Models

The Models module executes well-known models such as DuPont analysis and the Discounted Cash Flow (DCF) model, using data retrieved from the Toolkit module.

Every function of the Models module has its own page showing how to use it with the MCP and in Python. Pick one from the sidebar on the left.Every function of the Models module has its own page showing how to use it with the MCP and in Python. Pick one from the documentation menu.

Use it in Claude, ChatGPT or another AI assistant through the Finance Toolkit MCP, or install the Python package:

pip install financetoolkit -U

Getting Started

The Models module combines ratios, market data and financial statements into the well-known models an analyst reaches for when a single ratio isn’t enough: DuPont analysis to see what drives Return on Equity, the Weighted Average Cost of Capital (WACC), a Discounted Cash Flow (DCF) valuation, the Altman Z-Score, Piotroski F-Score and Beneish M-Score for financial health and earnings quality, and growth models such as the Sustainable Growth Rate and the Graham Number. Every model is calculated for each ticker and each period, so you see how the result changed over time rather than a single snapshot.

This section uses Apple, Tesla, Meta and Amazon from 2005 onwards.

Loading the Data

The Models module is part of the Toolkit class. Financial statements, historical prices and treasury rates are collected the first time a model needs them and reused for every call after that, which keeps the number of requests to a minimum. This example uses annual data; add quarterly=True for quarterly data, which requires a premium plan from Financial Modeling Prep.

To load the data for the four companies:

import numpy as np
import pandas as pd

from financetoolkit import Toolkit

companies = Toolkit(
    ["AAPL", "TSLA", "META", "AMZN"],
    api_key="FINANCIAL_MODELING_PREP_KEY",
    start_date="2005-01-01",
)

Extended DuPont Analysis

The DuPont analysis explains Return on Equity by splitting it into parts. The extended (five-step) version multiplies the interest burden (how much of operating profit survives interest), the tax burden (how much survives tax), the operating margin, the asset turnover and the equity multiplier. Two companies with the same ROE can get there in very different ways: one through margins, another through leverage, and that difference matters for how sustainable the return is.

To run the extended DuPont analysis for every company:

companies.models.get_extended_dupont_analysis()

Which gives the five components and the resulting ROE, here for the last ten years with a tab per company:

Apple’s ROE of 171% in 2025 comes mostly from its equity multiplier of 5.5x: years of share buybacks have left it with very little book equity, so each dollar of profit is spread over a small equity base. Meta earns an even higher operating margin, 41% against Apple’s 32%, with an equity multiplier of only 1.6x, which is why its ROE of 30% is far lower but arguably of higher quality. Amazon’s early years (not shown in the chart) are an example of why the decomposition matters: with equity close to zero in 2005, its ROE came out at several thousand percent.

Weighted Average Cost of Capital

The WACC is the blended return a company has to earn for its shareholders and lenders, weighted by the market value of equity and debt. The cost of equity follows from the Capital Asset Pricing Model (the risk-free rate plus beta times the market risk premium), the cost of debt from interest expense over total debt, after tax.

Like almost every function in the Toolkit, the WACC accepts growth=True to return the change from one period to the next instead of the level, and lag sets how many periods back that change is measured. A list of lags returns all of them at once. To calculate the growth of every WACC component over one, two and three years:

companies.models.get_weighted_average_cost_of_capital(growth=True, lag=[1, 2, 3])

Which gives, for Apple’s WACC itself:

The level itself is more useful for most analyses, and standardize=True converts each component into standard deviations from its own historical mean, which puts the market value of equity (in dollars) and the cost of debt (a rate) on the same scale. show_full_results=True returns the components next to the WACC. To get both views:

wacc = companies.models.get_weighted_average_cost_of_capital()

companies.models.get_weighted_average_cost_of_capital(
    standardize=True, show_full_results=True
).loc["AMZN"]

Which shows the WACC of the four companies over the last ten years, and in the second tab Amazon’s WACC next to its cost of equity and cost of debt, each in standard deviations from its own mean:

The four lines move almost in step, because the cost of equity dominates every one of them. For Amazon, the standardized WACC and cost of equity lie nearly on top of each other: equity is about 94% of its capital at market value, so the cost of debt barely moves the result.

