############################################################################## # Understanding the impact of Growth and Margin profile on B2B SaaS Valuations # Dataset: 106 B2B SaaS companies # Author: Ramu Arunachalam (ramu@acapital.com) # Created: 06/20/21 # Datset last updated: 06/09/21 ############################################################################### import joblib as jl import pandas as pd import plotly.express as px import plotly.graph_objects as go import statsmodels.api as sm import streamlit as st from statsmodels.stats.outliers_influence import variance_inflation_factor from transformers import pipeline from transformers import TapasTokenizer, TapasForQuestionAnswering import json import requests file_date = '2021-06-11' saas_filename_all = f'{file_date}-comps_B2B_ALL.csv' saas_filename_high_growth = f'{file_date}-comps_B2B_High_Growth.csv' def get_scatter_fig(df, x, y): fig = px.scatter(df, x=x, y=y, hover_data=['Name'], title=f'{y} vs {x}') df_r = df[[y] + [x]].dropna() model = sm.OLS(df_r[y], sm.add_constant(df_r[x])).fit() regline = sm.OLS(df_r[y], sm.add_constant(df_r[x])).fit().fittedvalues fig.add_trace(go.Scatter(x=df_r[x], y=model.predict(), mode='lines', marker_color='black', name='Best-fit', line=dict(width=4, dash='dot'))) return fig latex_dict = {'EV / NTM Revenue': r'''\frac{EV}{Rev_{NTM}}''', 'EV / 2021 Revenue': r'''\frac{EV}{Rev_{2021}}''', 'EV / NTM Gross Profit': r'''\frac{EV}{GP_{NTM}}''', 'EV / 2021 Gross Profit': r'''\frac{EV}{GP_{2021}}''', 'NTM Revenue Growth': r'''Rev\,Growth_{NTM}''', '2021 Revenue Growth': r'''Rev\,Growth_{2021}''', 'Growth adjusted EV / LTM Revenue': r'''\frac{EV}{Rev_{LTM}}\cdot\frac{1}{Growth_{NTM}}''', 'Growth adjusted EV / 2020 Revenue': r'''\frac{EV}{Rev_{2020}}\cdot\frac{1}{Growth_{2021}}''' } class RegressionInput: def __init__(self, df, x_vars, y_var): self.df = df self.x_vars = x_vars self.y_var = y_var self._hash = tuple([jl.hash(df), tuple(self.x_vars), tuple([self.y_var])]) return def hash(self): return self._hash class RegressionOutput: def __init__(self, reg_input, df_r, model, df_pvalues, vif_data): self.df_r = df_r self.model = model self.df_pvalues = df_pvalues self.vif_data = vif_data self.plot_figs = dict() # Regression equation self.eq_str = latex_dict.get(reg_input.y_var, reg_input.y_var) + r'''= \beta_0''' for x, i in zip(reg_input.x_vars, range(len(reg_input.x_vars))): self.eq_str += rf'''+\beta_{{{i + 1}}}\cdot {{{latex_dict.get(x, x)}}}''' self.eq_str += r'''+\epsilon''' self.eq_str = self.eq_str.replace("%", "\%").replace("&", "\&").replace("$", "\$") # Compute regression plots and save them # Plot residuals for x in reg_input.x_vars: self.plot_figs[x] = sm.graphics.plot_regress_exog(self.model, x) self._hash = tuple([reg_input.hash(), jl.hash(df_r), id(model), jl.hash(df_pvalues), jl.hash(vif_data)]) return def hash(self): return self._hash def reg_input_hash(reg_input): h = reg_input.hash() # st.info(f"reg_input_hash: h = {h}") return h def reg_output_hash(reg_output): h = reg_output.hash() # st.info(f'reg_output hash = {h}') return h class Experiment: id_num = 0 def __init__(self): df_main = pd.read_csv(saas_filename_all) # Clean: 2x --> 2, 80% --> 80, $3,000 --> 3000 df_obj = df_main[set(df_main.columns) - {'Name'}].select_dtypes(['object']) df_main[df_obj.columns] = df_obj \ .apply(lambda x: x.str.strip('x')) \ .apply(lambda x: x.str.strip('%')) \ .replace(',', '', regex=True) \ .replace('\$', '', regex=True) cols = df_main.columns for c in cols: try: df_main[c] = pd.to_numeric(df_main[c]) except: pass