#@title Calculate the Implied Cash Flow Growth Rate

from scipy.optimize import minimize_scalar
import math

# set parameters
current_price_per_share = df['share_price']
shares_outstanding_in_millions = df['shares_(diluted)'] / 1000000
owners_income = df['owners_income'] / 1000000

def growth_needed(x, current_price_per_share, shares_outstanding_in_millions, owners_income):
  # set growth rates and cost of capital
  fcf_growth_1_to_5 = x / 100
  fcf_growth_6_to_10 = fcf_growth_1_to_5 / 2   # half the rate of year 1-5
  terminal_growth_rate = .03  # constant
  cost_of_capital = .1  #constant

  # calculate ten years of Free Cash Flow and the Terminal Value
  FCF_01 = owners_income * (1 + fcf_growth_1_to_5)
  FCF_02 = FCF_01 * (1 + fcf_growth_1_to_5)
  FCF_03 = FCF_02 * (1 + fcf_growth_1_to_5)
  FCF_04 = FCF_03 * (1 + fcf_growth_1_to_5)
  FCF_05 = FCF_04 * (1 + fcf_growth_1_to_5)
  FCF_06 = FCF_05 * (1 + fcf_growth_6_to_10)
  FCF_07 = FCF_06 * (1 + fcf_growth_6_to_10)
  FCF_08 = FCF_07 * (1 + fcf_growth_6_to_10)
  FCF_09 = FCF_08 * (1 + fcf_growth_6_to_10)
  FCF_10 = FCF_09 * (1 + fcf_growth_6_to_10)
  term_value = (FCF_10 * (1 + terminal_growth_rate)) / (cost_of_capital - terminal_growth_rate)

  # calcuate the Present Value for each period
  PV_01 = FCF_01 * (1 /(( 1 + cost_of_capital) ** 1))
  PV_02 = FCF_02 * (1 /(( 1 + cost_of_capital) ** 2))
  PV_03 = FCF_03 * (1 /(( 1 + cost_of_capital) ** 3))
  PV_04 = FCF_04 * (1 /(( 1 + cost_of_capital) ** 4))
  PV_05 = FCF_05 * (1 /(( 1 + cost_of_capital) ** 5))
  PV_06 = FCF_06 * (1 /(( 1 + cost_of_capital) ** 6))
  PV_07 = FCF_07 * (1 /(( 1 + cost_of_capital) ** 7))
  PV_08 = FCF_08 * (1 /(( 1 + cost_of_capital) ** 8))
  PV_09 = FCF_09 * (1 /(( 1 + cost_of_capital) ** 9))
  PV_10 = FCF_10 * (1 /(( 1 + cost_of_capital) ** 10))
  PV_TV = term_value * (1 /(( 1 + cost_of_capital) ** 11))

  #sum the Present Values and calculate the value per share
  intrinsic_value = PV_01 + PV_02 + PV_03 + PV_04 + PV_05 + PV_06 + PV_07 + PV_08 + PV_09 + PV_10 + PV_TV
  intrinsic_value_per_share = intrinsic_value / shares_outstanding_in_millions

  # calculate the growth rate in year 1-5 needed to match the current share price
  # the square and square root are to force to zero before adding back the growth rate
  return ((math.sqrt((intrinsic_value_per_share - current_price_per_share) ** 2)) + x )

res = minimize_scalar(growth_needed, method='bounded', bounds=(-50, 100), args=(current_price_per_share, shares_outstanding_in_millions, owners_income,))
# notice the trailing comma in the Args function to make it a tuple
df['implied_growth'] = res.x / 100