Altman Z-Score and Piotroski F-Score

The Altman Z-Score combines five ratios (working capital, retained earnings, EBIT, the market value of equity against liabilities, and sales, each relative to total assets) into one measure of the chance of bankruptcy. A score above 2.99 is considered safe, below 1.81 a sign of distress. The Piotroski F-Score awards one point for each of nine criteria on profitability, leverage and liquidity, and operating efficiency, so a score of 8 or 9 points to a company whose fundamentals are improving and 0 to 2 to one whose fundamentals are deteriorating.

To calculate the Altman Z-Score and select Amazon:

altman_z_score = companies.models.get_altman_z_score()

altman_z_score.loc["AMZN"]

Which gives the Z-Score of the four companies over the last ten years with both thresholds, and in the second tab Amazon’s score split into its five weighted parts (1.2 times working capital, 1.4 times retained earnings, 3.3 times EBIT and 1.0 times sales, each over total assets, plus 0.6 times the market value of equity over total liabilities):

Tesla was in the distress zone in 2016 and 2017 (1.18 and 1.30) and in the grey zone in 2018 and 2019, before the jump in its market value lifted it to 17 in 2020. Amazon slipped just below the safe line in 2022, at 2.94: the second tab shows that its market value part fell from 3.65 to 1.62 that year, while EBIT turned slightly negative.

To calculate the Piotroski F-Score and select Apple:

piotroski_score = companies.models.get_piotroski_score()

piotroski_score.loc["AAPL"]

Which shows, for the last five years, which criteria Apple met (1) or missed (0):

To compare the total score of all four companies over time:

piotroski_score.loc[:, "Piotroski Score", :].T

Which gives the score for the last six years, and in the second tab the 2025 score split into Piotroski’s three groups of criteria:

Tesla’s score fell from 8 in 2022 to 3 in 2023, when it missed the criteria for the change in return on assets, accruals, leverage, gross margin and asset turnover; Apple and Amazon scored 7 or 8 in each of the last three years. In 2025 Apple earned all three points on leverage and liquidity, against one for Tesla and Meta.

Enterprise Value and Intrinsic Valuation

The Enterprise Value breakdown shows how the Toolkit gets from market capitalization to enterprise value: add total debt, minority interest and preferred equity, and subtract cash. The intrinsic valuation runs a DCF: it projects free cash flow forward at a growth rate, adds a terminal value at the perpetual growth rate, discounts both at the WACC and divides the resulting equity value by the number of shares. The three inputs are yours to set, which makes it easy to test how sensitive the fair value is to each of them.

To get the Enterprise Value breakdown, and a DCF with 5% growth, 2.5% perpetual growth and a WACC of 9.4%:

companies.models.get_enterprise_value_breakdown()

companies.models.get_intrinsic_valuation(
    growth_rate=0.05, perpetual_growth_rate=0.025, weighted_average_cost_of_capital=0.094
)

Which gives, for Apple’s Enterprise Value in USD billions:

And for the intrinsic value per share next to the latest share price:

With these inputs, every company trades well above its DCF value, which mostly says that the market expects much more than 5% growth. Amazon shows the limits of a free cash flow DCF: it reinvests most of its operating cash flow, so its free cash flow, and with it the intrinsic value, is small compared to the size of the business.

DuPont Analysis and Growth Opportunities

The base DuPont analysis splits Return on Equity into three parts: the net profit margin, the asset turnover and the equity multiplier, which shows whether ROE is driven by profitability, efficient use of assets or leverage. The Present Value of Growth Opportunities (PVGO) splits the share price into the value of the current earnings, if they stayed flat forever (earnings per share divided by the WACC), and the remainder, which is what the market pays for future growth.

To run the DuPont analysis standardized for Apple, and the PVGO for every company:

companies.models.get_dupont_analysis(standardize=True).loc["AAPL"]

companies.models.get_present_value_of_growth_opportunities()

Which shows how far each component of Apple’s ROE is from its own historical average, in standard deviations:

Since 2021 the net profit margin, the asset turnover and the equity multiplier have all been above their own averages, which is rare: before 2021 the margin and the asset turnover often moved in opposite directions. The equity multiplier moved the furthest, to 1.8 standard deviations above its mean in 2023.

