Customer-Based Corporate Valuation for Subscription-Based Businesses

Author

Abdullah Mahmood

Published

July 19, 2026

0.1 Source

This model presented in this notebook is a direct implementation of Daniel M. McCarthy, Peter S. Fader and Bruce G. S. Hardie’s 2016 paper Valuing Subscription-Based Businesses Using Publicly Disclosed Customer Data.

I will also implement the models proposed by Gupta, Sunil, Donald R. Lehmann, and Jennifer Ames Stuart in their 2004 paper Valuing Customers, and Schulze, Christian, Bernd Skiera, and Thorsten Wiesel in their 2012 paper Linking Customer and Financial Metrics to Shareholder Value: The Leverage Effect in Customer-Based Valuation as benchmarks.

0.2 Imports

Code

import pandas as pd
import matplotlib.pyplot as plt

%config InlineBackend.figure_formats = ['svg']

1 Introduction

The subscription-based business model—where customers pay recurring fees for ongoing access to a product or service—has seen significant growth beyond its traditional domains of media and telecom. Today, it underpins a wide range of consumer and B2B offerings, including SaaS (e.g., Microsoft 365), meal kits (e.g., Blue Apron), and consumer goods (e.g., Dollar Shave Club). A key driver of this model’s appeal is the predictability of revenue streams.

As subscription businesses scale, they increasingly disclose customer-related metrics such as churn, acquisition cost (CAC), average revenue per user (ARPU), and customer lifetime value (CLV). These metrics are critical for understanding a firm’s future cash flows—especially since, in subscription settings, customer behavior largely drives economic value. Equity analysts and investors now routinely incorporate this data into valuation models, with subscriber base growth often serving as a key signal.

In this notebook, I implement the framework (and its models) from McCarthy, Fader, and Bruce (2016), which estimates firm value using only publicly disclosed customer data. Central to this framework are models of the firm’s acquisition and retention processes, which accommodate factors such as customer heterogeneity, duration dependence, seasonality, and changes in population size.

We explicitly account for the fact that publicly reported data are typically aggregated (temporally and across customers) and suffer from missingness (i.e., the reported data are not available for all periods).

I begin by reviewing the principles of customer-based corporate valuation and the nature of the data available from subscription firms. I then introduce models for acquisition, retention, and spending behavior, and estimate their parameters using historical data from two publicly traded firms: Dish Network (DISH) and Sirius XM (SIRI).

Once validated, the model is used to generate forward-looking estimates of customer behavior, firm-level revenue, and ultimately, equity value. I also highlight additional strategic insights that emerge from the estimated parameters and model outputs.

2 The Logic of Customer-Based Corporate Valuation

2.1 Valuation 101

The framework summarized here is a discounted cash flow (DCF) model, which is the de-facto industry standard way in which operating assets are valued within the financial community. At the heart of any such valuation exercise is the estimation of period-by-period FCF, central to which are estimates of period-by-period revenue.

Denoting the value of the firm at time \(T\) by \(\text{SHV}_T\) (for shareholder value), we have

\[ \text{SHV}_T = \text{OA} + \text{NOA}_T - \text{ND}_T \]

The value of a firm’s operating assets (\(\text{OA}\)) is equal to the sum of all expected future free cash flows (FCFs) the firm will generate, discounted at the weighted average cost of capital (\(\text{WACC}\)):

\[ \text{OA}_T = \sum_{t=0}^{\infty} \frac{\text{FCF}_{T+t}}{(1+\text{WACC})^{t}} \]

FCF is equal to the net operating profit after taxes (\(\text{NOPAT}\)) minus the difference between capital expenditures (\(\text{CAPEX}\)) and depreciation and amortization (\(\text{D\&A}\)), minus the change in non-financial working capital (\(\Delta\text{NFWC}\)):

\[ \text{FCF}_t = \text{NOPAT}_t - (\text{CAPEX}_t - \text{D\&A}_t) - \Delta\text{NFWC}_t \]

