Setup

Setup for the later calculations, importing necessary packages and defining initial configurations.

from dataclasses import dataclass
import numpy as np
import numpy_financial as npf
            

Inputs

Defining the inputs for the model using a data class to store the parameters.

@dataclass
class ModelInputs:
    n_phones: float = 100000
    price_scrap: float = 50000
    price_phone: float = 500
    cost_machine_adv: float = 1000000
    cogs_phone: float = 250
    n_life: int = 10
    n_machines: int = 5
    d_1: float = 100000
    g_d: float = 0.2
    max_year: float = 20
    interest: float = 0.05
    cash_flows = [0]
    machines_purchased = 0
    elasticity: float = 100
    demand_constant: float = 300000

model_data = ModelInputs()
            

Investment or Scrap

Functions to determine machine purchases, advertising decisions, and machine scrap years.

def investment(data, year):
    if year <= data.n_machines:
        data.machines_purchased += 1
    else:
        data.d_1 = data.d_1 * (data.g_d + 1)
            

def machine_lifecycle(data, year):
    if year in range(data.n_life + 1, data.n_life + data.n_machines + 1):
        data.machines_purchased -= 1
        return True
    else:
        return False
            

Cash Flow

Calculates the cash flows using revenue, costs, and scrap value.

def calculation(data, phones_sold_values, scrap_values):
    revenue = phones_sold_values * data.price_phone
    cost_of_production = phones_sold_values * data.cogs_phone
    scrap = data.price_scrap if scrap_values else 0
    cash_flow = revenue - cost_of_production - data.cost_machine_adv + scrap
    data.cash_flows.append(cash_flow)
            

Main Model

Iterates over the years and calculates the machine investments, scraps, supply, demand, and cash flows.

for year in range(1, model_data.max_year + 1):
    investment_decision = investment(model_data, year)
    scrap_value = machine_lifecycle(model_data, year)
    supply = model_data.machines_purchased * model_data.n_phones
    demand = model_data.d_1
    phones_sold_values = demand if supply > demand else supply
    calculation(model_data, phones_sold_values, scrap_value)
            

Outputs

Displays the calculated cash flows and NPV.

cash_flows = model_data.cash_flows
npv = npf.npv(model_data.interest, model_data.cash_flows)
year = 0
for x in cash_flows[1:]:
    year += 1
    print(f'Year {year}: ${x:,.0f}')
print(f'NPV: ${npv:,.0f}')
            

Python Code Output

Year 1: $24,000,000
Year 2: $24,000,000
Year 3: $24,000,000
Year 4: $24,000,000
Year 5: $24,000,000
Year 6: $29,000,000
Year 7: $35,000,000
Year 8: $42,200,000
Year 9: $50,840,000
Year 10: $61,208,000
Year 11: $73,699,600
Year 12: $74,050,000
Year 13: $49,050,000
Year 14: $24,050,000
Year 15: $-950,000
Year 16: $-1,000,000
Year 17: $-1,000,000
Year 18: $-1,000,000
Year 19: $-1,000,000
Year 20: $-1,000,000
NPV: $369,276,542