##############################################################################
# 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()