The most important ingredient of FCF is \(\text{NOPAT}\), which is a measure of the underlying profitability of the operating assets of the firm. \(\text{NOPAT}\) is equal to revenues (\(\text{REV}\)) times the contribution margin ratio (\(1 - \text{VC}\)) minus fixed operating costs (\(\text{FC}\)), after taxes (where \(\text{TR}\) is the corporate tax rate for the firm):

\[ \text{NOPAT}_t = \left(\text{REV}_t \times (1 - \text{VC}) - \text{FC}_t \right) \times \left(1- \text{TR}_t\right) \]

2.2 A Data Structure for Subscription-Based Businesses

\(R(m)\) -> Monthly revenue
\(m = 1\) -> first month of commercial operations
\(C(m, m’)\) -> number of customers acquired by the firm in month \(m\) who are still active in month \(m’\)
\(A(m) = C(m, m’)\) -> number of customers acquired each month by the firm
\(L(m)\) -> number of customers “lost” each month
\(L(m)\) = 0 if m = 0, else \(C(., m-1) - [C(., m) - C(m,m)]\)
- eg. \(L(3) = C(., 2) - [C(., 3) - C(3,3)]\) \[ L(m) = \begin{cases} 0 &\quad m =1 \\ C(., m-1) - [C(., m) - C(m,m)]&\quad m = 2,3,4, \ldots \end{cases} \]
Aggregate churn rate = \(L(m)/C(.,m-1)\)
\(ARPU(m)\) -> Average revenue per subscriber in a given month
\(ARPU(m) = R(m) \big/ \frac{C(.,m-1) + C(.,m)}{2}\)
- (The denominator is the average number of customers the firm has during month \(m\).)
\(q\) quarter is a temporal aggregation of the true underlying process.
\(q = 1\) is equivalent to \(m=\{1,2,3\}\).
\(\text{END}_q = C(., 3q)\)
\(\text{ADD}_q = A(3q-2) + A(3q-1) + A(3q)\)
\(\text{LOSS}_q = L(3q-2) + L(3q-1) + L(3q)\)
\(REV_q = R(3q-2) + R(3q-1) + R(3q)\)
Objective: generate long-run projections of \(R(m)\) and \(A(M)\) using parameters estimated from \(\text{ADD}\), \(\text{LOSS}\), \(\text{END}\) and \(\text{REV}\) numbers
Account for missing data:
- Left-censoring - Disclosure records of paying customers does not start from the beginning of commercial operations.
- Some measures are reported for some period of time (e.g., \(\text{END}\)) before being complemented by other measures (e.g., \(\text{ADD}\) and \(\text{LOSS}\)).
Account for aggregation (quarterly reports to monthly figures)
- Publicly disclosed customer data is typically reported quarterly with the associated unit of time being the quarter, whereas the firm is operating on a finer time interval (which, for the purposes of our analysis, we assume to be the month).
US Census Bureau’s Housing Vacancies and Homeownership CPS/HVS
Quarterly Estimates of the Housing Inventory:

Alternative Source: FRED (EOCCUSQ176N) Housing Inventory Estimate: Occupied Housing Units in the United States

Units: Thousands of Units, Not Seasonally Adjusted
Frequency: Quarterly
Notes: A housing unit is occupied if a person or group of persons is living in it at the time of the interview or if the occupants are only temporarily absent, as for example, on vacation. The persons living in the unit must consider it their usual place of residence or have no usual place of residence elsewhere. The count of occupied housing units is the same as the count of households.

Code

file_path = "data/quarterly-estimates-housing-inventory-US.csv"
household_full = pd.read_csv(file_path)
household_full

	Year	Q1	Q2	Q3	Q4
0	1965	56848	57459	57846	57850
1	1966	57676	58646	58925	58696
2	1967	58493	59143	60133	60133
3	1968	60451	60739	61196	61423
4	1969	61759	62141	62412	62730
...	...	...	...	...	...
59	2020	124391	126780	126703	125805
60	2021	125944	126155	126914	127430
61	2022	127574	127990	128307	129396
62	2023	129234	130100	130386	131206
63	2024	131092	131414	132114	132404

64 rows × 5 columns

Code

file_path = "data/revised-quarterly-estimates-housing-inventory-US.csv"
household_revised = pd.read_csv(file_path)
household_revised

