R/stan_funcs_legacy.R

In TracyRage/fun_valuation: Personal fundamental analysis tool

#' Get the posterior distribution of after_tax EBITs 5Y ahead (LEGACY)
#' @description
#' This function calculates EBIT cash flow posteriors 5 years ahead
#' @param company_after_tax_ebit **Number** Current company after_tax EBIT
#' @param company_growth **Number** Current company growth rate
#' @param company_reinvestment_rate **Number** Current company reinvestment rate
#' @param sigma_ebit **Vector** Y2Y EBIT numeric differences across
#' companies, which are similar to the current firm of interest
#' @param sigma_reinvestment_rate **Vector** Y2Y CapEx numeric differences across
#' companies, which are similar to the current firm of interest
#' @param N **Number** Length of sigma_ebit and sigma_reinvestment_rate (both should be same length)
#' @return **List** Fitted STAN model and the medians (CI 95%) of relevant parameters
#' @examples
#' # get_stan_ebit_flow(company_after_tax_ebit=1444,
#'                     # company_growth = 0.045,
#'                     # company_reinvestment_rate = 0.4,
#'                     # sigma_ebit = c(400,299,376,420,500),
#'                     # sigma_reinvestment_rate = c(100,200,150,175,90),
#'                     # N = length(sigma_ebit))
#' @importFrom rstan stan
#' @importFrom tidyr pivot_wider
#' @importFrom dplyr select
#' @importFrom broom.mixed tidy
#' @export
get_stan_ebit_flow <- function(company_after_tax_ebit,
                               company_growth,
                               company_reinvestment_rate,
                               sigma_ebit,
                               sigma_reinvestment_rate,
                               N) {
  ### Centrilize the priors
  data <- list(after_tax_ebit = company_after_tax_ebit,
               growth = company_growth,
               reinvestment = company_reinvestment_rate,
               sigma_ebit = sigma_ebit,
               sigma_rr = sigma_reinvestment_rate,
               N = N)

  ### Describe the STAN model
  ebit_flow_model <- "
          data {
              int <lower=1> N;
              real after_tax_ebit;
              real growth;
              real reinvestment;
              vector[N] sigma_ebit;
              vector[N] sigma_rr;
          }

          parameters {
              real ebit_flow_1;
              real ebit_flow_2;
              real ebit_flow_3;
              real ebit_flow_4;
              real ebit_flow_5;
              real rr_1;
              real rr_2;
              real rr_3;
              real rr_4;
              real rr_5;

          }

          model {
              ebit_flow_1 ~ normal(after_tax_ebit * (1+growth) ^ 1, sigma_ebit);
              ebit_flow_2 ~ normal(after_tax_ebit * (1+growth) ^ 2, sigma_ebit);
              ebit_flow_3 ~ normal(after_tax_ebit * (1+growth) ^ 3, sigma_ebit);
              ebit_flow_4 ~ normal(after_tax_ebit * (1+growth) ^ 4, sigma_ebit);
              ebit_flow_5 ~ normal(after_tax_ebit * (1+growth) ^ 5, sigma_ebit);

              rr_1 ~ normal(ebit_flow_1 * reinvestment, sigma_rr);
              rr_2 ~ normal(ebit_flow_2 * reinvestment, sigma_rr);
              rr_3 ~ normal(ebit_flow_2 * reinvestment, sigma_rr);
              rr_4 ~ normal(ebit_flow_2 * reinvestment, sigma_rr);
              rr_5 ~ normal(ebit_flow_2 * reinvestment, sigma_rr);

          }

"
  ### Fit the model
  fit_model <- stan(model_code = ebit_flow_model, data = data,
                   iter = 5000 * 4, chains = 4, cores = 2,
                   seed = 110)

  ### Tidy the model output
  tidy_ebits_flow <- tidy(fit_model, conf.int=T, conf.level=0.95) %>%
    select(term, estimate) %>%
    pivot_wider(names_from = term, values_from = estimate)

  return(list(fitted_model = fit_model,
              parameters = tidy_ebits_flow))