df_main['2021 Revenue Growth'] = (df_main['2021 Analyst Revenue Estimates'].astype(float) / df_main[ '2020 Revenue'].astype( float) - 1) * 100 df_main = df_main[df_main['Name'].notna()] self.tickers_all = list(df_main[df_main['Name'].isin(['Median', 'Mean']) == False]['Name']) df_main_hg = pd.read_csv(saas_filename_high_growth) df_main_hg = df_main_hg[df_main_hg['Name'].notna()] self.tickers_hg = list(df_main_hg[df_main_hg['Name'].isin(['Median', 'Mean']) == False]['Name']) self.tickers_excl_hg = list(set(self.tickers_all) - set(self.tickers_hg)) self.df_main = df_main self.df = df_main self.reg_input = None self.reg_output = None return def get_tickers(self, growth='High'): if growth == 'High': return self.tickers_hg elif growth == 'Low': return self.tickers_excl_hg else: return self.tickers_all def filter(self, by): if by == 'High growth only': tickers = self.tickers_hg elif by == 'All (excl. high growth)': tickers = self.tickers_excl_hg else: tickers = self.tickers_all self.df = self.df_main[self.df_main['Name'].isin(tickers)] # type of dataset return self def set_fwd_timeline(self, type): self.rev_g = f'{type} Revenue Growth' self.rev_mult = f'EV / {type} Revenue' self.gp_mult = f'EV / {type} Gross Profit' self.gm = f'Gross Margin' # To avoid double counting growth, for growth-adjusted multiples # we take the forward growth rate with the current revenue multiple rev_mult = 'LTM' if type == 'NTM' else '2020' self.growth_adj_mult = f'Growth adjusted EV / {rev_mult} Revenue' self.df[self.growth_adj_mult] = self.df[f'EV / {rev_mult} Revenue'] / self.df[self.rev_g] return self def get_y_metric_list(self): return [self.rev_mult, self.gp_mult, self.growth_adj_mult, self.rev_g] def get_x_metric_list(self): return self.df.select_dtypes(['float', 'int']).columns def to_frame(self): return self.df @st.cache(suppress_st_warning=True, hash_funcs={RegressionInput: reg_input_hash, RegressionOutput: reg_output_hash}) def _regression(self, reg_input): df = reg_input.df reg_x_vars = reg_input.x_vars reg_y = reg_input.y_var if not reg_x_vars: return None df_r = df[[reg_y] + reg_x_vars].dropna() # Run the regression X = df_r[reg_x_vars] X = sm.add_constant(X) model = sm.OLS(df_r[reg_y], X).fit() # Compute Variance Inflation Factors df_v = df_r[reg_x_vars] vif_data = None if len(df_v.columns) >= 2: # VIF dataframe vif_data = pd.DataFrame() vif_data["feature"] = df_v.columns # calculating VIF for each feature vif_data["VIF"] = [variance_inflation_factor(df_v.values, i) for i in range(len(df_v.columns))] # pvalue dataframe df_pvalues = model.params.to_frame().reset_index().rename(columns={'index': 'vars', 0: 'Beta'}) df_pvalues['p-value'] = model.pvalues.to_frame().reset_index().rename(columns={0: 'p-value'})['p-value'] df_pvalues['Statistical Significance'] = 'Low' df_pvalues.loc[df_pvalues['p-value'] <= 0.05, 'Statistical Significance'] = 'High' df_pvalues = df_pvalues[df_pvalues['vars'] != 'const'] return RegressionOutput(reg_input, df_r, model, df_pvalues, vif_data) def regression(self, reg_x_vars, reg_y_var): self.reg_input = RegressionInput(self.df, reg_x_vars, reg_y_var) self.reg_output = self._regression(self.reg_input) return self def print(self, show_detail=False): # Print regression equation st.latex(self.reg_output.eq_str) def highlight_significant_rows(val): color = 'green' if val['p-value'] <= 0.05 else 'red' return [f"color: {color}"] * len(val) st.subheader("Summary", anchor='summary') st.write(f"1. N = {len(self.reg_output.df_r)} companies") # Assess model fit if self.reg_output.model.rsquared * 100 > 30: st.write(f"2. Model fit is **good** R ^ 2 = {self.reg_output.model.rsquared * 100: .2f}%") if self.reg_output.model.f_pvalue < 0.05: st.write(f"3. Model is **statistically significant** (F-test = {self.reg_output.model.f_pvalue:.2f})") else: st.write( f"3. The regression is **NOT statistically significant** (F-test = {self.reg_output.model.f_pvalue:.2f})") else: st.write(f"2. Model fit is **poor** (R ^ 2 = {self.reg_output.model.rsquared * 100: .2f}%)") # Check for Multicolinearity if ( self.reg_output.vif_data is not None and len(self.reg_output.vif_data[self.reg_output.vif_data['VIF'] > 10]) > 0 ): st.write("4. **Potential multicolinearity**") else: st.write("4. **NO multicolinearity**") # print p-values st.write('***') for _, row in self.reg_output.df_pvalues.iterrows(): str = 'strong' if row['Statistical Significance'] == 'High' else 'weak' st.write(f"* There is a **{str} relationship** between *'{self.reg_input.y_var}'* and *'{row['vars']}'*") st.table(self.reg_output.df_pvalues.set_index('vars').style.apply(highlight_significant_rows, axis=1)) if show_detail: # Show details st.subheader("Details:", anchor='details') # Plot residuals for k, f in self.reg_output.plot_figs.items(): st.write(f"Plotting residuals for **{k}**") st.pyplot(f) # st.pyplot(f) st.markdown('***') st.write(self.reg_output.model.summary()) st.markdown('***') if self.reg_output.vif_data is not None: st.write("Variance Inflation Factors") st.table(self.reg_output.vif_data.set_index('feature')) return self def workbench(show_detail): fwd_time = st.sidebar.selectbox('Timeline', ('2021', 'NTM')) slice_by_growth = st.sidebar.radio("B2B SaaS Dataset", ['High growth only', 'All', 'All (excl. high growth)']) e = Experiment().set_fwd_timeline(fwd_time).filter(slice_by_growth) st.sidebar.write("**Regression:**") y_sel = st.sidebar.radio("Target metric", e.get_y_metric_list()) st.sidebar.text("Select independent variable(s)") st.header("Regression") # Check if user selected revenue growth and/or gross margin reg_x_cols = [i for i in [e.rev_g, e.gm] if st.sidebar.checkbox(i, value={e.rev_g: True, e.gm: True}, key=i)] remaining_cols = list(set(e.get_x_metric_list()) - {e.rev_g, e.gm}) reg_x_cols += st.sidebar.multiselect("Additional independent variables:", remaining_cols) e.regression(reg_x_vars=reg_x_cols, reg_y_var=y_sel).print(show_detail) ## Plots #st.header("Plots") #for _, x in zip(range(4), e.reg_input.x_vars): # st.plotly_chart(get_scatter_fig(e.to_frame(), x=x, y=e.reg_input.y_var)) #st.plotly_chart(get_scatter_fig(e.to_frame(), x=e.gm, y=e.reg_input.y_var)) st.subheader("Dataset") st.expander('Table Output') \ .table(e.to_frame()[['Name'] + [y_sel] + reg_x_cols] .set_index('Name') .sort_values(y_sel, ascending=False)) st.expander('Full Raw Table Output').table(e.df_main) st.sidebar.info(f"""*{len(e.df)} companies selected* *Prices as of {file_date}*""") return def get_dataset(filter='All'): e = Experiment() df = e.set_fwd_timeline('2021').to_frame()[['Name'] + ['EV / 2021 Revenue', '2021 Revenue Growth','Gross Margin']].set_index('Name') high_growth_tickers = e.get_tickers(growth='High') low_growth_tickers = e.get_tickers(growth='Low') high_growth_tickers = set(high_growth_tickers).intersection(set(df.index.values.tolist())) df.loc[high_growth_tickers,'Category'] = 'High Growth' low_growth_tickers = set(low_growth_tickers).intersection(set(df.index.values.tolist())) df.loc[low_growth_tickers,'Category'] = 'Low Growth' df = df[df['Category'].notna()] if filter == 'High Growth': return df.loc[high_growth_tickers] elif filter == 'Low