And the year-end share price split into the value of current earnings and the PVGO, with the PVGO per share over the last ten years in the second tab:

At the end of 2025, $551 of Meta’s share price of $658, or 84%, was growth the market expected rather than earnings it already made; for Tesla it was 99%. The WACC sets that split, and with a WACC of 21% to 34% in 2025 (it follows the realized market return), current earnings are worth little. In flat market years it works the other way: Apple’s WACC of about 1% in 2011 and 2015 made earnings divided by the WACC very large and its PVGO deeply negative, one more reason to smooth the WACC before using it in a valuation.

Beneish M-Score

The Beneish M-Score is a probabilistic model for detecting earnings manipulation, a companion to the Altman Z-Score and the Piotroski F-Score. It combines eight indices, such as days sales in receivables, gross margin, asset quality and total accruals, each comparing this year to last year. A score above roughly -1.78 suggests a higher likelihood that earnings are being manipulated.

To calculate the Beneish M-Score and select Tesla:

beneish_m_score = companies.models.get_beneish_m_score()

beneish_m_score.loc["TSLA"]

Which gives the M-Score of the four companies over the last ten years against the -1.78 threshold, and in the second tab what moved Tesla’s 2023 score: each of its eight indices against a neutral year (an index of 1, accruals of 0), times the weight the model gives it:

Tesla is the only one above the threshold, at 0.39 in 2016 and at -1.62 in 2023, while the other three stay well below it. A neutral year scores -2.48; in 2023 the asset quality index (a larger share of assets that are neither current assets nor property, plant and equipment) added 0.37 points, a lower gross margin 0.21 and sales growth 0.17. A year above the line is a reason to look closer at those components, not proof of manipulation.

Sustainable and Internal Growth Rate

The Sustainable Growth Rate (SGR) and the Internal Growth Rate (IGR) estimate how fast a company can grow without raising new equity. The SGR is ROE times the retention ratio and assumes leverage stays the same; the IGR is based on ROA and assumes no new debt at all, so it is always the more conservative of the two.

To calculate both:

companies.models.get_sustainable_growth_rate()

companies.models.get_internal_growth_rate()

Which gives both rates for every company; here Apple against Meta over the last ten years:

Apple’s SGR of 148% is another effect of its small equity base; its IGR of 36% is the more realistic figure for how fast it could grow from its own profits. Meta, with little debt, shows how close the two can be: an SGR of 28% against an IGR of 21%.

Graham Number

The Graham Number is Benjamin Graham’s conservative estimate of the most a defensive investor should pay for a share: the square root of 22.5 times earnings per share times book value per share. It only has meaning for profitable companies with a positive book value; otherwise the result is empty.

To compare the latest Graham Number with the current share price:

graham_number = companies.models.get_graham_number().iloc[:, -1]
current_price = companies.get_historical_data()["Adj Close"].iloc[-1].drop("Benchmark")

pd.DataFrame(
    {
        "Graham Number": graham_number,
        "Current Price": current_price,
        "Price / Graham Number": current_price / graham_number,
    }
)

Which gives the current share price as a multiple of the Graham Number:

None of the four comes close to Graham’s limit: Tesla’s price of $373.71 is 15.8 times its Graham Number of $23.73, Apple’s $339.50 is 11.8 times $28.73, and Meta and Amazon trade at about 3.3 times theirs. That is what you would expect for growth companies: the formula has no room for growth at all and was written for a very different kind of stock.

Using the Models Directly

Every model is also available as a plain function in financetoolkit.models, so you can run it on your own numbers without the Toolkit class. This is useful when you have data from another source or want to test a scenario. The example below fills the DuPont analysis with Apple’s reported figures for fiscal 2018 to 2022:

from financetoolkit.models import dupont_model

years = [2018, 2019, 2020, 2021, 2022]

dupont_model.get_dupont_analysis(
    net_income=pd.Series(
        [59531000000, 55256000000, 57411000000, 94680000000, 99803000000], index=years
    ),
    total_revenue=pd.Series(
        [265595000000, 260174000000, 274515000000, 365817000000, 394328000000],
        index=years,
    ),
    average_total_assets=pd.Series(
        [np.nan, 365725000000, 338516000000, 323888000000, 351002000000],
        index=years,
    ),
    average_total_equity=pd.Series(
        [np.nan, 107147000000, 90488000000, 65339000000, 63090000000], index=years
    ),
)

Which returns:

These results closely match the figures Apple reports for those fiscal years, which end in September.