}

#' Get FCFF 5Y ahead (LEGACY)
#' @description
#' This function calculates FCFF 5 years ahead
#' @param df **Data Frame** EBIT and reinvestment flow 5Y ahead
#' @param wacc **Number** Firm cost
#' @return **List** FCFF NPV
#' @export
get_fcff <- function(df, wacc) {
  fcff_1 <- df$ebit_flow_1 - df$rr_1
  fcff_2 <- df$ebit_flow_2 - df$rr_2
  fcff_3 <- df$ebit_flow_3 - df$rr_3
  fcff_4 <- df$ebit_flow_4 - df$rr_4
  fcff_5 <- df$ebit_flow_5 - df$rr_5
  npv <- fcff_1/(1+wacc)^1+fcff_2/(1+wacc)^2+fcff_3/(1+wacc)^3+fcff_4/(1+wacc)^4+fcff_5/(1+wacc)^5

  return(c(fcff_1=fcff_1,
           fcff_2=fcff_2,
           fcff_3=fcff_3,
           fcff_4=fcff_4,
           fcff_5=fcff_5,
           npv=npv))
}

#' Get the posterior distribution of NPV (LEGACY)
#' @description
#' This function calculates NPV posterior
#' @param df **Data Frame** NPV value
#' @param wacc **Number** Company default rate
#' @return **Tibble** NPV posterior
#' @examples
#' #get_stan_npv(npv=3374, default_rate=0.15)
#' @importFrom rstan stan
#' @importFrom broom.mixed tidy
#' @export
get_stan_npv <- function(npv_df, default_rate) {
  ### Centralize the priors
  npv_data <- list(npv = as.numeric(npv_df[6]),
                   default_rate = default_rate)

  ### Describe the STAN model
  npv_flow_model <- "
          data {
              real npv;
              real default_rate;
          }

          parameters {
              real npv_var;
          }

          model {
              npv_var ~ normal(npv, npv*default_rate);
          }

  "

  ### Fit the model
  npv_model <- stan(model_code = npv_flow_model, data = npv_data,
                   iter = 5000 * 4, chains = 4, cores = 2,
                   seed = 110)

  tidy_npv <- tidy(npv_model, conf.int=T, conf.level=0.95)



}

#' Get the posterior distribution of terminal year EBIT (LEGACY)
#' @description
#' This function calculates terminal year EBIT posterior
#' @param ebit_flow_5 EBIT Y5 value
#' @param roic **Number** Company ROIC
#' @param growth **Number** Company growth
#' @param sigma_ebit **Vector** Y2Y EBIT numeric differences across
#' @param N **Number** Length of sigma_ebit and sigma_reinvestment_rate, both should be same length
#' companies, which similar with the current firm of interest
#' @return **Tibble** Terminal EBIT posterior
#' @examples
#' # get_terminal_ebit(N=5, growth_roic_reinv_sigma=c(0.2,0.5,0.25,0.3,0.4),
#'  #  ebit_flow_5=as.numeric(tidy_ebits_flows$parameters[5]),
#'  #  sigma_ebit = c(400,299,376,420,500),
#'  #  roic=0.25,
#'  #  growth=0.045)
#' @importFrom rstan stan
#' @importFrom broom.mixed tidy
#' @export
get_stan_terminal_ebit <- function(N, growth_roic_reinv_sigma,
                                   ebit_flow_5,
                                   sigma_ebit,
                                   roic,
                                   growth) {
  ### Centralize the priors
  terminal_ebit_data <- list(N=N, growth_roic_reinv_sigma=growth_roic_reinv_sigma,
                             ebit_flow_5=ebit_flow_5,
                             sigma_ebit = sigma_ebit,
                             roic=roic,
                             growth=growth)

  ### Describe the STAN model
  terminal_ebit_model <-  "

          data {
              int <lower=1> N;
              vector[N] growth_roic_reinv_sigma;
              real ebit_flow_5;
              vector[N] sigma_ebit;
              real roic;
              real growth;
          }

          parameters {
              real terminal_ebit;
              real reinvestment_rate;
          }

          model {
              terminal_ebit ~ normal(ebit_flow_5*(1+growth), sigma_ebit);
              reinvestment_rate ~ normal(1-(growth/roic), growth_roic_reinv_sigma);
          }