Growth': return df.loc[low_growth_tickers] return df def summary(e1, e2, e3, e4): st.header("High Growth B2B SaaS") st.markdown(""" For high growth B2B SaaS, ***revenue growth*** (*not profitability*) ***drives valuation*** * *Valuation multiples* are well explained by *revenue growth* * Model fit is good (High R^2) * Revenue growth is a statistically significant factor (low p-value) * *Gross Margin* does not influence *valuation multiples* * Poor relationship between Revenue multiples and Gross margin (high p-value) """) with st.expander("More info"): e1.print(True) st.markdown(""" * Looking at Free Cash Flow % instead of Gross Margin yield similar results * Model fit is good (High R^2) * *Revenue growth* is a statistically significant factor (low p-value) * *FCF Margin* does not influence *valuation multiples* * Poor relationship between Revenue multiples and FCF margin (high p-value) """) with st.expander("More info"): e2.print(True) st.markdown('***') st.header("B2B SaaS (excluding high growth)") st.markdown(""" For the rest of B2B SaaS (i.e non high growth SaaS), the picture is less clear * *Revenue growth* by itself doesn't adequately explain *valuation multiples* * Model fit is poor (low R^2) * But *Revenue growth* is still a statistically significant factor (low p-value) * *Gross Margin* does not influence *valuation multiples* * Poor relationship between Revenue multiples and Gross margin (high p-value) """) with st.expander("More info"): e3.print(True) st.markdown(""" * Looking at Free Cash Flow % instead of Gross Margin improves model fit * FCF Margin* has a **small positive effect** on *valuation multiples* * Low p-value but small Beta. * But overall *revenue growth* still has a much **larger effect** on valuation multiples than profitability * Low p-value and higher Beta relative to FCF % """) with st.expander("More info"): e4.print(True) return def make_api_call(queries, df:pd.DataFrame): API_TOKEN = "api_DjJYjFpAQfQkhpfzncoRuuKuuLWrSzHdav" headers = {"Authorization": f"Bearer {API_TOKEN}"} API_URL = "https://api-inference.huggingface.co/models/google/tapas-base-finetuned-wtq" st.sidebar.info("Using ** google/tapas-large-finetuned-wtq**") def query(payload): response = requests.post(API_URL, headers=headers, json=payload) return response.json() table_dict = df.to_dict(orient='list') output = query({ "inputs": { "query": queries, "table": table_dict }}) return output def nlu_query_use_api(): df = get_dataset(filter='High Growth').dropna().reset_index().rename(columns={'Name':'Company','EV / 2021 Revenue':'Revenue Multiple','2021 Revenue Growth':'Growth Rate'}) df['Revenue Multiple'] = df['Revenue Multiple'].round(2).apply(str) df['Growth Rate'] = df['Growth Rate'].round(2).apply(str) df['Gross Margin'] = df['Gross Margin'].round(2).apply(str) df = df[['Company','Revenue Multiple','Growth Rate','Gross Margin']] with st.expander("Dataset"): st.table(df) questions = ['How many companies are in this dataset?', 'Which company has the highest growth rate?', 'Which company has the highest gross margin?', 'Which company trades at the highest revenue multiple?', 'List all companies with growth rates greater than 40?', 'What is the average gross margin for companies in this dataset?', 'What is the average trading multiple?' ] st.sidebar.write("Sample questions:") st.sidebar.caption("[Copy and Paste any of these questions into the textbox below]") for i in questions: st.sidebar.markdown(f"* {i}") queries = st.text_area("Enter Question:", 'How many companies are in this dataset?') #queries = ['Which