	Year	Q1	Q2	Q3	Q4
0	2000	NaN	102274	102896	103646
1	2001	103456.0	103411	104228	104698
2	2002	104719.0	105276	105527	105759
3	2003	105884.0	105989	106068	106505
4	2004	106738.0	107020	107932	108735
5	2005	108863.0	109057	109736	110281
6	2006	110350.0	110560	110779	111096
7	2007	110715.0	111342	111251	111724
8	2008	111326.0	111601	111939	111823
9	2009	111862.0	112453	112381	112485
10	2010	112500.0	112726	112941	113445
11	2011	113119.0	113399	113559	114102
12	2012	114145.0	114228	114741	115125
13	2013	114778.0	115244	115415	115712
14	2014	115552.0	115992	116253	117686
15	2015	117360.0	117702	117799	118264
16	2016	118038.0	118772	119129	119226
17	2017	119435.0	119447	119669	120821
18	2018	120662.0	121143	121267	122396
19	2019	122255.0	122329	122617	123848
20	2020	124299.0	126726	126672	125814
21	2021	125996.0	126279	127090	127696
22	2022	127928.0	128206	128580	129718
23	2023	129600.0	130044	130312	131113
24	2024	130982.0	131414	132114	132404

Code

household_full_lf = (
    pd.wide_to_long(household_full, stubnames="Q", i="Year", j="Quarter")
    .sort_index()
    .rename(columns={"Q": "Total Household"})
)
household_rev_lf = (
    pd.wide_to_long(household_revised, stubnames="Q", i="Year", j="Quarter")
    .sort_index()
    .rename(columns={"Q": "Total Household"})
)
household_rev_lf.plot(figsize=(9, 4), linewidth=0.75, color="k");

Code

dish_op_res = pd.read_csv(
    'data/DISH - ADD-LOSS-END.csv', 
    index_col='Date', 
    parse_dates=True,
    dayfirst=True
).sort_index()
dish_op_res.tail()

	Year	Quarter	Service revenue	Total Revenue	Subscriber Acquisition Costs (SAC)	Equipment Capitalized	Pay-TV Subscribers	Pay-TV Subscriber additions, gross	Implied Subscriber additions, gross	Pay-TV Subscriber additions, net	Implied Pay-TV Subscriber additions, net	Pay-TV Churn Rate (average monthly)	Pay-TV SAC per Subscriber (average)	Pay-TV ARPU (average monthly)	Combined Additions	Combined Net Additions
Date
2014-03-31	2014	1	3556187.0	3594198.0	NaN	NaN	14.097	0.639	NaN	0.040	0.040	0.0142	862.0	82.36	0.639	0.040
2014-06-30	2014	2	3645101.0	3688119.0	NaN	NaN	14.053	0.656	NaN	-0.044	-0.044	0.0166	846.0	84.15	0.656	-0.044
2014-09-30	2014	3	3647850.0	3679351.0	NaN	NaN	14.041	0.691	NaN	-0.012	-0.012	0.0167	861.0	84.39	0.691	-0.012
2014-12-31	2014	4	3645953.0	3681719.0	NaN	NaN	13.978	0.615	NaN	-0.063	-0.063	0.0159	853.0	83.77	0.615	-0.063
2015-03-31	2015	1	3693530.0	3724228.0	NaN	NaN	13.844	0.723	NaN	-0.134	-0.134	0.0164	667.0	85.73	0.554	-0.134

Code

# Gross Customer Acquisition Every Quarter
dish_ADD = dish_op_res['Combined Additions'] * 1000
# Surviving Customers at the End of Quarter
dish_END = dish_op_res['Pay-TV Subscribers'] * 1000
# Customer Churn Every Quarter
dish_LOSS = (
    dish_op_res["Pay-TV Subscribers"].shift(periods=1)
    + dish_op_res["Combined Additions"]
    - dish_op_res["Pay-TV Subscribers"]
) * 1000

