0.145, 0.15]
Function to calculate NPV
def calculate_npv(rate, cash_flow):
npv = 0
for t in range(len(cash_flow)):
npv += cash_flow[t]/(1+rate)**t
return npv
npvs_a = list()
for rate in discount_rate:
npv_a = calculate_npv(rate,project_a)
npvs_a.append(npv_a)
Graphical Representation
plt.plot(discount_rate,npvs_a, linewidth = 3.0, color = "green", label = "Project X")
plt.axhline(y=0, linewidth = 0.5, color = "black")
plt.title('NPV Profile: Project X')
plt.xlabel('Discount Rate')
plt.ylabel('Net Present Value')
plt.legend()
plt.show()
Output Graph
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