company has the highest gross margin?'] output = make_api_call(queries=queries, df=df) if 'error' in output: st.write(output['error']) else: try: df_output = pd.DataFrame.from_dict(output['cells']) if output['aggregator'] == 'COUNT': st.info(f"[COUNT] Answer: {df_output[0].count()}") elif output['aggregator'] == 'SUM': st.info(f"[SUM] Answer: {df_output[0].astype(float).sum().round(2)}") elif output['aggregator'] == 'AVERAGE': st.info(f"[AVERAGE] Answer: {df_output[0].astype(float).mean().round(2)}") else: st.info(f"Answer is {output['answer']}") except ValueError: st.write(output) with st.expander("Raw Output"): st.write(output) return def nlu_query(): from torch_scatter import scatter st.header("NLU Query") model_name = 'google/tapas-large-finetuned-wtq' model = TapasForQuestionAnswering.from_pretrained(model_name) tokenizer = TapasTokenizer.from_pretrained(model_name) df = get_dataset().dropna().reset_index().rename(columns={'Name':'Company','EV / 2021 Revenue':'Revenue Multiple','2021 Revenue Growth':'Growth Rate'}) df['Revenue Multiple'] = df['Revenue Multiple'].round(2).apply(str) df['Growth Rate'] = df['Growth Rate'].round(2).apply(str) df['Gross Margin'] = df['Gross Margin'].round(2).apply(str) df = df[['Company','Revenue Multiple','Growth Rate','Gross Margin']] st.table(df) queries = ['How many companies are in the dataset', 'Which company has the highest growth rate?','Which company has the highest gross margin?'] st.write(queries) #queries = st.text_area('Ask a question') inputs = tokenizer(table=df, queries=queries, padding='max_length', return_tensors="pt") outputs = model(**inputs) predicted_answer_coordinates, predicted_aggregation_indices = tokenizer.convert_logits_to_predictions( inputs, outputs.logits.detach(), outputs.logits_aggregation.detach()) inputs = tokenizer(table=df, queries=queries, padding='max_length', return_tensors="pt") id2aggregation = {0: "NONE", 1: "SUM", 2: "AVERAGE", 3:"COUNT"} aggregation_predictions_string = [id2aggregation[x] for x in predicted_aggregation_indices] answers = [] for coordinates in predicted_answer_coordinates: if len(coordinates) == 1: # only a single cell: answers.append(df.iat[coordinates[0]]) else: # multiple cells cell_values = [] for coordinate in coordinates: cell_values.append(df.iat[coordinate]) answers.append(", ".join(cell_values)) st.write(answers) st.write(aggregation_predictions_string) return def main(): #st.set_page_config(initial_sidebar_state="collapsed") sel = st.sidebar.radio("Menu", ['NLU Question Answer','Summary', 'Workbench']) show_detail = True # pre compute three experiments # Experiment 1 e1 = Experiment() \ .set_fwd_timeline('2021') \ .filter('High growth only') e1.regression(reg_x_vars=[e1.rev_g, e1.gm], reg_y_var=e1.rev_mult) # Experiment 2 e2 = Experiment() \ .set_fwd_timeline('2021') \ .filter('High growth only') e2.regression(reg_x_vars=[e2.rev_g, 'LTM FCF %'], reg_y_var=e2.rev_mult) # Experiment 3 e3 = Experiment() \ .set_fwd_timeline('2021') \ .filter('All (excl. high growth)') e3.regression(reg_x_vars=[e3.rev_g, e3.gm], reg_y_var=e3.rev_mult) # Experiment 4 e4 = Experiment() \ .set_fwd_timeline('2021') \ .filter('All (excl. high growth)') e4.regression(reg_x_vars=[e4.rev_g, 'LTM FCF %'], reg_y_var=e4.rev_mult) if sel == 'NLU Question Answer': st.title("Query Dataset") return nlu_query_use_api() elif sel == 'Workbench': st.title('Impact of Growth and Margins on Valuation') return workbench(True) else: st.title('Impact of Growth and Margins on Valuation') return summary(e1, e2, e3, e4) if __name__ == "__main__": main()