Code

def dish_plot_format(ax, data):
    # Recession bar
    ax.axvspan(pd.to_datetime("12/1/2007"), pd.to_datetime("06/1/2009"), color='gray', alpha=0.3)
    # Padding
    pad = pd.DateOffset(months=12)
    ax.set_xlim(data.index.min() - pad, data.index.max() + pad)
    # x-ticks
    ax.set_xticks(data.index[::8])
    ax.set_xticklabels([f"Q{((d.month-1)//3)+1} {d.year}" for d in data.index[::8]], rotation=45)
    plt.tight_layout()
    plt.show()
    return

Code

# Gross Customer Acquisition Every Quarter
_, ax = plt.subplots(figsize=(9, 4))
dish_ADD.plot(ax=ax, color='k', linewidth=0.75, title='ADD', ylim=(-70, 1200))
dish_plot_format(ax, dish_ADD)

Code

# Customer Churn Every Quarter
_, ax = plt.subplots(figsize=(9, 4))
dish_LOSS.plot(ax=ax, color="k", linewidth=0.75, title="LOSS", ylim=(-70, 1000))
dish_plot_format(ax, dish_LOSS)

Code

# Surviving Customers at the End of Quarter
_, ax = plt.subplots(figsize=(9, 4))
dish_END.plot(ax=ax, color='k', linewidth=0.75, title='END', ylim=(-800,16000))
dish_plot_format(ax, dish_END)

Number of vehicles on the road data:

Data description: - Units: Number of Units - Frequency: Annually - Notes: Total number of registered private, commercial (incl. taxicabs), and public automobiles in the US every year (excluding buses, trucks, and motorcycles)

Code

reg_cars = pd.read_csv('data/us_registered_vehicles.csv', index_col='Year')
reg_cars.tail()

	Registered Automobiles
Year
2019	108547710
2020	105135300
2021	102724349
2022	99666377
2023	96901563

Code

reg_cars.plot(y='Registered Automobiles', figsize=(9, 4), color='k', linewidth=0.75);

Vehicle sales data (for macroeconomic covariate):

Data description: - Autos–all passenger cars, including station wagons. - Light trucks–trucks up to 14,000 pounds gross vehicle weight, including minivans and - Sport utility vehicles. Prior to the 2003 Benchmark Revision light trucks were up to 10,000 pounds. - Heavy trucks–trucks more than 14,000 pounds gross vehicle weight. - Columns: - Autos – not seasonally adjusted (Thousands)
- Light Trucks – not seasonally adjusted (Thousands)
- Light Total –not seasonally adjusted (Thousands)
- Total – not seasonally adjusted (Thousands)
- Autos (SAAR) – seasonally adjusted at annual rates (Millions)
- Light Trucks (SAAR) – seasonally adjusted at annual rates (Millions)
- Light Total (SAAR) – seasonally adjusted at annual rates (Millions) - Total (SAAR) – seasonally adjusted at annual rates (Millions)

Code

new_vehicle_sales = pd.read_csv(
    'data/us_new_passenger_car_sales.csv',
    index_col='Date',
    parse_dates=True,
    dayfirst=True)
new_vehicle_sales.tail()

	Month	Year	Autos	Light Trucks	Light Total	Total	Autos (SAAR)	Light Trucks (SAAR)	Light Total (SAAR)	Total (SAAR)
Date
2024-11-01	November	2024	250.101	1123.392	1373.493	1411.970	3.074369	13.585438	16.659807	17.150438
2024-12-01	December	2024	245.098	1249.122	1494.220	1539.189	3.039268	13.829528	16.868796	17.322678
2025-01-01	January	2025	197.367	905.660	1103.027	1138.497	2.840438	12.651473	15.491911	15.983576
2025-02-01	February	2025	219.794	1000.994	1220.788	1252.337	2.951624	13.059812	16.011436	16.447194
2025-03-01	March	2025	287.595	1297.795	1585.390	1620.008	3.114295	14.652515	17.766811	18.170024

Code

new_vehicle_sales.plot(y='Light Total', figsize=(9, 4), color='k', linewidth=0.75);

Code

new_vehicle_sales.plot(y='Light Total (SAAR)', figsize=(9, 4), color='k', linewidth=0.75);