"
  ### Fit the model
  terminal_ebit_fit <- stan(model_code = terminal_ebit_model, data = terminal_ebit_data,
                    iter = 5000 * 4, chains = 4, cores = 2,
                    seed = 110)

  tidy(terminal_ebit_fit, conf.int=T, conf.level=0.95)

}


#' Calculate terminal value (LEGACY)
#' @description
#' This function calculates terminal value
#' @param terminal_ebit **Number** EBIT and reinvestment flow 5Y ahead
#' @param wacc **Number** Firm cost
#' @param growth **Number** Firm growth
#' @param reinvestment_rate **Number** Reinvestment rate
#' @return **List** FCFF NPV
#' @export
get_tv_value <- function(terminal_ebit,
                         reinvestment_rate,
                         wacc,
                         growth) {
  tv <- terminal_ebit*reinvestment_rate/(wacc-growth)
}

#' Get the posterior distribution of terminal value
#' @description
#' This function calculates terminal value posterior
#' @param default_rate Firm default rate
#' @param tv **Number** Firm terminal value
#' @return **Tibble** Terminal EBIT posterior
#' @examples
#' # get_stan_terminal_value(tv=14677, default_rate=0.15)
#' @importFrom rstan stan
#' @importFrom broom.mixed tidy
get_stan_terminal_value <- function(tv, default_rate) {
  ### Centralize the priors
  tv_data <- list(tv=tv,
                  default_rate = default_rate)

  ### Describe the STAN model
  terminal_value_model <- "
          data {
              real tv;
              real default_rate;
          }

          parameters {
              real var_tv;
          }

          model {
              var_tv ~ normal(tv, tv*default_rate);
          }

"

  ### Fit the model
  tv_model <- stan(model_code = terminal_value_model, data = tv_data,
                   iter = 5000 * 4, chains = 4, cores = 2,
                   seed = 110)


  tidy_tv <- tidy(tv_model, conf.int=T, conf.level=0.95)

}

#' Calculate equity value (LEGACY)
#' @description
#' This function calculates equity value
#' @param npv **Number** FCFF net present value
#' @param wacc **Number** Firm cost
#' @param cash **Number** Firm cash
#' @param debt **Number** Firm debt
#' @return **Number** Equity value
#' @examples
#' # equity_value <- get_equity_value(npv = 150,
#'                                  # tv = 175,
#'                                  # wacc = 0.15,
#'                                  # cash = 300,
#'                                  # debt = 750)
#' @export
get_equity_value <- function(npv, tv, wacc, cash, debt) {
  value_operating_assets <- npv + tv / (1+wacc)^5
  value_equity <- value_operating_assets + cash - debt
}


#' Calculate value per share posterior (LEGACY)
#'@description
#' This function calculates value per share posterior
#' @param equity_value *Number* Firm equity
#' @param ind_stock_price_sd **Vector** Industry stock price standard deviation
#' @param share_outstanding **Number** Number of shares outstanding in millions
#' @param N **Number** Length of ind_stock_price_sd vector
#' @return **Tibble** Value per share posterior
#' @examples
#' # get_stan_value_per_share(N=5, equity_value=700, share_outstanding, ind_stock_price_sd)
#' @importFrom rstan stan
#' @importFrom broom.mixed tidy
#' @export
get_stan_value_per_share <- function(equity_value, ind_stock_price_sd,
                                     share_outstanding, N) {
  ### Centralize the priors
  assets_data <- list(N=5, equity_value=equity_value,
                      share_outstanding=share_outstanding,
                      ind_stock_price_sd = ind_stock_price_sd)

  ### Describe the STAN model
  operating_assests_model <-  "
          data {
              int <lower=1> N;
              real equity_value;
              real share_outstanding;
              vector[N] ind_stock_price_sd;
          }

          parameters {
              real value_per_share;
          }

          model {
              value_per_share ~ normal(equity_value / share_outstanding, ind_stock_price_sd);
          }

"


  ### Fit the model
  asset_model <- stan(model_code = operating_assests_model, data = assets_data,
                      iter = 5000 * 4, chains = 4, cores = 2,
                      seed = 110)

  tidy_asset <- tidy(asset_model, conf.int=T, conf.level=0.95)

  return(list(model=asset_model, df=tidy_asset))

}